{"id":6718,"date":"2024-07-30T16:01:01","date_gmt":"2024-07-30T08:01:01","guid":{"rendered":""},"modified":"2024-07-30T16:01:01","modified_gmt":"2024-07-30T08:01:01","slug":"\u77e9\u9635\u94fe\u4e58\u6cd5\u95ee\u9898_\u4e09\u9636\u77e9\u9635\u76f8\u4e58\u600e\u4e48\u7b97","status":"publish","type":"post","link":"https:\/\/mushiming.com\/6718.html","title":{"rendered":"\u77e9\u9635\u94fe\u4e58\u6cd5\u95ee\u9898_\u4e09\u9636\u77e9\u9635\u76f8\u4e58\u600e\u4e48\u7b97"},"content":{"rendered":"<p><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"display: none;\"> \n <path stroke-linecap=\"round\" d=\"M5,0 0,2.5 5,5z\" id=\"raphael-marker-block\" style=\"-webkit-tap-highlight-color: rgba(0, 0, 0, 0);\"><\/path> \n<\/svg> <\/p>\n<div class=\"toc\">\n<h4>\u52a8\u6001\u89c4\u5212\u2014\u2014\u77e9\u9635\u94fe\u76f8\u4e58\u95ee\u9898\uff08C\u4ee3\u7801\u5b9e\u73b0\uff09<\/h4>\n<ul>\n<li>\u5f15\u5165<\/li>\n<li>\n<ul>\n<li>\u77e9\u9635\u8fde\u4e58\u7684\u5f00\u9500<\/li>\n<li>\u52a0\u62ec\u53f7\u7684\u65b9\u5f0f\u603b\u6570<\/li>\n<\/ul>\n<\/li>\n<li>\u7528\u52a8\u6001\u89c4\u5212\u6cd5\u89e3\u51b3\u77e9\u9635\u94fe\u76f8\u4e58\u95ee\u9898<\/li>\n<li>\n<ul>\n<li>\u4f18\u5316\u5b50\u7ed3\u6784<\/li>\n<li>\u9012\u5f52\u6c42\u89e3\u65b9\u6848<\/li>\n<li>\u91cd\u53e0\u5b50\u95ee\u9898&amp;\u6784\u9020\u6700\u4f18\u89e3<\/li>\n<\/ul>\n<\/li>\n<li>\u4e00\u9053\u9898\u76ee<\/li>\n<li>\n<ul>\n<li>\u9898\u9762<\/li>\n<li>AC\u4ee3\u7801<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<h2>\u5f15\u5165<\/h2>\n<h3>\u77e9\u9635\u8fde\u4e58\u7684\u5f00\u9500<\/h3>\n<p>\u7ed9\u51fa\u4e00\u4e2a\u6709n\u4e2a\u77e9\u9635(\u4efb\u4f55\u76f8\u90bb\u7684\u4e24\u4e2a\u77e9\u9635\u5747\u76f8\u5bb9)\u7684\u77e9\u9635\u5e8f\u5217<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \uff08 &lt; A 1 , A 2 , \u2026 , A n &gt; ) \uff08&lt;A_1,A_2,\u2026,A_n&gt;) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5782em; vertical-align: -0.0391em;\"><\/span><span class=\"mord cjk_fallback\">\uff08<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.87777em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">&gt;<\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u6c42\u5b83\u4eec\u7684\u4e58\u79ef<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> ( A 1 A 2 \u2026 A n ) (A_1A_2\u2026A_n) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u4e00\u822c\u7684\u505a\u6cd5\u662f\u6309\u7167\u4ece\u5de6\u5230\u53f3\u7684\u987a\u5e8f\u4e00\u4e2a\u4e00\u4e2a\u6c42\u77e9\u9635\u7684\u79ef\uff0c\u4f46\u662f\u77e9\u9635\u4e58\u6cd5\u662f\u6ee1\u8db3\u7ed3\u5408\u7387\u7684\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u7ed9\u5e8f\u5217\u52a0\u4e0a\u62ec\u53f7\u89c4\u5b9a\u77e9\u9635\u8fde\u4e58\u7684\u6c42\u89e3\u987a\u5e8f\u3002<br \/> \u77e9\u9635\u8fde\u4e58\u5168\u62ec\u53f7\uff1a\u4ec5\u6709\u4e00\u4e2a\u77e9\u9635\uff0c\u6216\u8005\u4e24\u4e2a\u201c\u77e9\u9635\u8fde\u4e58\u5168\u62ec\u53f7\u201d\u7684\u4e58\u79ef\u4e14\u5916\u5c42\u5305\u62ec\u4e00\u4e2a\u62ec\u53f7\uff0c\u4f8b\u5982\uff1a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> ( A 1 ( ( A 2 A 3 ) A 4 ) ) (A_1((A_2A_3)A_4)) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">4<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u4e00\u5bf9\u89c4\u6a21\u5206\u522b\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p \u00d7 q p\u00d7q <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.77777em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">p<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">q<\/span><\/span><\/span><\/span><\/span>\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> q \u00d7 r q\u00d7r <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.77777em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">q<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">r<\/span><\/span><\/span><\/span><\/span>\u7684\u77e9\u9635\u76f8\u4e58\u7684\u4e58\u6cd5\u5f00\u9500\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p q r pqr <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">p<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">q<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">r<\/span><\/span><\/span><\/span><\/span>\u3002\u5bf9\u4e8e\u77e9\u9635\u8fde\u4e58\u95ee\u9898\uff0c\u91c7\u7528\u4e0d\u540c\u7684\u52a0\u62ec\u53f7\u65b9\u5f0f\uff0c\u53ef\u80fd\u5bfc\u81f4\u4e0d\u540c\u7684\u751a\u81f3\u5dee\u5f02\u5de8\u5927\u7684\u4e58\u6cd5\u5f00\u9500\u3002<\/p>\n<blockquote>\n<p>\u7ed9\u5b9a\u4e09\u4e2a\u77e9\u9635<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> A 1 A 2 A 3 A_1A_2A_3 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u4ed6\u4eec\u7684\u89c4\u6a21\u5206\u522b\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> 10 \u00d7 100 10\u00d7100 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\">0<\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> 100 \u00d7 5 100\u00d75 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\">0<\/span><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> 5 \u00d7 50 5\u00d750 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">5<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">5<\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>\u3002<br \/> \u6309\u7167<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> ( ( A 1 A 2 ) A 3 ) ((A_1A_2)A_3) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u7684\u987a\u5e8f\u8fd0\u7b97\u7684\u4e58\u6cd5\u5f00\u9500\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> 10 \u00d7 100 \u00d7 5 + 10 \u00d7 50 \u00d7 5 = 7500 10\u00d7100\u00d75 + 10\u00d750\u00d75 = 7500 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\">0<\/span><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">5<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">5<\/span><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">5<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">7<\/span><span class=\"mord\">5<\/span><span class=\"mord\">0<\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>\u3002<br \/> \u4f46\u6309\u7167<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> ( A 1 ( A 2 A 3 ) ) (A_1(A_2A_3)) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u7684\u987a\u5e8f\u8fd0\u7b97\u7684\u4e58\u6cd5\u5f00\u9500\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> 100 \u00d7 5 \u00d7 50 + 10 \u00d7 100 \u00d7 50 = 75000 100\u00d75\u00d750 + 10\u00d7100\u00d750 = 75000 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\">0<\/span><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">5<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">5<\/span><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\">0<\/span><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">5<\/span><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">7<\/span><span class=\"mord\">5<\/span><span class=\"mord\">0<\/span><span class=\"mord\">0<\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>\u3002<br \/> \u540e\u8005\u662f\u524d\u8005\u7684<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> 10 10 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>\u500d\u3002<\/p>\n<\/blockquote>\n<p>\u56e0\u6b64\u4e3a\u4e86\u4f7f\u77e9\u9635\u4e58\u6cd5\u8fd0\u7b97\u901f\u5ea6\u66f4\u5feb\uff0c\u53ef\u4ee5\u9884\u5148\u8ba1\u7b97\u51fa\u6700\u597d\u7684\u7ed9\u77e9\u9635\u94fe\u52a0\u62ec\u53f7\u7684\u65b9\u5f0f\u4ee5\u51cf\u5c0f\u603b\u4e58\u6cd5\u5f00\u9500\u3002<\/p>\n<h3>\u52a0\u62ec\u53f7\u7684\u65b9\u5f0f\u603b\u6570<\/h3>\n<p>\u4ee4<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> P ( n ) P(n) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">n<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u8868\u793a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> n n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">n<\/span><\/span><\/span><\/span><\/span>\u4e2a\u77e9\u9635\u8fde\u4e58\u65f6\u6240\u6709\u53ef\u80fd\u7684\u5168\u62ec\u53f7\u7684\u4e2a\u6570\u3002<br \/> \u5982\u679c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> n = 1 n=1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\uff0c\u53ea\u6709\u4e00\u79cd\u65b9\u6cd5\u52a0\u62ec\u53f7<br \/> \u5982\u679c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> n &gt; = 2 n&gt;=2 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5782em; vertical-align: -0.0391em;\"><\/span><span class=\"mord mathdefault\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">&gt;<\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.36687em; vertical-align: 0em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span>\uff0c\u5219\u5728\u8fd9\u4e9b\u77e9\u9635\u91cc\u9762\u53ef\u4ee5\u627e\u5230\u4e00\u4e2a\u5206\u5272\u4f4d\u7f6e\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> A k A_k <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e0e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> A k + 1 A_{k+1} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.891661em; vertical-align: -0.208331em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e2d\u95f4\uff0c\u5c06\u6240\u6709\u7684\u5206\u5272\u65b9\u5f0f\u7d2f\u52a0\u3002<br \/> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> P ( n ) = { 1 , if&nbsp; n &nbsp;=1&nbsp; \u2211 k = 1 n \u2212 1 &nbsp; P ( k ) P ( n \u2212 k ) , if&nbsp; n &nbsp;\u2265&nbsp;odd P(n)= \\begin{cases} 1, &amp; \\text {if $n$ =1 } \\\\\\sum_{k=1}^{n-1} \\ P(k)P(n-k) , &amp; \\text{if $n$ \u2265 odd} \\end{cases} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">n<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.00003em; vertical-align: -1.25003em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size4\">{<br \/>\n         <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.69em;\"><span class=\"\" style=\"top: -3.69em;\"><span class=\"pstrut\" style=\"height: 3.008em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><span class=\"\" style=\"top: -2.25em;\"><span class=\"pstrut\" style=\"height: 3.008em;\"><\/span><span class=\"mord\"><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.954008em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mspace\">&nbsp;<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.13889em;\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.19em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 1em;\"><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.69em;\"><span class=\"\" style=\"top: -3.69em;\"><span class=\"pstrut\" style=\"height: 3.008em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">if&nbsp;<\/span><span class=\"mord mathdefault\">n<\/span><span class=\"mord\">&nbsp;=1&nbsp;<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.25em;\"><span class=\"pstrut\" style=\"height: 3.008em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">if&nbsp;<\/span><span class=\"mord mathdefault\">n<\/span><span class=\"mord\">&nbsp;\u2265&nbsp;odd<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.19em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u8fd9\u4e2a\u9012\u5f52\u7ed3\u679c\u5c06\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03a9 ( 2 n ) \\Omega(2^n) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\">\u03a9<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \uff08\u8fd9\u4e2a\u8ba1\u7b97\u4e5f\u53ef\u4ee5\u4ece\u53e6\u4e00\u4e2a\u89d2\u5ea6\u8003\u8651\uff1a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> n n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">n<\/span><\/span><\/span><\/span><\/span>\u4e2a\u4f4d\u7f6e\u53ef\u4ee5\u9009\u62e9\u63d2\u5165\u6216\u8005\u4e0d\u63d2\u5165\u62ec\u53f7\uff0c\u90a3\u4e48\u603b\u7ed3\u679c\u5c31\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> 2 n 2^n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.664392em; vertical-align: 0em;\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\uff09\u7684\u3002\u5982\u679c\u91c7\u7528\u66b4\u529b\u679a\u4e3e\u6765\u8ba1\u7b97\u6700\u4f18\u62ec\u53f7\u5206\u5272\u65b9\u5f0f\u7684\u8bdd\u5c06\u6d88\u8017\u5927\u91cf\u7684\u65f6\u95f4<\/p>\n<h2>\u7528\u52a8\u6001\u89c4\u5212\u6cd5\u89e3\u51b3\u77e9\u9635\u94fe\u76f8\u4e58\u95ee\u9898<\/h2>\n<h3>\u4f18\u5316\u5b50\u7ed3\u6784<\/h3>\n<p>\u5728\u8ba1\u7b97<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> A i A i + 1 \u2026 A k A k + 1 \u2026 A j A_iA_{i+1}\u2026A_kA_{k+1}\u2026A_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.969438em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u6700\u4f18\u62ec\u53f7\u5212\u5206\u65b9\u6848\u7684\u65f6\u5019\uff0c\u6211\u4eec\u5148\u627e\u5230\u4e00\u4e2a\u6700\u4f73\u5206\u5272\u65b9\u6848\u628a\u8fd9\u4e2a\u77e9\u9635\u5217\u4ee5<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> A k A k + 1 A_kA_{k+1} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.891661em; vertical-align: -0.208331em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e3a\u8fb9\u754c\u5212\u5206\u6210\u4e24\u5757\uff0c\u770b\u6210\u8ba1\u7b97<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> A i A i + 1 \u2026 A k A_iA_{i+1}\u2026A_k <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.891661em; vertical-align: -0.208331em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> A k + 1 \u2026 A j A_{k+1}\u2026A_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.969438em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u4e4b\u540e\u518d\u5206\u522b\u5728\u8fd9\u4e24\u5757\u77e9\u9635\u91cc\u5bfb\u627e\u6700\u4f73\u8fb9\u754c\u7ee7\u7eed\u5212\u5206\uff0c\u4e0d\u65ad\u5f62\u6210\u66f4\u5c0f\u7684\u5b50\u95ee\u9898\u3002<br \/> \u4e0b\u9762\u8bc1\u660e\u6bcf\u4e00\u4e2a\u5b50\u95ee\u9898\u7684\u6700\u4f18\u62ec\u53f7\u5212\u5206\u65b9\u6848\u5408\u5e76\u8d77\u6765\u5c31\u662f\u6574\u4e2a\u95ee\u9898\u7684\u6700\u4f18\u62ec\u53f7\u5212\u5206\u65b9\u6848\u3002<\/p>\n<blockquote>\n<p><strong>\u8bc1\u660e\uff1a<\/strong> \u5bf9\u4e8e\u77e9\u9635\u94fe<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> A i A i + 1 \u2026 A k A k + 1 \u2026 A j A_iA_{i+1}\u2026A_kA_{k+1}\u2026A_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.969438em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u5bfb\u627e\u5230\u4e00\u4e2a\u6700\u4f73\u5206\u5272\u5c06\u5176\u5212\u5206\u6210<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> ( A i A i + 1 \u2026 A k ) ( A k + 1 \u2026 A j ) (A_iA_{i+1}\u2026A_k) (A_{k+1}\u2026A_j) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.03611em; vertical-align: -0.286108em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\uff0c\u8bb0\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> M \u22c5 N M\u00b7N <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.10903em;\">M<\/span><span class=\"mpunct\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.10903em;\">N<\/span><\/span><\/span><\/span><\/span>\uff08M\uff0cN\uff0cP\u5747\u4ee3\u8868\u7684\u662f\u4e58\u6cd5\u8ba1\u7b97\u6b21\u6570\uff09\u3002<br \/> \u5982\u679c\u5bf9\u4e8e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> A i A i + 1 \u2026 A k A_iA_{i+1}\u2026A_k <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.891661em; vertical-align: -0.208331em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c\u80fd\u627e\u5230\u4e00\u4e2a\u66f4\u4f73\u7684\u62ec\u53f7\u5212\u5206\u65b9\u6848\u7684\u8bdd\uff0c\u5f97\u5230\u7684\u7ed3\u679c\u5e94\u8be5\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> P P <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.13889em;\">P<\/span><\/span><\/span><\/span><\/span>\uff0c\u4e14<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> P &lt; M P&lt;M <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.72243em; vertical-align: -0.0391em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.13889em;\">P<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.10903em;\">M<\/span><\/span><\/span><\/span><\/span>\u3002\u8fd9\u6837\u539f\u77e9\u9635\u94fe\u7684\u6700\u4f73\u5206\u5272\u65b9\u6848\u5c31\u5e94\u8be5\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> P \u22c5 N P\u00b7N <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.13889em;\">P<\/span><span class=\"mpunct\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.10903em;\">N<\/span><\/span><\/span><\/span><\/span>\u800c\u4e0d\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> M \u22c5 N M\u00b7N <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.10903em;\">M<\/span><span class=\"mpunct\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.10903em;\">N<\/span><\/span><\/span><\/span><\/span>\u4e86\u3002<br \/> \u6240\u4ee5\u6bcf\u4e00\u4e2a\u5b50\u77e9\u9635\u94fe\u7684\u6700\u4f73\u5212\u5206\u65b9\u6848\u5408\u5e76\u5728\u4e00\u8d77\u5c31\u662f\u6574\u4e2a\u77e9\u9635\u94fe\u7684\u6700\u4f73\u5212\u5206\u65b9\u6848\u3002<\/p>\n<\/blockquote>\n<p>\u57fa\u4e8e\u6700\u4f73\u5b50\u7ed3\u6784\uff0c\u6211\u4eec\u53ef\u4ee5\u4ece\u5b50\u95ee\u9898\u7684\u6700\u4f18\u89e3\u6784\u9020\u539f\u95ee\u9898\u7684\u6700\u4f18\u89e3\u3002<\/p>\n<h3>\u9012\u5f52\u6c42\u89e3\u65b9\u6848<\/h3>\n<p>\u73b0\u5728\u8981\u8ba1\u7b97\u77e9\u9635\u94fe<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> A i A i + 1 \u2026 A k A k + 1 \u2026 A j A_iA_{i+1}\u2026A_kA_{k+1}\u2026A_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.969438em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">i<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u6700\u4f18\u62ec\u53f7\u5212\u5206\u65b9\u6848\uff0c\u6700\u4f18\u62ec\u53f7\u5212\u5206\u5373\u4f7f\u4e58\u6cd5\u6b21\u6570\u6700\u5c11\u7684\u65b9\u6848\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u7528\u4e00\u4e2a\u4e8c\u7ef4\u6570\u7ec4<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m [ i , j ] m[i,j] <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>\u6765\u5b58\u50a8\u4ece<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> i i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.65952em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">i<\/span><\/span><\/span><\/span><\/span>\u5230<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> j j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.85396em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><\/span>\u7684\u8fd9<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> j \u2212 i + 1 j-i+1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.85396em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.74285em; vertical-align: -0.08333em;\"><\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u4e2a\u77e9\u9635\u6d88\u8017\u7684\u6700\u5c11\u4e58\u6cd5\u6b21\u6570\uff0c\u6bd4\u5982<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m [ 1 , n ] m[1,n] <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mopen\">[<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\">n<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>\u5b58\u653e\u7684\u5c31\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> A 1 A_1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u8fde\u4e58\u5230<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> A n A_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6240\u6d88\u8017\u7684\u6700\u5c11\u4e58\u6cd5\u6b21\u6570\uff0c\u4e0b\u9762\u6765\u770b\u770b\u5982\u4f55\u8ba1\u7b97<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m [ i , j ] m[i,j] <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>\u3002<br \/> \u5728\u4f18\u5316\u5b50\u7ed3\u6784\u91cc\u9762\u6211\u4eec\u63d0\u5230\u4e86\uff0c\u4e00\u4e2a\u95ee\u9898\u7684\u6700\u4f18\u62ec\u53f7\u5212\u5206\u65b9\u6848\u7b49\u4e8e\u4e24\u4e2a\u5b50\u95ee\u9898\u62ec\u53f7\u5212\u5206\u95ee\u9898\u7684\u5408\u5e76\u3002\u540c\u6837\u7684\uff0c\u6d88\u8017\u7684\u4e58\u6cd5\u6b21\u6570\u4e5f\u662f\u4e24\u4e2a\u5b50\u95ee\u9898\u7684\u5408\u5e76\u3002\u4e0d\u8fc7\u8fd9\u91cc\u8981\u6ce8\u610f\u7684\u662f\uff0c\u5206\u522b\u8ba1\u7b97\u5b8c\u4e24\u4e2a\u5b50\u77e9\u9635\u94fe\u4e4b\u540e\u8fd8\u9700\u8981\u628a\u524d\u540e\u4e24\u4e2a\u4e58\u5728\u4e00\u8d77\u3002\u4e0b\u9762\u6211\u4eec\u89c4\u5b9a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p p <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">p<\/span><\/span><\/span><\/span><\/span>\u662f\u8bfb\u5165\u7684\u6bcf\u4e2a\u77e9\u9635\u7684\u884c\u5217\u6570\uff0c\u4e0b\u6807\u4ece<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> 0 0 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>\u5f00\u59cb\u3002<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> n n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">n<\/span><\/span><\/span><\/span><\/span>\u4e2a\u77e9\u9635\u53ea\u4f1a\u8bfb\u5165<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> n + 1 n+1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.66666em; vertical-align: -0.08333em;\"><\/span><span class=\"mord mathdefault\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u4e2a\u6570\u636e\uff0c\u6bcf\u76f8\u90bb\u4e24\u4e2a\u6570\u4ee3\u8868\u4e00\u4e2a\u77e9\u9635\u7684\u884c\u5217\u3002<\/p>\n<blockquote>\n<p>\u6bd4\u5982\u8981\u6c423\u4e2a\u77e9\u9635\u7684\u8fde\u4e58\uff0c\u8bfb\u51654\u4e2a\u6570\u636e\uff0cp<sub>0<\/sub>=10\uff0cp<sub>1<\/sub>=20\uff0cp<sub>2<\/sub>=30\uff0cp<sub>4<\/sub>=40\u3002\u90a3\u4e48\u7b2c\u4e00\u4e2a\u77e9\u9635\u662f10\u00d720\u7684\uff0c\u7b2c\u4e8c\u4e2a\u77e9\u9635\u662f20\u00d730\u7684\uff0c\u7b2c\u4e09\u4e2a\u77e9\u9635\u662f30\u00d740\u7684\u3002\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u77e9\u9635A<sub>i<\/sub>\u7684\u884c\u6570=p<sub>i-1<\/sub>,\u5217\u6570=p<sub>i<\/sub>\uff0c\u8fd9\u4e2a\u7ed3\u8bba\u540e\u9762\u5c31\u4f1a\u7528\u5230\u3002<\/p>\n<\/blockquote>\n<p>\u8fd9\u91cc\u5047\u8bbe\u6211\u4eec\u5df2\u7ecf\u627e\u5230\u4e86\u6700\u4f73\u5206\u5272\u70b9<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> k k <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.69444em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><\/span>\u4f4d\u4e8e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> A k A_k <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> A k + 1 A_{k+1} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.891661em; vertical-align: -0.208331em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e4b\u95f4\uff0c\u5219<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m [ i , j ] m[i,j] <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>\u7684\u8ba1\u7b97\u516c\u5f0f\u662f\uff1a<br \/> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> m [ i , j ] = m [ i , k ] + m [ k + 1 , j ] + p i \u2212 1 p k p j m[i,j]=m[i,k]+m[k+1,j]+p_{i-1}p_kp_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u8fd9\u91cc<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m [ i , j ] m[i,j] <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>\u662f\u8981\u6c42\u7684\u6700\u540e\u7684\u603b\u6700\u5c11\u7684\u4e58\u6cd5\u6b21\u6570\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> A k A_k <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.83333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> A k + 1 A_{k+1} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.891661em; vertical-align: -0.208331em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e2d\u95f4\u662f\u6700\u4f73\u7684\u5206\u5272\u70b9\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m [ i , k ] m[i,k] <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>\u662f\u5206\u5272\u70b9\u524d\u9762\u7684\u77e9\u9635\u8fde\u4e58\u7684\u6700\u5c11\u6b21\u6570\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m [ k + 1 , j ] m[k+1,j] <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>\u662f\u5206\u5272\u70b9\u540e\u9762\u7684\u77e9\u9635\u8fde\u4e58\u7684\u6700\u5c11\u6b21\u6570\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p i \u2212 1 p k p j p_{i-1}p_kp_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u5c06\u524d\u540e\u4e24\u4e2a\u77e9\u9635\u94fe\u7684\u7ed3\u679c\u5408\u6210\u6700\u7ec8\u77e9\u9635\u65f6\u6d88\u8017\u7684\u4e58\u6cd5\u6b21\u6570\u3002<\/p>\n<blockquote>\n<p>\u4e3a\u4ec0\u4e48\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p i \u2212 1 p k p j p_{i-1}p_kp_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \uff1f<br \/> \u4e24\u4e2a\u77e9\u9635\u76f8\u4e58\u7684\u65f6\u5019\u5f97\u5230\u7684\u7ed3\u679c\u77e9\u9635\u53d6\u5f97\u662f\u7b2c\u4e00\u4e2a\u77e9\u9635\u7684\u884c\u548c\u7b2c\u4e8c\u4e2a\u77e9\u9635\u7684\u5217\u3002<br \/> \u90a3\u4e48\u524di\u5230k\u4e2a\u77e9\u9635\u76f8\u4e58\u7684\u7ed3\u679c\u53d6\u5f97\u5c31\u662f\u7b2c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> i i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.65952em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">i<\/span><\/span><\/span><\/span><\/span>\u4e2a\u77e9\u9635\u7684\u884c\u548c\u7b2c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> k k <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.69444em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><\/span>\u4e2a\u77e9\u9635\u7684\u5217\uff0c\u5e94\u7528\u4e0a\u9762\u7684\u7ed3\u8bba\u7684\u8bdd\u5c31\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p i \u2212 1 p_{i-1} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.638891em; vertical-align: -0.208331em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p k p_k <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u540c\u7406\u7b2c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> k + 1 k+1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.77777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u5230<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> j j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.85396em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><\/span>\u4e2a\u77e9\u9635\u76f8\u4e58\u7684\u7ed3\u679c\u53d6\u5f97\u5c31\u662f\u7b2c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> k + 1 k+1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.77777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u4e2a\u77e9\u9635\u7684\u884c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p k p_k <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c\u7b2c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> j j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.85396em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><\/span>\u4e2a\u77e9\u9635\u7684\u5217<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p j p_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c<br \/> \u4e00\u5bf9\u89c4\u6a21\u5206\u522b\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p \u00d7 q p\u00d7q <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.77777em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">p<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">q<\/span><\/span><\/span><\/span><\/span>\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> q \u00d7 r q\u00d7r <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.77777em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">q<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">r<\/span><\/span><\/span><\/span><\/span>\u7684\u77e9\u9635\u76f8\u4e58\u7684\u4e58\u6cd5\u5f00\u9500\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p q r pqr <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">p<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">q<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.02778em;\">r<\/span><\/span><\/span><\/span><\/span>\uff0c\u56e0\u6b64\u8fd9\u4e24\u4e2a\u77e9\u9635\uff08<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p i \u2212 1 p_{i-1} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.638891em; vertical-align: -0.208331em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p k p_k <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p k p_k <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00d7<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p j p_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\uff09\u76f8\u4e58\u7684\u4e58\u6cd5\u5f00\u9500\u5c31\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p i \u2212 1 p k p j p_{i-1}p_kp_j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.716668em; vertical-align: -0.286108em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u3002<\/p>\n<\/blockquote>\n<p>\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u5f97\u5230\u4e86\u6bcf\u4e00\u4e2a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m [ i , j ] m[i,j] <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>\u7684\u8ba1\u7b97\u516c\u5f0f\uff0c\u4f46\u8fd9\u662f\u57fa\u4e8e\u6700\u4f73\u5206\u5272\u70b9<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> k k <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.69444em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><\/span>\u5df2\u7ecf\u627e\u5230\u4e86\u7684\u60c5\u51b5\u3002\u5b9e\u9645\u4e0a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> k k <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.69444em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><\/span>\u662f\u6211\u4eec\u9700\u8981\u5bfb\u627e\u7684\u4e1c\u897f\uff0c\u800c\u8fd9\u4e2a\u5206\u5272\u70b9\u4e00\u5b9a\u5728<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> i i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.65952em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">i<\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> j j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.85396em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><\/span>\u4e2d\u95f4\uff0c\u56e0\u6b64<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m [ i , j ] m[i,j] <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>\u662f\u5bf9<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> k k <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.69444em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><\/span>\u53d6<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> i i <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.65952em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">i<\/span><\/span><\/span><\/span><\/span>\u5230<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> j j <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.85396em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><\/span>\u4e2d\u7684\u4efb\u610f\u503c\u5f97\u5230\u7684\u7ed3\u679c\u4e2d\u53d6\u6700\u5c0f\uff0c\u5b83\u7684\u6700\u7ec8\u8ba1\u7b97\u516c\u5f0f\u5e94\u8be5\u4e3a\uff1a<br \/> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> m [ i , j ] = { 0 , if&nbsp; i &nbsp;= j &nbsp; min \u2061 i \u2264 k \uff1c j &nbsp; { m [ i , k ] + m [ k + 1 , j ] + p i \u2212 1 p k p j } , if&nbsp; i &lt; j m[i,j]= \\begin{cases} 0, &amp; \\text {if $i$ =$j$ } \\\\\\min_{ i\u2264k\uff1cj } \\ \\lbrace m[i,k]+m[k+1,j]+p_{i-1}p_kp_j\\rbrace , &amp; \\text{if $i$&lt;$j$} \\end{cases} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.00003em; vertical-align: -1.25003em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em;\"><span class=\"delimsizing size4\">{<br \/>\n         <!-- --><\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.69em;\"><span class=\"\" style=\"top: -3.69em;\"><span class=\"pstrut\" style=\"height: 3.008em;\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><span class=\"\" style=\"top: -2.25em;\"><span class=\"pstrut\" style=\"height: 3.008em;\"><\/span><span class=\"mord\"><span class=\"mop\"><span class=\"mop\">min<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">\u2264<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mord cjk_fallback mtight\">\uff1c<\/span><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\">&nbsp;<\/span><span class=\"mopen\">{<br \/>\n                <!-- --><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.336108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.311664em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.286108em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">}<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.19em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 1em;\"><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.69em;\"><span class=\"\" style=\"top: -3.69em;\"><span class=\"pstrut\" style=\"height: 3.008em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">if&nbsp;<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mord\">&nbsp;=<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mord\">&nbsp;<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.25em;\"><span class=\"pstrut\" style=\"height: 3.008em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">if&nbsp;<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mord\">&lt;<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.19em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u5bf9\u6b64\u6211\u4eec\u53ef\u4ee5\u5199\u51fa\u7528\u9012\u5f52\u6c42\u89e3\u7684c\u4ee3\u7801\uff1a<\/p>\n<pre><code class=\"prism language-c\"><span class=\"token macro property\">#<span class=\"token directive keyword\">define<\/span> INFINITY <\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">RECURSIVE_MATRIX_CHAIN<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> p<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><span class=\"token keyword\">int<\/span> i<span class=\"token punctuation\">,<\/span><span class=\"token keyword\">int<\/span> j<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> <span class=\"token keyword\">int<\/span> k<span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token operator\">==<\/span>j<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> m<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token operator\">=<\/span>INFINITY<span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span>k<span class=\"token operator\">=<\/span>i<span class=\"token punctuation\">;<\/span>k<span class=\"token operator\">&lt;<\/span>j<span class=\"token punctuation\">;<\/span>j<span class=\"token operator\">++<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> q<span class=\"token operator\">=<\/span><span class=\"token function\">RECURSIVE_MATRIX_CHAIN<\/span><span class=\"token punctuation\">(<\/span>p<span class=\"token punctuation\">,<\/span>i<span class=\"token punctuation\">,<\/span>k<span class=\"token punctuation\">)<\/span><span class=\"token operator\">+<\/span><span class=\"token function\">RECURSIVE_MATRIX_CHAIN<\/span><span class=\"token punctuation\">(<\/span>p<span class=\"token punctuation\">,<\/span>k<span class=\"token operator\">+<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span>j<span class=\"token punctuation\">)<\/span><span class=\"token operator\">+<\/span>p<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">-<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token operator\">*<\/span>p<span class=\"token punctuation\">[<\/span>k<span class=\"token punctuation\">]<\/span><span class=\"token operator\">*<\/span>p<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>q<span class=\"token operator\">&lt;<\/span>m<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> m<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token operator\">=<\/span>q<span class=\"token punctuation\">;<\/span> <span class=\"token punctuation\">}<\/span> <span class=\"token keyword\">return<\/span> m<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token punctuation\">}<\/span> <\/code><\/pre>\n<p>\u65f6\u95f4\u590d\u6742\u5ea6\u5206\u6790\uff1a<br \/> <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> T ( 1 ) \u2265 1 , T(1)\u22651, <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.13889em;\">T<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.83888em; vertical-align: -0.19444em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><\/span><\/span><br \/> <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> T ( n ) \u2265 1 + \u2211 k = 1 n \u2212 1 &nbsp; ( T ( k ) + T ( n \u2212 k ) + 1 ) = 2 \u2211 i = 1 n \u2212 1 &nbsp; T ( i ) + n \u2265 2 n \u2212 1 T(n)\u22651+\\sum_{k=1}^{n-1} \\ (T(k)+T(n-k)+1)=2\\sum_{i=1}^{n-1} \\ T(i)+n\u22652^{n-1} <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.13889em;\">T<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">n<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.25372em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.954008em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\">&nbsp;<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.13889em;\">T<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.13889em;\">T<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.25372em; vertical-align: -0.29971em;\"><\/span><span class=\"mord\">2<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.954008em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">i<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mspace\">&nbsp;<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.13889em;\">T<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.77194em; vertical-align: -0.13597em;\"><\/span><span class=\"mord mathdefault\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.814108em; vertical-align: 