{"id":272,"date":"2020-04-15T20:08:15","date_gmt":"2020-04-15T12:08:15","guid":{"rendered":"http:\/\/47.103.223.234:100\/?p=272"},"modified":"2020-04-15T21:45:12","modified_gmt":"2020-04-15T13:45:12","slug":"%e5%8c%ba%e9%97%b4dp-%e4%be%8b%e9%a2%98","status":"publish","type":"post","link":"http:\/\/www.zyhcoding.club\/index.php\/2020\/04\/15\/%e5%8c%ba%e9%97%b4dp-%e4%be%8b%e9%a2%98\/","title":{"rendered":"\u533a\u95f4dp–\u4f8b\u9898"},"content":{"rendered":"

\u4ee5\u540e\u505a\u7684\u9898\u76ee\u5c31\u5728\u8fd9\u603b\u7ed3\uff0c\uff0c\uff0c<\/p>\n

\u77f3\u5b50\u5408\u5e76 \u6d1b\u8c37P1880<\/a><\/h4>\n

\u9898\u610f\uff1a\u4e00\u4e9b\u77f3\u5b50\u5806\u56f4\u4e00\u5708\uff0c\u76f8\u90bb\u7684\u4e24\u5806\u77f3\u5b50\u53ef\u4ee5\u5408\u5e76\u6210\u4e00\u5806\uff0c\u4e24\u5806\u77f3\u5b50\u5408\u5e76\u540e\uff0c\u4ea7\u751f\u7684\u5206\u6570\u4e3a\u5408\u5e76\u7684\u4e00\u5806\u7684\u77f3\u5b50\u7684\u6570\u76ee\uff0c\u6c42\u8fd9\u4e9b\u77f3\u5b50\u5806\u5408\u5e76\u6210\u4e00\u5806\u540e\u4ea7\u751f\u5206\u6570\u7684\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\u3002
\n\u77f3\u5b50\u5806\u6570\u76een<=100.
\n\u5206\u6790\uff1a\u8003\u8651\u5230\u6570\u636e\u5f88\u5c0f\uff0cO(n^3)\u4ee5\u5185\u7684\u590d\u6742\u5ea6\u90fd\u53ef\uff0c\u91c7\u7528O(n^3)\u7684\u4f5c\u6cd5\u3002\u9996\u5148\u77f3\u5b50\u662f\u56f4\u6210\u4e00\u5708\u7684\uff0c\u628a\u4ed6\u5206\u89e3\u6210\u957f\u5ea6\u4e3a2n\u7684\u94fe\u3002dp[i][j]\u8868\u793a\u4ecei\u5230j\u5185\u7684\u77f3\u5b50\u5408\u5e76\u6210\u4e00\u5806\u540e\u7684\u6700\u5927\u503c\/\u6700\u5c0f\u503c\u3002
\n\u5148\u8003\u8651\u57fa\u672c\u7684\u7ebf\u6027dp\uff0c\u5373\u6bcf\u6b21\u65b0\u52a0\u5165\u4e00\u5806\u77f3\u5b50a[i]\uff0c\u7136\u540e\u66f4\u65b0\u533a\u95f4\u5185\u6700\u4f18\u89e3\uff0c\u8981\u4f9d\u6b21\u66f4\u65b0\u4ece1-i\u5206\u522b\u5230i\u5185\u7684\u503c\u3002\u66f4\u65b0\u987a\u5e8f\u662fdp[i][i]-dp[1][i]\uff0c\u5bf9\u4e8e\u6bcf\u6b21\u66f4\u65b0\u7684\u4e00\u4e2a\u533a\u95f4dp[j][i]\uff0c\u8fd8\u662f\u8981\u66b4\u529b\u5339\u914d\u6700\u4f18\u503c\u3002\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b<\/p>\n

\n

dp1[j][i] = max(dp1[j][i],dp1[j][k]+dp1[k+1][i]+num[j][i])
\ndp2[j][i] = min(dp2[j][i],dp2[j][k]+dp2[k+1][i]+num[j][i])
\nj<=k<i<\/strong><\/p>\n<\/blockquote>\n

dp\u6570\u7ec4\u7684\u521d\u59cb\u503c\u8981\u6839\u636e\u9700\u8981\u800c\u5b9a\uff0c0\u8fd8\u662fINFINITY\u3002
\n\u7b2c\u4e00\u5c42\u5faa\u73af\u4ece1-2n\uff0c\u8868\u793a\u6bcf\u6b21\u65b0\u52a0\u5165\u4e00\u5806\u77f3\u5b50i\uff0c\u7b2c\u4e8c\u6b21\u5faa\u73af\u4ecei\u52301\uff0c\u7b2c\u4e09\u5c42\u5faa\u73af\u4ecek\u5230i\u3002<\/p>\n

