{"id":7323,"date":"2024-04-07T14:01:01","date_gmt":"2024-04-07T06:01:01","guid":{"rendered":""},"modified":"2024-04-07T14:01:01","modified_gmt":"2024-04-07T06:01:01","slug":"\u6c42\u89e3\u6700\u957f\u4e0a\u5347\u5b50\u5e8f\u5217\u7684\u4e09\u79cd\u65b9\u6cd5","status":"publish","type":"post","link":"https:\/\/mushiming.com\/7323.html","title":{"rendered":"\u6c42\u89e3\u6700\u957f\u4e0a\u5347\u5b50\u5e8f\u5217\u7684\u4e09\u79cd\u65b9\u6cd5"},"content":{"rendered":"<p style=\"margin-left:0cm;\"><strong>\u52a8\u6001\u89c4\u5212O(N^2)<\/strong><\/p>\n<p style=\"margin-left:0cm;\">\u8fd9\u79cd\u7b97\u6cd5\u4e3b\u8981\u662f\u4f9d\u9760\u524d\u9762\u5df2\u7ecf\u5f97\u51fa\u7684\u6700\u957f\u9012\u589e\u5b50\u5e8f\u5217\uff0c\u6765\u63a8\u51fa\u5f53\u524d\u7684\u6700\u957f\u9012\u589e\u5b50\u5e8f\u5217\u3002<\/p>\n<p style=\"margin-left:0cm;\"><strong>\u4f8b\uff1a<\/strong>\u5f53\u524d\u904d\u5386\u5230m\u65f6\uff0c\u503c\u4e3an<\/p>\n<p style=\"margin-left:0cm;\">(1)dp[ m ]=1\uff0cn\u4e3a\u5f53\u524d\u6700\u5927\u503c<\/p>\n<p style=\"margin-left:0cm;\">(2)dp[ m ]=max(dp[ m ],dp[ 1~ m]+1),n\u8981\u5927\u4e8e\u5f53\u524d\u7684\u6570\u624d\u80fd\u8fdb\u884c\u6bd4\u8f83\uff0c+1\u8868\u793a\u628am\u70b9\u4e5f\u7b97\u5165\u5e8f\u5217\u4e2d<\/p>\n<p style=\"margin-left:0cm;\"><strong>\u4ee3\u7801\u5982\u4e0b\uff1a<\/strong><\/p>\n<pre class=\"language-java prettyprint linenums\"><code class=\"language-cpp\">#include&lt;cstdio&gt;\n#include&lt;cstring&gt;\n#include&lt;algorithm&gt;\nusing namespace std;\nconst int N=1010;\nint t[N];\nint dp[N];\nint main()\n{\n    int n;\n    scanf(\"%d\",&amp;n);\n    for(int i=1;i&lt;=n;i++)\n        scanf(\"%d\",&amp;t[i]);\n    int ant=1;\n    for(int i=1;i&lt;=n;i++)\n    {\n        dp[i]=1;\n        for(int j=0;j&lt;i;j++)\n            if(t[j]&lt;t[i])\n            {\n                dp[i]=max(dp[i],dp[j]+1);\n                ant=max(ant,dp[i]);\n            }\n                \n    }\n    printf(\"%d\\n\",ant);\n    return 0;\n}<\/code><\/pre>\n<p><strong>\u8f93\u51fa\u5e8f\u5217\uff1a<\/strong>\u53ef\u4ee5\u8bbe\u7f6e\u4e00\u4e2a\u6570\u7ec4\u6765\u8bb0\u5f55\u7b2c i \u4e2a\u6570\u7684\u9012\u589e\u5b50\u5e8f\u5217\u7531\u54ea\u4e2a\u6570\u5f97\u5230\uff0c\u7c7b\u4f3c\u4e8e\u5e76\u67e5\u96c6&nbsp;<\/p>\n<\/p>\n<p><strong>DP+\u4e8c\u5206NlogN<\/strong><\/p>\n<p>DP+\u4e8c\u5206 \u5206\u4e3a\u4e24\u79cd\u60c5\u51b5\uff0c\u5f53\u904d\u5386\u5230\u7b2ci\u4e2a\u6570m\u65f6\uff0cm\u6bd4\u7ef4\u62a4\u7684\u9012\u589e\u5e8f\u5217\u6570\u7ec4\u6700\u540e\u4e00\u4e2a\u6570\u8fd8\u8981\u5927\u65f6\uff0c\u5c06m\u589e\u52a0\u5230\u6570\u7ec4\u672b\u5c3e\u4e2d\uff0c\u6570\u7ec4\u957f\u5ea6+1\u3002\u5426\u5219\uff0c\u5728\u6570\u7ec4\u4e2d\u4e8c\u5206\u67e5\u627e\u521a\u597d\u5927\u4e8em\u7684\u6570\uff0c\u5e76\u66ff\u6362\u3002<\/p>\n<p><strong>\u4f8b\uff1a<\/strong>\u5047\u8bbe\u5b58\u5728\u4e00\u4e2a\u5e8f\u5217d[1..9] ={ 2\uff0c1 \uff0c5 \uff0c3 \uff0c6\uff0c4\uff0c 8 \uff0c9\uff0c 7}\uff0c\u53ef\u4ee5\u770b\u51fa\u6765\u5b83\u7684LIS\u957f\u5ea6\u4e3a5\u3002<br \/> \u4e0b\u9762\u4e00\u6b65\u4e00\u6b65\u8bd5\u7740\u627e\u51fa\u5b83\u3002<br \/> \u6211\u4eec\u5b9a\u4e49\u4e00\u4e2a\u5e8f\u5217B\uff0c\u7136\u540e\u4ee4 i = 1 to 9 \u9010\u4e2a\u8003\u5bdf\u8fd9\u4e2a\u5e8f\u5217\u3002<br \/> \u6b64\u5916\uff0c\u6211\u4eec\u7528\u4e00\u4e2a\u53d8\u91cfLen\u6765\u8bb0\u5f55\u73b0\u5728\u6700\u957f\u7b97\u5230\u591a\u5c11\u4e86<\/p>\n<p> \u9996\u5148\uff0c\u628ad[1]\u6709\u5e8f\u5730\u653e\u5230B\u91cc\uff0c\u4ee4B[1] = 2\uff0c\u5c31\u662f\u8bf4\u5f53\u53ea\u67091\u4e00\u4e2a\u6570\u5b572\u7684\u65f6\u5019\uff0c\u957f\u5ea6\u4e3a1\u7684LIS\u7684\u6700\u5c0f\u672b\u5c3e\u662f2\u3002\u8fd9\u65f6Len=1<\/p>\n<p> \u7136\u540e\uff0c\u628ad[2]\u6709\u5e8f\u5730\u653e\u5230B\u91cc\uff0c\u4ee4B[1] = 1\uff0c\u5c31\u662f\u8bf4\u957f\u5ea6\u4e3a1\u7684LIS\u7684\u6700\u5c0f\u672b\u5c3e\u662f1\uff0cd[1]=2\u5df2\u7ecf\u6ca1\u7528\u4e86\uff0c\u5f88\u5bb9\u6613\u7406\u89e3\u5427\u3002\u8fd9\u65f6Len=1<\/p>\n<p> \u63a5\u7740\uff0cd[3] = 5\uff0cd[3]&gt;B[1]\uff0c\u6240\u4ee5\u4ee4B[1+1]=B[2]=d[3]=5\uff0c\u5c31\u662f\u8bf4\u957f\u5ea6\u4e3a2\u7684LIS\u7684\u6700\u5c0f\u672b\u5c3e\u662f5\uff0c\u5f88\u5bb9\u6613\u7406\u89e3\u5427\u3002\u8fd9\u65f6\u5019B[1..2] = 1, 5\uff0cLen\uff1d2<\/p>\n<p> \u518d\u6765\uff0cd[4] = 3\uff0c\u5b83\u6b63\u597d\u52a0\u57281,5\u4e4b\u95f4\uff0c\u653e\u57281\u7684\u4f4d\u7f6e\u663e\u7136\u4e0d\u5408\u9002\uff0c\u56e0\u4e3a1\u5c0f\u4e8e3\uff0c\u957f\u5ea6\u4e3a1\u7684LIS\u6700\u5c0f\u672b\u5c3e\u5e94\u8be5\u662f1\uff0c\u8fd9\u6837\u5f88\u5bb9\u6613\u63a8\u77e5\uff0c\u957f\u5ea6\u4e3a2\u7684LIS\u6700\u5c0f\u672b\u5c3e\u662f3\uff0c\u4e8e\u662f\u53ef\u4ee5\u628a5\u6dd8\u6c70\u6389\uff0c\u8fd9\u65f6\u5019B[1..2] = 1, 3\uff0cLen = 