{"id":1107,"date":"2009-11-25T19:07:35","date_gmt":"2009-11-25T11:07:35","guid":{"rendered":"http:\/\/www.slyar.com\/blog\/?p=1107"},"modified":"2014-04-22T13:57:38","modified_gmt":"2014-04-22T05:57:38","slug":"longest-ordered-subsequence","status":"publish","type":"post","link":"http:\/\/www.slyar.com\/blog\/longest-ordered-subsequence.html","title":{"rendered":"\u6700\u957f\u4e0a\u5347\u5b50\u5e8f\u5217(LIS)\u957f\u5ea6\u7684O(nlogn)\u7b97\u6cd5"},"content":{"rendered":"<p>\u6587\u7ae0\u4f5c\u8005\uff1a<span style=\"color: #0000ff;\">\u59dc\u5357(Slyar) <\/span>\u6587\u7ae0\u6765\u6e90\uff1aSlyar Home (<a title=\"Slyar\" href=\"http:\/\/www.slyar.com\" target=\"_blank\">www.slyar.com<\/a>) \u8f6c\u8f7d\u8bf7\u6ce8\u660e\uff0c\u8c22\u8c22\u5408\u4f5c\u3002<\/p>\n<p>\u521a\u624d\u7528O(n^2)\u7684DP\u7b97\u6cd5\u505a\u4e86\u6700\u957f\u4e0a\u5347\u5b50\u5e8f\u5217\uff0c\u5177\u4f53\u89c1<a title=\"POJ2533\" href=\"http:\/\/www.slyar.com\/blog\/poj-2533-cpp.html\" target=\"_blank\">POJ2533\u89e3\u9898\u62a5\u544a<\/a>\u3002\u540e\u6765\u5728\u7f51\u4e0a\u770b\u5230\u8bf4LIS\u95ee\u9898\u6709O(nlogn)\u7684\u7b97\u6cd5\uff0c\u4e8e\u662f\u62ff\u6765\u5c0f\u7814\u7a76\u4e86\u4e00\u4e0b\u3002<\/p>\n<p>\u8fd9\u4e2a\u7b97\u6cd5\u5176\u5b9e\u5df2\u7ecf\u4e0d\u662fDP\u4e86\uff0c\u6709\u70b9\u50cf\u8d2a\u5fc3\u3002\u81f3\u4e8e\u590d\u6742\u5ea6\u964d\u4f4e\u5176\u5b9e\u662f\u56e0\u4e3a\u8fd9\u4e2a\u7b97\u6cd5\u91cc\u9762\u7528\u5230\u4e86\u4e8c\u5206\u641c\u7d22\u3002\u672c\u6765\u6709N\u4e2a\u6570\u8981\u5904\u7406\u662fO(n)\uff0c\u6bcf\u6b21\u8ba1\u7b97\u8981\u67e5\u627eN\u6b21\u8fd8\u662fO(n)\uff0c\u4e00\u5171\u5c31\u662fO(n^2)\uff1b\u73b0\u5728\u641c\u7d22\u6362\u6210\u4e86O(logn)\u7684\u4e8c\u5206\u641c\u7d22\uff0c\u603b\u7684\u590d\u6742\u5ea6\u5c31\u53d8\u4e3aO(nlogn)\u4e86\u3002<\/p>\n<p>\u8fd9\u4e2a\u7b97\u6cd5\u7684\u5177\u4f53\u64cd\u4f5c\u5982\u4e0b(by RyanWang):<\/p>\n<p>\u5f00\u4e00\u4e2a\u6808\uff0c\u6bcf\u6b21\u53d6\u6808\u9876\u5143\u7d20top\u548c\u8bfb\u5230\u7684\u5143\u7d20temp\u505a\u6bd4\u8f83\uff0c\u5982\u679ctemp &gt; top \u5219\u5c06temp\u5165\u6808\uff1b\u5982\u679ctemp &lt; top\u5219\u4e8c\u5206\u67e5\u627e\u6808\u4e2d\u7684\u6bd4temp\u5927\u7684\u7b2c1\u4e2a\u6570\uff0c\u5e76\u7528temp\u66ff\u6362\u5b83\u3002 \u6700\u957f\u5e8f\u5217\u957f\u5ea6\u5373\u4e3a\u6808\u7684\u5927\u5c0ftop\u3002<\/p>\n<p>\u8fd9\u4e5f\u662f\u5f88\u597d\u7406\u89e3\u7684\uff0c\u5bf9\u4e8ex\u548cy\uff0c\u5982\u679cx &lt; y\u4e14Stack[y] &lt; Stack[x],\u7528Stack[x]\u66ff\u6362Stack[y]\uff0c\u6b64\u65f6\u7684\u6700\u957f\u5e8f\u5217\u957f\u5ea6\u6ca1\u6709\u6539\u53d8\u4f46\u5e8f\u5217Q\u7684''\u6f5c\u529b''\u589e\u5927\u4e86\u3002<\/p>\n<p>\u4e3e\u4f8b\uff1a\u539f\u5e8f\u5217\u4e3a1\uff0c5\uff0c8\uff0c3\uff0c6\uff0c7<\/p>\n<p>\u6808\u4e3a1\uff0c5\uff0c8\uff0c\u6b64\u65f6\u8bfb\u52303\uff0c\u75283\u66ff\u63625\uff0c\u5f97\u52301\uff0c3\uff0c8\uff1b \u518d\u8bfb6\uff0c\u75286\u66ff\u63628\uff0c\u5f97\u52301\uff0c3\uff0c6\uff1b\u518d\u8bfb7\uff0c\u5f97\u5230\u6700\u7ec8\u6808\u4e3a1\uff0c3\uff0c6\uff0c7\u3002\u6700\u957f\u9012\u589e\u5b50\u5e8f\u5217\u4e3a\u957f\u5ea64\u3002<\/p>\n<p>\u7528\u8be5\u7b97\u6cd5\u5b8c\u6210POJ2533\u7684\u5177\u4f53\u4ee3\u7801\u5982\u4e0b:<\/p>\n<p><!