0em;\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/> \u65f6\u95f4\u590d\u6742\u5ea6\u5e76\u6ca1\u6709\u597d\u4e8e\u66b4\u529b\u679a\u4e3e\u6cd5\uff0c\u8fd9\u662f\u56e0\u4e3a\u9012\u5f52\u7684\u8fc7\u7a0b\u4e2d\u91cd\u53e0\u7684\u5b50\u95ee\u9898\u88ab\u53cd\u590d\u8ba1\u7b97\u6d6a\u8d39\u4e86\u5927\u91cf\u65f6\u95f4\u3002<\/p>\n<h3>\u91cd\u53e0\u5b50\u95ee\u9898&amp;\u6784\u9020\u6700\u4f18\u89e3<\/h3>\n<p>\u57fa\u4e8e\u4e0a\u9762\u7684\u601d\u8def\u6211\u4eec\u53d1\u73b0\u53ef\u4ee5\u5c06\u5df2\u7ecf\u8ba1\u7b97\u51fa\u6765\u7684<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> m [ i , j ] m[i,j] <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">m<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathdefault\">i<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.05724em;\">j<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>\u7ed3\u679c\u76f4\u63a5\u586b\u5165\u8868\u4e2d\uff0c\u51cf\u5c11\u5197\u4f59\u7684\u9012\u5f52\u8ba1\u7b97\u3002\u540c\u65f6\u6211\u4eec\u989d\u5916\u5b9a\u4e49\u4e00\u4e2a\u4e8c\u7ef4\u6570\u7ec4<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> s s <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">s<\/span><\/span><\/span><\/span><\/span>\u7528\u4ee5\u8bb0\u5f55\u6bcf\u6b21\u5206\u5272\u7684\u4f4d\u7f6e\u3002\u5177\u4f53\u7684\u5b9e\u73b0\u539f\u56e0\u5728\u4ee3\u7801\u4e2d\u5907\u6ce8\u3002<\/p>\n<blockquote>\n<p>\u6bd4\u5982<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> 5 5 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>\u4e2a\u77e9\u9635\u8fde\u4e58\uff0c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> s [ 1 , 5 ] s[1,5] <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">s<\/span><span class=\"mopen\">[<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">5<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>\u5b58\u7684\u5c31\u662f\u8fd9\u4e00\u4e2a\u5e8f\u5217\u7684\u7b2c\u4e00\u4e2a\u5206\u5272\u70b9\uff0c\u5047\u8bbe\u662f<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> 3 3 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span>\uff0c\u90a3\u4e48\u63a5\u4e0b\u6765\u7684\u5206\u5272\u70b9\u5c31\u8981\u5728<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> s [ 1 , 3 ] s[1,3] <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">s<\/span><span class=\"mopen\">[<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">3<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> s [ 4 , 5 ] s[4,5] <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\">s<\/span><span class=\"mopen\">[<\/span><span class=\"mord\">4<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">5<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span>\u91cc\u627e\uff0c\u4e00\u76f4\u627e\u5230<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> s s <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\">s<\/span><\/span><\/span><\/span><\/span>\u7684\u4e24\u4e2a\u4e0b\u6807\u76f8\u7b49\u4e3a\u6b62\u3002<\/p>\n<\/blockquote>\n<p>\u636e\u6b64\u6211\u4eec\u53ef\u4ee5\u5199\u51faC\u4ee3\u7801\uff1a<\/p>\n<pre><code class=\"prism language-c\"><span class=\"token macro property\">#<span class=\"token directive keyword\">define<\/span> INFINITY <\/span> <span class=\"token keyword\">void<\/span> <span class=\"token function\">MATRIX_CHAIN_ORDER<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> p<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span><span class=\"token keyword\">int<\/span> length<span class=\"token punctuation\">)<\/span><span class=\"token comment\">\/\/\u7528\u4e8e\u8ba1\u7b97m\u548cs\u7684\u51fd\u6570<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> <span class=\"token keyword\">int<\/span> n<span class=\"token punctuation\">;<\/span> n<span class=\"token operator\">=<\/span>length<span class=\"token operator\">-<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">int<\/span> i<span class=\"token punctuation\">,<\/span>j<span class=\"token punctuation\">,<\/span>k<span class=\"token punctuation\">,<\/span>q<span class=\"token punctuation\">,<\/span>l<span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token operator\">=<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span>i<span class=\"token operator\">&lt;=<\/span>n<span class=\"token punctuation\">;<\/span>i<span class=\"token operator\">++<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> m<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token operator\">=<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u53ea\u6709\u4e00\u4e2a\u77e9\u9635\u7684\u65f6\u5019\u4e58\u6cd5\u4ee3\u4ef7\u4e3a0<\/span> <span class=\"token punctuation\">}<\/span> <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span>l<span class=\"token operator\">=<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">;<\/span>l<span class=\"token operator\">&lt;=<\/span>n<span class=\"token punctuation\">;<\/span>l<span class=\"token operator\">++<\/span><span class=\"token punctuation\">)<\/span><span class=\"token comment\">\/\/\u6c42\u89e3\u7684\u987a\u5e8f\u662f\u81ea\u5e95\u5411\u4e0a\u7684\uff0c\u5148\u4ece\u89c4\u6a21\u6700\u5c0f\u76842\u4e2a\u77e9\u9635\u94fe\u6c42\u8d77\u4e00\u76f4\u6c42\u5230\u77e9\u9635\u94fe\u957f\u5ea6\u4e3an\u4e3a\u6b62<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token operator\">=<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span>i<span class=\"token operator\">&lt;=<\/span>n<span class=\"token operator\">-<\/span>l<span class=\"token operator\">+<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span>i<span class=\"token operator\">++<\/span><span class=\"token punctuation\">)<\/span><span class=\"token comment\">\/\/i\u7528\u4e8e\u51b3\u5b9a\u4e00\u4e2a\u77e9\u9635\u94fe\u7684\u8d77\u70b9\uff0c\u8fd9\u4e2a\u8d77\u70b9\u7684\u8303\u56f4\u5c31\u57281~n-l+1\uff08\u603b\u957f\u5ea6-\u5f53\u524d\u957f\u5ea6+\u5f53\u524d\u957f\u5ea6\u4e2d\u591a\u51cf\u7684\u4ee3\u8868\u6700\u9760\u540e\u7684\u8d77\u70b9\u76841\uff09\u4e2d\u95f4<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> j<span class=\"token operator\">=<\/span>i<span class=\"token operator\">+<\/span>l<span class=\"token operator\">-<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/j\u51b3\u5b9a\u4e00\u4e2a\u77e9\u9635\u94fe\u7684\u7ec8\u70b9\uff0c\u7ec8\u70b9\u5c31\u5728i+j-1\uff08\u8d77\u70b9+\u957f\u5ea6-\u957f\u5ea6\u4e2d\u8d77\u70b9\u7684\u91cd\u590d\u8ba1\u6570\uff09<\/span> m<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token operator\">=<\/span>INFINITY<span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span>k<span class=\"token operator\">=<\/span>i<span class=\"token punctuation\">;<\/span>k<span class=\"token operator\">&lt;<\/span>j<span class=\"token punctuation\">;<\/span>k<span class=\"token operator\">++<\/span><span class=\"token punctuation\">)<\/span><span class=\"token comment\">\/\/\u5728i\u548cj\u4e2d\u5bfb\u627ek\uff0c\u4e4b\u540e\u5c31\u548c\u4e0a\u9762\u7684\u601d\u8def\u662f\u4e00\u6837\u7684\u4e86<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> q<span class=\"token operator\">=<\/span>m<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>k<span class=\"token punctuation\">]<\/span><span class=\"token operator\">+<\/span>m<span class=\"token punctuation\">[<\/span>k<span class=\"token operator\">+<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token operator\">+<\/span>p<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">-<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token operator\">*<\/span>p<span class=\"token punctuation\">[<\/span>k<span