2<\/p>\n<p> \u7ee7\u7eed\uff0cd[5] = 6\uff0c\u5b83\u57283\u540e\u9762\uff0c\u56e0\u4e3aB[2] = 3, \u800c6\u57283\u540e\u9762\uff0c\u4e8e\u662f\u5f88\u5bb9\u6613\u53ef\u4ee5\u63a8\u77e5B[3] = 6, \u8fd9\u65f6B[1..3] = 1, 3, 6\uff0c\u8fd8\u662f\u5f88\u5bb9\u6613\u7406\u89e3\u5427\uff1f Len = 3 \u4e86\u5662\u3002<\/p>\n<p> \u7b2c6\u4e2a, d[6] = 4\uff0c\u4f60\u770b\u5b83\u57283\u548c6\u4e4b\u95f4\uff0c\u4e8e\u662f\u6211\u4eec\u5c31\u53ef\u4ee5\u628a6\u66ff\u6362\u6389\uff0c\u5f97\u5230B[3] = 4\u3002B[1..3] = 1, 3, 4\uff0c Len\u7ee7\u7eed\u7b49\u4e8e3<\/p>\n<p> \u7b2c7\u4e2a, d[7] = 8\uff0c\u5b83\u5f88\u5927\uff0c\u6bd44\u5927\uff0c\u55ef\u3002\u4e8e\u662fB[4] = 8\u3002Len\u53d8\u62104\u4e86<\/p>\n<p> \u7b2c8\u4e2a, d[8] = 9\uff0c\u5f97\u5230B[5] = 9\uff0c\u55ef\u3002Len\u7ee7\u7eed\u589e\u5927\uff0c\u52305\u4e86\u3002<\/p>\n<p> \u6700\u540e\u4e00\u4e2a, d[9] = 7\uff0c\u5b83\u5728B[3] = 4\u548cB[4] = 8\u4e4b\u95f4\uff0c\u6240\u4ee5\u6211\u4eec\u77e5\u9053\uff0c\u6700\u65b0\u7684B[4] =7\uff0cB[1..5] = 1, 3, 4, 7, 9\uff0cLen = 5\u3002<\/p>\n<p> \u4e8e\u662f\u6211\u4eec\u77e5\u9053\u4e86LIS\u7684\u957f\u5ea6\u4e3a5\u3002<\/p>\n<\/p>\n<p><strong>\u4ee3\u7801\u5982\u4e0b\uff1a<\/strong><\/p>\n<pre class=\"language-java prettyprint linenums\"><code class=\"language-cpp\">#include&lt;cstdio&gt;\n#include&lt;cstring&gt;\n#include&lt;algorithm&gt;\nusing namespace std;\nconst int N=1e5+10;\nconst int inf=0X3f3f3f3f;\nint tmp[N];\nint n;\nint er_left(int r,int x)\n{\n\tint l=1,mid;\n\t\n\twhile(l&lt;r)\n\t{\n\t    mid=l+r&gt;&gt;1;\n\t\tif(tmp[mid]&gt;=x)\n\t\t\tr=mid;\n\t\telse\n\t\t\tl=mid+1;\n\t}\n\treturn r;\n}\nint main()\n{\n\tscanf(\"%d\",&amp;n);\n\tint ans=0;\n\tint c;\n\ttmp[0]=-inf;\n\tfor(int i=1;i&lt;=n;i++)\n\t{\n\t\tscanf(\"%d\",&amp;c);\n\t\tif(c&gt;tmp[ans])\n\t\t\ttmp[++ans]=c;\n\t\telse\n\t\t\ttmp[er_left(ans,c)]=c;\n\t}\n\tprintf(\"%d\\n\",ans);\n\treturn 0;\n}<\/code><\/pre>\n<p>\u8f93\u51fa\u5e8f\u5217\uff1a\u53ef\u4ee5\u8bbe\u7f6e\u4e24\u4e2a\u6570\u7ec4\uff0cpos[ ],pre[ ]\u3002pos\u7528\u6765\u8bb0\u5f55tmp\u4f4d\u7f6e\u4e0a\u662f\u7b2c\u51e0\u4e2a\u6570\uff0cpre\u7528\u6765\u8bb0\u5f55\u6bcf\u4e2a\u6570\u7684\u524d\u4e00\u4e2a\u6570&nbsp;<\/p>\n<p>\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n<pre class=\"language-java prettyprint linenums\"><code class=\"language-cpp\">#include&lt;cstdio&gt;\n#include&lt;cstring&gt;\n#include&lt;algorithm&gt;\nusing