{"id":1181,"date":"2024-09-14T09:00:00","date_gmt":"2024-09-14T01:00:00","guid":{"rendered":"https:\/\/seanxd.com\/?p=1181"},"modified":"2024-08-23T08:06:46","modified_gmt":"2024-08-23T00:06:46","slug":"zerojudge-d768","status":"publish","type":"post","link":"https:\/\/seanxd.com\/zh\/zerojudge-d768\/","title":{"rendered":"ZeroJudge D768: Bicoloring"},"content":{"rendered":"\n\n\n<h4 class=\"wp-block-heading\">\u540c\u984c\uff1aUVa 10004 &#8211; Bicoloring<\/h4>\n\n\n\n<p>1976 \u5e74\uff0c\u5728\u96fb\u8166\u5354\u52a9\u4e4b\u4e0b\u8b49\u660e\u4e86 4 \u8272\u5730\u5716\u7406\u8ad6 (Four Color Map Theorem\uff09\u3002\u5c31\u662f\u50c5\u4ee5 4 \u7a2e\u984f\u8272\u5728\u5730\u5716\u4e0a\u4e0d\u540c\u7684\u5340\u57df\u5857\u8272\uff0c\u4f7f\u5f97\u76f8\u9130\u7684\u5340\u57df\u984f\u8272\u5747\u4e0d\u76f8\u540c\u3002<\/p>\n\n\n\n<p>\u73fe\u5728\uff0c\u4f60\u8981\u89e3\u6c7a\u4e00\u500b\u985e\u4f3c\uff0c\u4f46\u6bd4\u8f03\u7c21\u55ae\u7684\u554f\u984c\u3002\u7d66\u4f60\u4e00\u500b\u76f8\u9023\u7684\u5716\uff0c\u8acb\u4f60\u5728\u7bc0\u9ede\u4e0a\u5857\u8272 (\u53ea\u6709 2 \u7a2e\u4e0d\u540c\u7684\u984f\u8272\uff09\uff0c\u4e26\u4e14\u56de\u7b54\u662f\u5426\u53ef\u4ee5\u4f7f\u5f97\u76f8\u9130\u7684\u7bc0\u9ede\u984f\u8272\u5747\u4e0d\u76f8\u540c\u3002\u70ba\u4e86\u4f7f\u554f\u984c\u7c21\u55ae\u4e00\u4e9b\uff0c\u4f60\u53ef\u4ee5\u5047\u8a2d\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6c92\u6709\u7bc0\u9ede\u6703\u6709\u9023\u5411\u81ea\u5df1\u7684\u908a\u3002<\/li>\n\n\n\n<li>\u908a\u662f\u6c92\u6709\u65b9\u5411\u6027\u7684\uff0c\u4e5f\u5c31\u662f\u8aaa\u5982\u679c\u7bc0\u9ede A \u53ef\u4ee5\u9023\u5230\u7bc0\u9ede B\uff0c\u90a3\u9ebc\u4ee3\u8868\u7bc0\u9ede B \u4e5f\u53ef\u4ee5\u9023\u5230\u7bc0\u9ede A\u3002<\/li>\n\n\n\n<li>\u5716\u5f62\u662f\u5f37\u9023\u901a\u7684\uff0c\u4e5f\u5c31\u662f\u8aaa\u4efb 2 \u7bc0\u9ede\u4e4b\u9593\u7686\u6709\u8def\u5f91\u76f8\u9023\u3002<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u7bc4\u4f8b\u6e2c\u8cc7<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u7bc4\u4f8b\u8f38\u5165<\/th><th>\u7bc4\u4f8b\u8f38\u51fa<\/th><\/tr><\/thead><tbody><tr><td>EOF \u8f38\u5165\uff0c\u6bcf\u7d44\u6e2c\u8a66\u8cc7\u6599\u7684\u7b2c\u4e00\u5217\u6709\u4e00\u500b\u6b63\u6574\u6578 N (1 &lt; N &lt; 200) \u4ee3\u8868\u7bc0\u9ede\u7684\u6578\u76ee\u3002\u7b2c\u4e8c\u5217\u6709\u4e00\u500b\u6b63\u6574\u6578 M\uff0c\u4ee3\u8868\u908a\u7684\u6578\u76ee\u3002\u63a5\u4e0b\u4f86\u7684 