class=\"token punctuation\">]<\/span><span class=\"token operator\">*<\/span>p<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>q<span class=\"token operator\">&lt;<\/span>m<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> m<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token operator\">=<\/span>q<span class=\"token punctuation\">;<\/span> s<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token operator\">=<\/span>k<span class=\"token punctuation\">;<\/span> <span class=\"token punctuation\">}<\/span> <span class=\"token punctuation\">}<\/span> <span class=\"token punctuation\">}<\/span> <span class=\"token punctuation\">}<\/span> <span class=\"token punctuation\">}<\/span> <span class=\"token keyword\">void<\/span> <span class=\"token function\">PRINT_OPTIML_PARENS<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i<span class=\"token punctuation\">,<\/span><span class=\"token keyword\">int<\/span> j<span class=\"token punctuation\">)<\/span><span class=\"token comment\">\/\/\u7528\u4e8e\u6253\u5370\u52a0\u62ec\u53f7\u65b9\u5f0f\u7684\u51fd\u6570<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token operator\">==<\/span>j<span class=\"token punctuation\">)<\/span> <span class=\"token function\">printf<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">\"A%d\"<\/span><span class=\"token punctuation\">,<\/span>i<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u5f53\u5e8f\u5217\u91cc\u53ea\u6709\u4e00\u9879\u7684\u65f6\u5019\u76f4\u63a5\u6253\u51fa<\/span> <span class=\"token keyword\">else<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> <span class=\"token function\">printf<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">\"(\"<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u6253\u51fa\u5de6\u62ec\u53f7<\/span> <span class=\"token function\">PRINT_OPTIML_PARENS<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token punctuation\">,<\/span>s<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u6253\u51fa\u5206\u5272\u70b9\u524d\u7684\u5143\u7d20<\/span> <span class=\"token function\">PRINT_OPTIML_PARENS<\/span><span class=\"token punctuation\">(<\/span>s<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token operator\">+<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span>j<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u6253\u51fa\u5206\u5272\u70b9\u540e\u7684\u5143\u7d20<\/span> <span class=\"token function\">printf<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">\")\"<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><span class=\"token comment\">\/\/\u6253\u51fa\u53f3\u62ec\u53f7<\/span> <span class=\"token punctuation\">}<\/span> <span class=\"token punctuation\">}<\/span> <\/code><\/pre>\n<h2>\u4e00\u9053\u9898\u76ee<\/h2>\n<h3>\u9898\u9762<\/h3>\n<p>\u9898\u76ee\u94fe\u63a5<br \/> \u7528\u52a0\u62ec\u53f7\u7684\u65b9\u5f0f\u7ed9\u51fa\u6700\u4f18\u7684\u77e9\u9635\u76f8\u4e58\u65b9\u6848<br \/> <strong>\u8f93\u5165<\/strong><br \/> \u591a\u7ec4\u6570\u636e\u8f93\u5165<br \/> \u7b2c\u4e00\u884c\u4e00\u4e2a\u6574\u6570 n\uff0c\u8868\u793a\u77e9\u9635\u94fe\u7684\u957f\u5ea6\uff081&lt;=n&lt;=300\uff09<br \/> \u63a5\u4e0b\u6765\u4e00\u884cn+1\u4e2a\u6570\u8868\u793a\u8fd9\u4e9b\u77e9\u9635\u7684\u884c\u6570\u548c\u5217\u6570<br \/> \u522b\u95ee\u6211\u4e3a\u4ec0\u4e48\u53ea\u6709n+1\u4e2a\u6570\uff0c\u6bcf\u76f8\u90bb\u7684\u4e24\u4e2a\u6570\u8868\u793a\u4e00\u4e2a\u77e9\u9635\u7684\u5927\u5c0f<br \/> <strong>\u8f93\u51fa<\/strong><br \/> \u5bf9\u4e8e\u6bcf\u7ec4\u6570\u636e\uff0c\u8f93\u51fa\u4e24\u884c\uff0c\u7b2c\u4e00\u884c\u4e3a\u8ba1\u7b97\u6b21\u6570\uff0c\u7b2c\u4e8c\u884c\u4e3a\u8ba1\u7b97\u65b9\u6848\uff0c\u7528\u52a0\u62ec\u53f7\u7684\u65b9\u5f0f\u7ed9\u51fa\u6700\u4f18\u7684\u77e9\u9635\u76f8\u4e58\u65b9\u6848<br \/> \u5982\u679c\u4e0d\u5e78\u6700\u4f18\u65b9\u6848\u4e0d\u552f\u4e00\uff0c\u9009\u62e9\u4f18\u5148\u8ba1\u7b97\u5de6\u8fb9\u7684\u77e9\u9635<br \/> <strong>\u8f93\u5165\u6837\u4f8b<\/strong><\/p>\n<blockquote>\n<p>3<br \/> 10 30 5 60<br \/> 3<br \/> 10 20 5 4<\/p>\n<\/blockquote>\n<p><strong>\u8f93\u51fa\u6837\u4f8b<\/strong><\/p>\n<blockquote>\n<p>4500<br \/> ((A1A2)A3)<br \/> 1200<br \/> ((A1A2)A3)<\/p>\n<\/blockquote>\n<p><strong>Hint<\/strong><br \/> \u5728\u7b2c\u4e8c\u7ec4\u6837\u4f8b\u4e2d\uff0c\u9009\u62e9((A1A2)A3)\u65f6\uff0c\u7ed3\u679c\u4e3a10\u00d720\u00d75+10\u00d75\u00d74=1200<br \/> \u9009\u62e9A1(A2A3)\u65f6\uff0c\u7ed3\u679c\u4e3a20\u00d75\u00d74 + 10\u00d720\u00d74 = 1200<br \/> \u8fd9\u65f6\u9009\u62e9\u7b2c\u4e00\u79cd\uff0c\u4f18\u5148\u8ba1\u7b97\u5de6\u8fb9\u7684\uff01<\/p>\n<h3>AC\u4ee3\u7801<\/h3>\n<pre><code class=\"prism language-c\"><span class=\"token macro property\">#<span class=\"token directive keyword\">include<\/span><span class=\"token string\">&lt;stdio.h&gt;<\/span><\/span> <span class=\"token macro property\">#<span class=\"token directive keyword\">include<\/span><span class=\"token string\">&lt;string.h&gt;<\/span><\/span> <span class=\"token macro property\">#<span class=\"token directive keyword\">include<\/span><span class=\"token string\">&lt;stdlib.h&gt;<\/span><\/span> <span class=\"token keyword\">int<\/span> N<span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">int<\/span> p<span class=\"token punctuation\">[<\/span><span class=\"token number\">305<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">int<\/span> m<span class=\"token punctuation\">[<\/span><span class=\"token number\">305<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">305<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">int<\/span> s<span class=\"token punctuation\">[<\/span><span class=\"token number\">305<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">305<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">void<\/span> <span class=\"token function\">MATRIX_CHAIN_ORDER<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> p<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> <span class=\"token keyword\">int<\/span> n<span class=\"token punctuation\">;<\/span> n<span class=\"token operator\">=<\/span>N<span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">int<\/span> i<span class=\"token punctuation\">,<\/span>j<span class=\"token punctuation\">,<\/span>k<span class=\"token punctuation\">,<\/span>q<span class=\"token punctuation\">,<\/span>l<span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token operator\">=<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span>i<span class=\"token operator\">&lt;=<\/span>n<span class=\"token punctuation\">;<\/span>i<span class=\"token operator\">++<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> m<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token operator\">=<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token punctuation\">}<\/span> <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span>l<span class=\"token operator\">=<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">;<\/span>l<span class=\"token operator\">&lt;=<\/span>n<span class=\"token punctuation\">;<\/span>l<span class=\"token operator\">++<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token operator\">=<\/span>n<span class=\"token operator\">-<\/span>l<span class=\"token operator\">+<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span>i<span class=\"token operator\">&gt;=<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span>i<span