{"id":637,"date":"2024-07-05T09:00:00","date_gmt":"2024-07-05T01:00:00","guid":{"rendered":"https:\/\/seanxd.com\/?p=637"},"modified":"2024-07-05T11:13:42","modified_gmt":"2024-07-05T03:13:42","slug":"zerojudge-f314","status":"publish","type":"post","link":"https:\/\/seanxd.com\/zh\/zerojudge-f314\/","title":{"rendered":"ZeroJudge F314: \u52c7\u8005\u4fee\u7149"},"content":{"rendered":"\n\n\n

\u8f38\u5165\u70ba N\uff0aM \u5927\u5c0f\u7684\u7684\u9663\u5217\uff0c\u6bcf\u4e00\u683c\u662f\u4e00\u500b\u4ecb\u65bc -100 \u8207 100 \u4e4b\u9593\u7684\u6574\u6578\uff0c\u8868\u793a\u7d93\u904e\u9019\u683c\u53ef\u4ee5\u7d2f\u7a4d\u7684\u7d93\u9a57\u503c\u3002
\u4f60\u53ef\u4ee5\u5f9e\u6700\u4e0a\u9762\u4e00\u6392\u4efb\u4f55\u4e00\u500b\u4f4d\u7f6e\u958b\u59cb\uff0c\u5728\u6700\u4e0b\u9762\u4e00\u6392\u4efb\u4f55\u4e00\u500b\u4f4d\u7f6e\u7d50\u675f<\/strong>\u3002
\u904e\u7a0b\u4e2d\u6bcf\u4e00\u6b65\u53ef\u4ee5\u9078\u64c7\u5f80\u5de6\u3001\u5f80\u53f3\u6216\u5f80\u4e0b\u8d70\uff0c\u4f46\u4e0d\u80fd\u8d70\u56de\u5df2\u7d93\u7d93\u904e\u7684\u4f4d\u7f6e<\/strong>\u3002
\u8acb\u4f60\u7b97\u51fa\u6700\u591a\u53ef\u4ee5\u7372\u5f97\u7684\u7d93\u9a57\u503c\u7e3d\u548c (\u53ef\u80fd\u662f\u8ca0\u6578)\u3002<\/p>\n\n\n\n

\u7bc4\u4f8b\u6e2c\u8cc7<\/h2>\n\n\n\n
\u7bc4\u4f8b\u8f38\u5165<\/th>\u7bc4\u4f8b\u8f38\u51fa<\/th><\/tr><\/thead>
\u7b2c\u4e00\u884c\u6709\u5169\u500b\u6b63\u6574\u6578 N \u548c M (1 <= N <= 50\uff0c1 <= M <= 10000)\u3002
\u63a5\u4e0b\u4f86 N \u884c\uff0c\u6bcf\u884c\u5305\u542b M \u500b\u6574\u6578\u3002\u7b2c i \u884c\u7684\u7b2c j \u500b\u6578\u5b57\u8868\u793a\u5728 (i, j) \u4f4d\u7f6e\u53ef\u4ee5\u5f97\u5230\u7684\u7d93\u9a57\u503c\u3002<\/td>		\u8f38\u51fa\u53ef\u4ee5\u7372\u5f97\u7684\u6700\u591a\u7d93\u9a57\u503c\u7e3d\u548c\u3002<\/td><\/tr>
1 5
2 1 4 -7 4<\/td>		7<\/td><\/tr><\/tbody><\/table>
ZeroJudge F314 \u7bc4\u4f8b\u6e2c\u8cc7<\/figcaption><\/figure>\n\n\n\n