--more--><\/p>\n<pre lang=\"c\" line=\"1\">\r\n#include <iostream>\r\n#define SIZE 1001\r\n\r\nusing namespace std;\r\n\r\nint main()\r\n{\r\n    int i, j, n, top, temp;\r\n    int stack[SIZE];\r\n    cin >> n;\r\n    \r\n    top = 0;\r\n    \/* \u7b2c\u4e00\u4e2a\u5143\u7d20\u53ef\u80fd\u4e3a0 *\/\r\n    stack[0] = -1;\r\n    for (i = 0; i < n; i++)\r\n    {\r\n        cin >> temp;\r\n        \/* \u6bd4\u6808\u9876\u5143\u7d20\u5927\u6570\u5c31\u5165\u6808 *\/\r\n        if (temp > stack[top])\r\n        {\r\n            stack[++top] = temp;\r\n        }\r\n        else\r\n        {\r\n            int low = 1, high = top;\r\n            int mid;\r\n            \/* \u4e8c\u5206\u68c0\u7d22\u6808\u4e2d\u6bd4temp\u5927\u7684\u7b2c\u4e00\u4e2a\u6570 *\/\r\n            while(low <= high)\r\n            {\r\n                mid = (low + high) \/ 2;\r\n                if (temp > stack[mid])\r\n                {\r\n                    low = mid + 1;\r\n                }\r\n                else\r\n                {\r\n                    high = mid - 1;\r\n                }\r\n            }\r\n            \/* \u7528temp\u66ff\u6362 *\/\r\n            stack[low] = temp;\r\n        }\r\n    }\r\n    \r\n    \/* \u6700\u957f\u5e8f\u5217\u6570\u5c31\u662f\u6808\u7684\u5927\u5c0f *\/\r\n    cout << top << endl;\r\n    \r\n    \/\/system(\"pause\");\r\n    return 0;\r\n}\r\n<\/pre>\n<p>\u8f6c\u8f7d\u8bf7\u6ce8\u660e\uff1a<a href=\"http:\/\/www.slyar.com\/blog\">Slyar Home<\/a> &raquo; <a href=\"http:\/\/www.slyar.com\/blog\/longest-ordered-subsequence.html\">\u6700\u957f\u4e0a\u5347\u5b50\u5e8f\u5217(LIS)\u957f\u5ea6\u7684O(nlogn)\u7b97\u6cd5<\/a><\/p>","protected":false},"excerpt":{"rendered":"<p>\u6587\u7ae0\u4f5c\u8005\uff1a\u59dc\u5357(Slyar) \u6587\u7ae0\u6765\u6e90\uff1aSlyar Home (www.slyar.com) \u8f6c\u8f7d\u8bf7\u6ce8\u660e\uff0c\u8c22\u8c22\u5408\u4f5c\u3002 \u521a\u624d\u7528O(n^2)\u7684DP\u7b97\u6cd5\u505a\u4e86\u6700\u957f\u4e0a\u5347\u5b50\u5e8f\u5217\uff0c\u5177\u4f53\u89c1POJ2533\u89e3\u9898\u62a5\u544a\u3002\u540e\u6765\u5728\u7f51\u4e0a\u770b\u5230\u8bf4LIS\u95ee\u9898\u6709O(nlogn)\u7684\u7b97\u6cd5\uff0c\u4e8e [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[17],"tags":[1007],"class_list":["post-1107","post","type-post","status-publish","format-standard","hentry","category-programing","tag-1007"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.2.1 - 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