class=\"token operator\">--<\/span><span class=\"token punctuation\">)<\/span><span class=\"token comment\">\/\/\u8fd9\u91cc\u552f\u4e00\u4e0d\u540c\u7684\u662f\uff0c\u56e0\u4e3a\u8981\u6c42\u5148\u7b97\u5de6\u8fb9\u7684\uff0c\u6240\u4ee5\u6539\u53d8\u4e86i\u548cj\u7684\u9009\u53d6\u987a\u5e8f<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> j<span class=\"token operator\">=<\/span>i<span class=\"token operator\">+<\/span>l<span class=\"token operator\">-<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> m<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token operator\">=<\/span><span class=\"token number\"><\/span><span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span>k<span class=\"token operator\">=<\/span>j<span class=\"token operator\">-<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span>k<span class=\"token operator\">&gt;=<\/span>i<span class=\"token punctuation\">;<\/span>k<span class=\"token operator\">--<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> q<span class=\"token operator\">=<\/span>m<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>k<span class=\"token punctuation\">]<\/span><span class=\"token operator\">+<\/span>m<span class=\"token punctuation\">[<\/span>k<span class=\"token operator\">+<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token operator\">+<\/span>p<span class=\"token punctuation\">[<\/span>i<span class=\"token operator\">-<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token operator\">*<\/span>p<span class=\"token punctuation\">[<\/span>k<span class=\"token punctuation\">]<\/span><span class=\"token operator\">*<\/span>p<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>q<span class=\"token operator\">&lt;<\/span>m<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> m<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token operator\">=<\/span>q<span class=\"token punctuation\">;<\/span> s<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token operator\">=<\/span>k<span class=\"token punctuation\">;<\/span> <span class=\"token punctuation\">}<\/span> <span class=\"token punctuation\">}<\/span> <span class=\"token punctuation\">}<\/span> <span class=\"token punctuation\">}<\/span> <span class=\"token punctuation\">}<\/span> <span class=\"token keyword\">void<\/span> <span class=\"token function\">PRINT_OPTIML_PARENS<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i<span class=\"token punctuation\">,<\/span><span class=\"token keyword\">int<\/span> j<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token operator\">==<\/span>j<span class=\"token punctuation\">)<\/span> <span class=\"token function\">printf<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">\"A%d\"<\/span><span class=\"token punctuation\">,<\/span>i<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">else<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> <span class=\"token function\">printf<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">\"(\"<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token function\">PRINT_OPTIML_PARENS<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token punctuation\">,<\/span>s<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token function\">PRINT_OPTIML_PARENS<\/span><span class=\"token punctuation\">(<\/span>s<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token operator\">+<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span>j<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token function\">printf<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">\")\"<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token punctuation\">}<\/span> <span class=\"token punctuation\">}<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token function\">main<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> <span class=\"token keyword\">int<\/span> i<span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span><span class=\"token function\">scanf<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">\"%d\"<\/span><span class=\"token punctuation\">,<\/span><span class=\"token operator\">&amp;<\/span>N<span class=\"token punctuation\">)<\/span><span class=\"token operator\">!=<\/span><span class=\"token constant\">EOF<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token operator\">=<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span>i<span class=\"token operator\">&lt;<\/span>N<span class=\"token operator\">+<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span>i<span class=\"token operator\">++<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{ \n   <!-- --><\/span> <span class=\"token function\">scanf<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">\"%d\"<\/span><span class=\"token punctuation\">,<\/span><span class=\"token operator\">&amp;<\/span>p<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token punctuation\">}<\/span> <span class=\"token function\">MATRIX_CHAIN_ORDER<\/span><span class=\"token punctuation\">(<\/span>p<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token function\">printf<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">\"%d\\n\"<\/span><span class=\"token punctuation\">,<\/span>m<span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>N<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token function\">PRINT_OPTIML_PARENS<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span>N<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token function\">printf<\/span><span class=\"token punctuation\">(<\/span><span class=\"token string\">\"\\n\"<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token function\">memset<\/span><span class=\"token punctuation\">(<\/span>m<span class=\"token punctuation\">,<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span><span class=\"token keyword\">sizeof<\/span><span class=\"token punctuation\">(<\/span>m<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token function\">memset<\/span><span class=\"token punctuation\">(<\/span>s<span class=\"token punctuation\">,<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span><span class=\"token keyword\">sizeof<\/span><span class=\"token punctuation\">(<\/span>s<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token punctuation\">}<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token punctuation\">}<\/span> <\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"\u77e9\u9635\u94fe\u4e58\u6cd5\u95ee\u9898_\u4e09\u9636\u77e9\u9635\u76f8\u4e58\u600e\u4e48\u7b97\u52a8\u6001\u89c4\u5212\u2014\u2014\u77e9\u9635\u94fe\u76f8\u4e58\u95ee\u9898\u5f15\u5165\u77e9\u9635\u8fde\u4e58\u7684\u5f00\u9500\u52a0\u62ec\u53f7\u7684\u65b9\u5f0f\u603b\u6570\u5f15\u5165\u77e9\u9635\u8fde\u4e58\u7684\u5f00\u9500\u7ed9\u51fa\u4e00\u4e2a...","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"_links":{"self":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/6718"}],"collection":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/comments?post=6718"}],"version-history":[{"count":0,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/6718\/revisions"}],"wp:attachment":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/media?parent=6718"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/categories?post=6718"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/tags?post=6718"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}