\u89e3\u984c\u601d\u8def<\/h2>\n\n\n\n

\u5c07\u8cc7\u6599\u6536\u5230\u4e00\u500b\u4e8c\u7dad\u9663\u5217\u300cv\u300d\u4e2d\uff0c\u4e26\u4e14\u518d\u5ba3\u544a\u4e09\u500b\u4e8c\u7dad\u9663\u5217\uff0c\u5206\u5225\u70ba\u300c\u7b54\u6848\u3001\u5de6\u524d\u7db4\u5408\u3001\u53f3\u524d\u7db4\u5408\u300d\u3002\u6536\u5b8c\u8cc7\u6599\u4e4b\u5f8c\u7279\u5225\u5224\u65b7\u7b2c\u4e00\u884c\u7684\u5de6\u53f3\u524d\u7db4\u5408\uff0c\u9700\u8981\u6ce8\u610f\u7684\u662f\u9032\u884c\u524d\u7db4\u5408\u904b\u7b97\u6642\uff0c\u5982\u679c\u6709\u767c\u751f\u524d\u9762\u90fd\u662f\u8ca0\u6578\u7684\u60c5\u6cc1\uff0c\u9019\u6a23\u5c31\u5c0d\u9020\u6210\u6578\u503c\u4e0d\u6b63\u78ba\uff0c\u6240\u4ee5\u76f8\u52a0\u524d\u7db4\u548c\u6642\u9700\u8981\u5ba3\u544a\u4e00\u500b sum \u8b8a\u6578\u4e26\u4e14\u9810\u8a2d\u70ba v[0][0]\uff0c\u5c07 sum = max(0, sum) + v[0][i]\u3002\u9019\u6a23\u5b50\u7684\u8a71\u5c31\u662f\u5224\u65b7\u524d\u9762\u7684\u524d\u7db4\u5408\u662f\u5426\u662f\u8ca0\u6578\uff0c\u4e26\u4e14\u5c07\u8f03\u5927\u503c\u52a0\u5230\u524d\u7db4\u5408\u4e2d\u3002\u5c07\u7b2c\u4e00\u884c\u7684\u300c\u7b54\u6848\u300d\u8a2d\u5b9a\u70ba\u8a72\u4f4d\u7f6e\u7684\u5de6\u53f3\u524d\u7db4\u5408\u8f03\u5927\u8005\u3002<\/p>\n\n\n\n

\u8dd1\u4e00\u500b For\u8ff4\u5708 \u5f9e 1 \u5230 N-1 (\u4e0d\u5305\u542b\u7b2c 0 \u884c\uff0c\u525b\u525b\u6709\u9032\u884c\u5224\u65b7\u4e86)\uff0c\u4e26\u4e14\u5224\u65b7\u5176\u5de6\u53f3\u524d\u7db4\u5408\u3002\u9019\u6b21\u6bd4\u8f03\u4e0d\u4e00\u6a23\u7684\u662f\u9084\u9700\u8981\u8003\u616e\u5f9e\u4e0a\u4e00\u884c\u5f80\u4e0b\u8d70\u5230\u76ee\u524d\u9019\u4e00\u884c\u7684\u60c5\u6cc1\u3002\u5982\u679c\u9032\u884c\u5224\u65b7\u6642\u8dd1\u5230\u908a\u754c (\u5373\u7b2c\u4e00\u500b\u6216\u6700\u5f8c\u4e00\u500b\u4f4d\u7f6e)\uff0c\u5247\u5c07\u9019\u500b\u4f4d\u7f6e\u7684\u524d\u7db4\u5408\u8a2d\u5b9a\u70ba\u300c\u4e0a\u4e00\u884c\u8a72\u4f4d\u7f6e\u7684\u7b54\u6848\u300d+\u300cv[i][j]\u300d\uff0c\u5426\u5247\u5c07\u9019\u500b\u4f4d\u7f6e\u7684\u524d\u7db4\u5408\u8a2d\u5b9a\u70ba max(\u524d\u4e00\u500b\u4f4d\u7f6e\u7684\u524d\u7db4\u5408, \u4e0a\u4e00\u884c\u8a72\u4f4d\u7f6e\u7684\u7b54\u6848 + v[i][j]\u3002<\/p>\n\n\n\n

