{"id":314,"date":"2022-12-11T12:25:36","date_gmt":"2022-12-11T04:25:36","guid":{"rendered":"https:\/\/muidar.com\/blog\/?p=314"},"modified":"2026-08-05T23:16:57","modified_gmt":"2026-08-05T15:16:57","slug":"dyamic-programming","status":"publish","type":"post","link":"https:\/\/muidar.com\/blog\/posts\/cmuidar\/dyamic-programming\/","title":{"rendered":"\u52a8\u6001\u89c4\u5212"},"content":{"rendered":"\n

\u52a8\u6001\u89c4\u5212 (Dynamic Programming\uff0cDP) \u662f\u4e00\u79cd\u89e3\u51b3\u95ee\u9898\u7684\u65b9\u6cd5\uff0c\u5b83\u5c06\u95ee\u9898\u5206\u89e3\u6210\u591a\u4e2a\u5b50\u95ee\u9898\uff0c\u901a\u8fc7\u6c42\u89e3\u8fd9\u4e9b\u5b50\u95ee\u9898\u5e76\u5c06\u5b83\u4eec\u7684\u89e3\u7ec4\u5408\u5728\u4e00\u8d77\uff0c\u6765\u6c42\u89e3\u539f\u95ee\u9898\u3002\u8fd9\u79cd\u65b9\u6cd5\u53ef\u4ee5\u89e3\u51b3\u8bb8\u591a\u7c7b\u578b\u7684\u95ee\u9898\uff0c\u5305\u62ec\u6700\u77ed\u8def\u5f84\u3001\u6700\u5927\u5b50\u5e8f\u5217\u548c\u7b49\u3002 <\/p>\n\n\n\n

\u4e0b\u9762\u6211\u4eec\u6765\u770b\u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\uff1a\u6c42\u89e3\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217\u95ee\u9898\u3002\u8fd9\u4e2a\u95ee\u9898\u6d89\u53ca\u4e24\u4e2a\u5b57\u7b26\u4e32\uff0c\u6211\u4eec\u8981\u627e\u5230\u5b83\u4eec\u7684\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217\u3002\u4f8b\u5982\uff0c\u5982\u679c\u6211\u4eec\u6709\u4e24\u4e2a\u5b57\u7b26\u4e32”ABCBDAB”\u548c”BDCABA”\uff0c\u90a3\u4e48\u5b83\u4eec\u7684\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217\u5c31\u662f”BCBA”\u3002 <\/p>\n\n\n\n

\u4e3a\u4e86\u6c42\u89e3\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528C++\u52a8\u6001\u89c4\u5212\u7684\u65b9\u6cd5\u3002\u9996\u5148\uff0c\u6211\u4eec\u8981\u6784\u5efa\u4e00\u4e2a\u4e8c\u7ef4\u6570\u7ec4dp[][]\uff0c\u5176\u4e2ddp[i][j]\u8868\u793a\u5b57\u7b26\u4e321\u7684\u524di\u4e2a\u5b57\u7b26\u548c\u5b57\u7b26\u4e322\u7684\u524dj\u4e2a\u5b57\u7b26\u7684\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217\u7684\u957f\u5ea6\u3002\u6211\u4eec\u4ece\u6570\u7ec4\u7684\u5de6\u4e0a\u89d2\u5f00\u59cb\uff0c\u6839\u636e\u5b57\u7b26\u4e321\u548c\u5b57\u7b26\u4e322\u7684\u6bcf\u4e2a\u5b57\u7b26\u6765\u66f4\u65b0\u6570\u7ec4dp[][]\u3002\u5982\u679c\u8fd9\u4e24\u4e2a\u5b57\u7b26\u76f8\u540c\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u5728\u5b83\u4eec\u7684\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217\u7684\u57fa\u7840\u4e0a\u518d\u52a0\u4e0a\u8fd9\u4e2a\u5b57\u7b26\uff0c\u6240\u4ee5dp[i][j]=dp[i-1][j-1]+1\u3002\u5426\u5219\uff0c\u6211\u4eec\u8981\u4ece\u5b57\u7b26\u4e321\u7684\u524di-1\u4e2a\u5b57\u7b26\u6216\u5b57\u7b26\u4e322\u7684\u524dj-1\u4e2a\u5b57\u7b26\u4e2d\u9009\u62e9\u4e00\u4e2a\u8f83\u957f\u7684\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217\uff0c\u6240\u4ee5dp[i][j]=max(dp[i-1][j],dp[i][j-1])\u3002<\/p>\n\n\n\n