#include <bits\/stdc++.h>\nusing namespace std;\nconst int m = 0x3f3f3f3f3f;\nint n;\nint a[205];\nint dp[205][205],dp2[205][205];\nint num[205][205];\nint main(){\n    int ans1 = 0,ans2 = m;\n    cin >> n;\n    for (int i=1;i<=n;i++){\n        cin >> a[i];\n        a[n+i] = a[i];\n    }\n    for (int i=1;i<=2*n;i++)    num[i][i] = a[i];\n    for (int i=2*n;i>=1;i--)    for (int j=i-1;j>=1;j--)\n        num[j][i] = num[j+1][i] + a[j];\n    for (int i=1;i<=2*n;i++)    for (int j=1;j<=2*n;j++)    dp2[i][j] = m;\n    for (int i=1;i<=2*n;i++)    dp2[i][i] = 0;\n    for (int i=1;i<=2*n;i++){\n        for (int j=i-1;j>=1;j--){\n            for (int k=j;k<=i-1;k++){\n                dp[j][i] = max(dp[j][i],dp[j][k]+dp[k+1][i]+num[j][i]);\n                dp2[j][i] = min(dp2[j][i],dp2[j][k]+dp2[k+1][i]+num[j][i]);\n            }\n        }\n    }\n    for (int i=1;i<=n;i++)    ans1 = max(ans1,dp[i][i+n-1]);\n    for (int i=1;i<=n;i++)    ans2 = min(ans2,dp2[i][i+n-1]);\n    cout << ans2 << endl;\n    cout << ans1 << endl;\n    return 0;\n}<\/code><\/pre>\n
[USACO16OPEN]248 G \u6d1b\u8c37P3146<\/a><\/h4>\n
\u9898\u610f\uff1a\u7ed9\u5b9a\u4e00\u5217\u6570\uff0c\u76f8\u90bb\u4e24\u4e2a\u76f8\u540c\u7684\u6570\u53ef\u4ee5\u5408\u5e76\u6210\u4e00\u4e2a\u6bd4\u539f\u6765\u59271\u7684\u6570\u3002\u6c42\u6700\u7ec8\u80fd\u5408\u5e76\u51fa\u6765\u7684\u6700\u5927\u6570\u3002(\u4e0d\u8981\u6c42\u6700\u7ec8\u4e00\u5b9a\u8981\u5408\u5e76\u62101\u4e2a\u6570)
\n\u6570\u636e\u91cfn<=248
\n\u5206\u6790\uff1a\u6570\u636e\u91cf\u4e5f\u5f88\u5c0f\uff0c\u540c\u4e0a\uff0cn^3\u7684\u533a\u95f4dp\u4f5c\u6cd5\u3002<\/p>\n
\n
dp[i][j] = max(dp[i][j],(dp[i][k]==dp[k+1][j]?dp[i][k]+1:0)) i<=k<j<\/strong><\/p>\n<\/blockquote>\n
#include <bits\/stdc++.h>\nusing namespace std;\n#pragma GCC optimize(2)\nint dp[250][250];\nint a[250],n;\nint main(){\n    std::ios::sync_with_stdio(false);\n    int ans = 0;\n    cin >> n;\n    for (int i=1;i<=n;i++)  cin >> a[i];\n    for (int i=1;i<=n;i++)  dp[i][i] = a[i];\n    for (int i=1;i<=n;i++){\n        for (int j=i-1;j>=1;j--){\n            for (int k=j;k<i;k++){\n                dp[j][i] = max(dp[j][i],(dp[j][k]==dp[k+1][i]?dp[j][k]+1:0));\n                ans = max(dp[j][i],ans);\n            }\n        }\n    }\n    cout << ans;\n    return 0;\n}<\/code><\/pre>\n
\u80fd\u91cf\u9879\u94fe P1063<\/a><\/h4>\n
\u9898\u610f\uff1a\u53bb\u770b\u94fe\u63a5\u5427\uff0c\uff0c\uff0c
\n\u5206\u6790\uff1a\u533a\u95f4dp\uff0c\u505a\u4e86\u51e0\u9053\u533a\u95f4dp\u540e\uff0c\u5dee\u4e0d\u591a\u53d1\u73b0\u5957\u8def\u90fd\u5dee\u4e0d\u591a\u3002\u533a\u522b\u5c31\u662f\u6700\u91cc\u9762\u7684\u90a3\u5c42\u5faa\u73af\uff0c\u56e0\u9898\u800c\u5f02\u3002<\/p>\n
#include <bits\/stdc++.h>\nusing namespace std;\nint n;\nint a[205];\nint dp[205][205];\nint main(){\n    int n,ans = 0;\n    cin >> n;\n    for (int i=1;i<=n;i++){\n        cin >> a[i];\n        a[i+n] = a[i];\n    }\n    a[2*n+1] = a[1];\n    for (int i=1;i<2*n;i++){\n        for (int j=i-1;j>=1;j--){\n            for (int k=j;k<i;k++){\n                dp[j][i] = max(dp[j][i],dp[j][k]+dp[k+1][i]+a[j]*a[k+1]*a[i+1]);\n            }\n        }\n    }\n    for (int i=1;i<=n;i++)  ans = max(ans,dp[i][i+n-1]);\n    cout << ans;\n    return 0;\n}<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
\u4ee5\u540e\u505a\u7684\u9898\u76ee\u5c31\u5728\u8fd9\u603b\u7ed3\uff0c\uff0c\uff0c \u77f3\u5b50\u5408\u5e76 \u6d1b\u8c37P1880 \u9898\u610f\uff1a\u4e00\u4e9b\u77f3\u5b50\u5806\u56f4\u4e00\u5708\uff0c\u76f8\u90bb\u7684\u4e24\u5806\u77f3\u5b50\u53ef\u4ee5\u5408 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[26],"tags":[],"_links":{"self":[{"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/posts\/272"}],"collection":[{"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/comments?post=272"}],"version-history":[{"count":10,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/posts\/272\/revisions"}],"predecessor-version":[{"id":286,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/posts\/272\/revisions\/286"}],"wp:attachment":[{"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/media?parent=272"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/categories?post=272"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/tags?post=272"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}