\u8f38\u51fa\u6642\u8f38\u51fa\u300c\u7b54\u6848\u9663\u5217\u300d\u6700\u5f8c\u4e00\u884c\u7684\u300c\u6700\u5927\u503c\u300d\u3002<\/p>\n\n\n\n

\u7bc4\u4f8b\u7a0b\u5f0f\u78bc\uff0dZeroJudge F314: \u52c7\u8005\u4fee\u7149<\/a><\/h3>\n\n\n\n
#include <iostream>\n#include <vector>\n#include <algorithm>\nusing namespace std;\n\nint N, M;\nvector<vector<int>>v, ans, lprefix, rprefix;\n\nvector<int> l1prefix() {\n    int sum = v[0][0];\n    vector<int>l;\n    l.push_back(sum);\n    for (int i = 1; i<M; i++) {\n        sum = max(0 , sum) + v[0][i];\n        l.push_back(sum);\n    }\n    return l;\n}\n\nvector<int> r1prefix() {\n    int sum = v[0][M-1];\n    vector<int>r;\n    r.push_back(sum);\n    for (int i = M-2; i>=0; i--) {\n        sum = max(0 , sum) + v[0][i];\n        r.push_back(sum);\n    }\n    reverse(r.begin(), r.end());\n    return r;\n}\n\nint main() {\n    cin.sync_with_stdio(0);\n    cin.tie(0);\n    cin >> N >> M;\n    for (int i = 0; i<N; i++) {\n        vector<int>hi, qq;\n        int sum = 0;\n        for (int j = 0; j<M; j++) {\n            int tmp;\n            cin >> tmp;\n            hi.push_back(tmp);\n            qq.push_back(0);\n            sum += tmp;\n        }\n        lprefix.push_back(qq);\n        rprefix.push_back(qq);\n        ans.push_back(qq);\n        v.push_back(hi);\n    }\n    const vector<int> l = l1prefix(), r = r1prefix();\n    for (int i = 0; i<M; i++) ans[0][i] = max(l[i], r[i]);\n    for (int i = 1; i<N; i++) {\n        for (int j = 0; j<M; j++) {\n            if (j == 0) lprefix[i][j] = ans[i-1][j] + v[i][j];\n            else lprefix[i][j] = max(lprefix[i][j-1], ans[i-1][j]) + v[i][j];\n        }\n        for (int j = M-1; j>=0; j--) {\n            if (j == M-1) rprefix[i][j] = ans[i-1][j] + v[i][j];\n            else rprefix[i][j] = max(rprefix[i][j+1], ans[i-1][j]) + v[i][j];\n            ans[i][j] = max(lprefix[i][j], rprefix[i][j]);\n        }\n    }\n    cout << *max_element(ans[N-1].begin(), ans[N-1].end()) << "\\n";\n}\n\n\/\/ZeroJudge F314\n\/\/Dr. SeanXD<\/code><\/pre><\/div>\n","protected":false},"excerpt":{"rendered":"
\u8f38\u5165\u70ba N\uff0aM \u5927\u5c0f\u7684\u7684\u9663\u5217\uff0c\u6bcf\u4e00\u683c\u662f\u4e00\u500b\u4ecb\u65bc -100 \u8207 100 \u4e4b\u9593\u7684\u6574\u6578\uff0c\u8868\u793a\u7d93\u904e\u9019\u683c\u53ef\u4ee5\u7d2f\u7a4d\u7684\u7d93\u9a57\u503c […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","footnotes":""},"categories":[25],"tags":[20,22,8,13,9],"class_list":["post-637","post","type-post","status-publish","format-standard","hentry","category-ioi-apcs","tag-20","tag-22","tag-8","tag-13","tag-9"],"blocksy_meta":[],"_links":{"self":[{"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/posts\/637","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/comments?post=637"}],"version-history":[{"count":3,"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/posts\/637\/revisions"}],"predecessor-version":[{"id":1053,"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/posts\/637\/revisions\/1053"}],"wp:attachment":[{"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/media?parent=637"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/categories?post=637"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/tags?post=637"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}