\u4ee3\u7801\uff1a<\/p>\n\n\n\n

\n\n#include <iostream>\n#include <cstring>\nusing namespace std;\nconst int N = 1010;\nint dp[N][N]; \/\/ dp[i][j]\u8868\u793a\u5b57\u7b26\u4e321\u7684\u524di\u4e2a\u5b57\u7b26\u548c\u5b57\u7b26\u4e322\u7684\u524dj\u4e2a\u5b57\u7b26\u7684\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217\u7684\u957f\u5ea6\nstring s1, s2; \/\/ \u5b58\u50a8\u4e24\u4e2a\u5b57\u7b26\u4e32\nint main() {\n\tcin >> s1 >> s2;\n\tmemset(dp, 0, sizeof dp); \/\/ \u5c06dp\u6570\u7ec4\u521d\u59cb\u5316\u4e3a0\n\t\/\/ \u586b\u5145dp\u6570\u7ec4\n\tfor (int i = 1; i <= s1.size(); i ++ )\n\t\tfor (int j = 1; j <= s2.size(); j ++ )\n                    if (s1[i-1] == s2[j-1]) \/\/ \u5982\u679c\u8fd9\u4e24\u4e2a\u5b57\u7b26\u76f8\u540c\n                        dp[i][j] = dp[i-1][j-1] + 1; \/\/ \u5728\u5b83\u4eec\u7684\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217\u7684\u57fa\u7840\u4e0a\u518d\u52a0\u4e0a\u8fd9\u4e2a\u5b57\u7b26\n                    else \/\/ \u5426\u5219\n                        dp[i][j] = max(dp[i-1][j], dp[i][j-1]); \/\/ \u4ece\u5b57\u7b26\u4e321\u7684\u524di-1\u4e2a\u5b57\u7b26\u6216\u5b57\u7b26\u4e322\u7684\u524dj-1\u4e2a\u5b57\u7b26\u4e2d\u9009\u62e9\u4e00\u4e2a\u8f83\u957f\u7684\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217\n    cout << dp[s1.size()][s2.size()] << endl; \/\/ \u8f93\u51fa\u6700\u957f\u516c\u5171\u5b50\u5e8f\u5217\u7684\u957f\u5ea6\n    return 0;\n}\n<\/code>\n<\/pre>\n\n\n\n
\u4e0a\u9762\u7684\u4ee3\u7801\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(|s1|*|s2|)\uff0c\u5176\u4e2d|s1|\u548c|s2|\u5206\u522b\u8868\u793a\u5b57\u7b26\u4e32s1<\/code>\u548cs2<\/code>\u7684\u957f\u5ea6\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
\u52a8\u6001\u89c4\u5212 (Dynamic Programming\uff0cDP) \u662f\u4e00\u79cd\u89e3\u51b3\u95ee\u9898\u7684\u65b9\u6cd5\uff0c\u5b83\u5c06\u95ee\u9898\u5206\u89e3\u6210\u591a\u4e2a\u5b50\u95ee\u9898\uff0c\u901a […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[34],"tags":[52,51],"class_list":["post-314","post","type-post","status-publish","format-standard","hentry","category-programming","tag-c","tag-programming"],"_links":{"self":[{"href":"https:\/\/muidar.com\/blog\/wp-json\/wp\/v2\/posts\/314","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/muidar.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/muidar.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/muidar.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/muidar.com\/blog\/wp-json\/wp\/v2\/comments?post=314"}],"version-history":[{"count":1,"href":"https:\/\/muidar.com\/blog\/wp-json\/wp\/v2\/posts\/314\/revisions"}],"predecessor-version":[{"id":2062,"href":"https:\/\/muidar.com\/blog\/wp-json\/wp\/v2\/posts\/314\/revisions\/2062"}],"wp:attachment":[{"href":"https:\/\/muidar.com\/blog\/wp-json\/wp\/v2\/media?parent=314"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/muidar.com\/blog\/wp-json\/wp\/v2\/categories?post=314"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/muidar.com\/blog\/wp-json\/wp\/v2\/tags?post=314"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}