namespace std;\nconst int N=1e5+10;\nconst int inf=0X3f3f3f3f;\nint a[N];\nint tmp[N];\nint pos[N];\nint pre[N]; \nint n;\nint er_left(int r,int x)\n{\n\tint l=1,mid;\n\t\n\twhile(l&lt;r)\n\t{\n\t    mid=l+r&gt;&gt;1;\n\t\tif(tmp[mid]&gt;=x)\n\t\t\tr=mid;\n\t\telse\n\t\t\tl=mid+1;\n\t}\n\treturn r;\n}\nint main()\n{\n\tscanf(\"%d\",&amp;n);\n\tint ans=0;\n\tint c;\n\ttmp[0]=-inf;\n\tfor(int i=1;i&lt;=n;i++)\n\t{\n\t\tscanf(\"%d\",&amp;c);\n\t\ta[i]=c;\n\t\tif(c&gt;tmp[ans])\n\t\t{\n\t\t\ttmp[++ans]=c;\n\t\t\tpos[ans]=i;\n\t\t\tpre[i]=pos[ans-1];\n\t\t}\n\t\telse\n\t\t{\n\t\t\tint t=er_left(ans,c);\n\t\t\ttmp[t]=c;\n\t\t\tpos[t]=i;\n\t\t\tpre[i]=pos[t-1];\n\t\t}\t\t\n\n\t}\n\tprintf(\"%d\\n\",ans);\n\twhile(pos[ans]&gt;=1)\n\t{\n\t\tprintf(\"%d \",a[pos[ans]]);\n\t\tpos[ans]=pre[pos[ans]];\n\t}\n\treturn 0;\n}<\/code><\/pre>\n<p>\u624b\u52a8\u6a21\u62df\u4e00\u4e0b\uff0c\u6bd4\u8f83\u5bb9\u6613\u7406\u89e3&nbsp;<\/p>\n<p><strong>LCS:<\/strong>\u6700\u540e\u4e00\u79cd\u65b9\u6cd5\u662f\u7528LCS\u6765\u6c42\uff0c\u5148\u5c06\u5e8f\u5217\u6392\u5e8f\uff0c\u6c42\u5e8f\u5217\u4e0e\u6392\u5e8f\u540e\u5e8f\u5217\u7684\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217\u5373\u53ef\u3002<\/p>\n<p><strong>LCS\u6a21\u677f<\/strong><\/p>\n<\/p>\n<\/p>\n<p style=\"margin-left:0cm;\">\n<p style=\"margin-left:0cm;\">\n<p style=\"margin-left:0cm;\">\n<p style=\"margin-left:0cm;\">\n<p style=\"margin-left:0cm;\">\n","protected":false},"excerpt":{"rendered":"\u6c42\u89e3\u6700\u957f\u4e0a\u5347\u5b50\u5e8f\u5217\u7684\u4e09\u79cd\u65b9\u6cd5\u52a8\u6001\u89c4\u5212O(N^2)\u8fd9\u79cd\u7b97\u6cd5\u4e3b\u8981\u662f\u4f9d\u9760\u524d\u9762\u5df2\u7ecf\u5f97\u51fa\u7684\u6700\u957f\u9012\u589e\u5b50\u5e8f\u5217\uff0c\u6765\u63a8\u51fa\u5f53\u524d\u7684\u6700\u957f\u9012\u589e\u5b50\u5e8f\u5217","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\/7323"}],"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=7323"}],"version-history":[{"count":0,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/7323\/revisions"}],"wp:attachment":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/media?parent=7323"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/categories?post=7323"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/tags?post=7323"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}