M \u5217\u6bcf\u5217\u6709 2 \u500b\u6574\u6578\u4ee3\u8868\u908a\u6240\u9023\u63a5\u7684 2 \u500b\u7bc0\u9ede\u7684\u4ee3\u865f\u3002\u9019 N \u500b\u7bc0\u9ede\u7684\u4ee3\u865f\u5206\u5225\u70ba 0 \u5230 N-1\u3002<br>N = 0 \u4ee3\u8868\u8f38\u5165\u7d50\u675f\u3002<\/td><td>\u5c0d\u6bcf\u4e00\u7d44\u6e2c\u8a66\u8cc7\u6599\u8f38\u51fa\u662f\u5426\u53ef\u4ee5\u7528 2 \u7a2e\u984f\u8272\u5857\u7bc0\u9ede\u4f7f\u5f97\u76f8\u9130\u7684\u7bc0\u9ede\u984f\u8272\u5747\u4e0d\u76f8\u540c\u3002\u82e5\u53ef\u4ee5\u8acb\u8f38\u51fa\uff1a\u300cBICOLORABLE.\u300d\uff0c\u5426\u5247\u8f38\u51fa\uff1a\u300cNOT BICOLORABLE.\u300d\u3002<\/td><\/tr><tr><td>3<br>3<br>0 1<br>1 2<br>2 0<br>9<br>8<br>0 1<br>0 2<br>0 3<br>0 4<br>0 5<br>0 6<br>0 7<br>0 8<br>0<\/td><td>NOT BICOLORABLE.<br>BICOLORABLE.<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">ZeroJudge D768 \u7bc4\u4f8b\u6e2c\u8cc7<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u89e3\u984c\u601d\u8def<\/h2>\n\n\n\n<p>\u4f7f\u7528 BFS \u7684\u65b9\u5f0f\u53bb\u5224\u65b7\u6bcf\u4e00\u500b\u9ede\u662f\u5426\u53ef\u4ee5\u8d70\u56de\u81ea\u5df1\u4e14\u984f\u8272\u4e00\u6a23\uff0c\u5982\u679c\u662f\u7684\u8a71\u5c31\u4ee3\u8868\u76f8\u9130\u7684\u7bc0\u9ede\u984f\u8272\u6703\u6709\u76f8\u540c\u7684\u60c5\u6cc1\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7bc4\u4f8b\u7a0b\u5f0f\u78bc\uff0d<a href=\"https:\/\/zerojudge.tw\/ShowProblem?problemid=d768\" target=\"_blank\" rel=\"noreferrer noopener\">ZeroJudge D768: Bicoloring<\/a><\/h3>\n\n\n\n<div class=\"hcb_wrap\"><pre class=\"prism line-numbers lang-cpp\" data-lang=\"C++\"><code>#include &lt;iostream&gt;\n#include &lt;map&gt;\n#include &lt;vector&gt;\nusing namespace std;\n\nmap&lt;int, vector&lt;int&gt;&gt;MAP;\nmap&lt;int, int&gt;walk;\nint N;\n\nint change(int c) {\n    if (c == 1) c = 2;\n    else c = 1;\n    return c;\n}\n\nbool BFS(const vector&lt;int&gt;start, const int target , int color) {\n    if (start.size() == 0) return true;\n    vector&lt;int&gt;newStart;\n    map&lt;int, int&gt;push;\n    for (int i = 0; i&lt;start.size(); i++) {\n        if (walk[start[i]] == color) return false;\n        walk[start[i]] = color;\n        for (int j = 0; j&lt;MAP[start[i]].size(); j++) {\n            const int num = MAP[start[i]][j];\n            if (walk[num] == 0 && push[num] == 0) {\n                push[num]++;\n                newStart.push_back(num);\n            }\n        }\n    }\n    change(color);\n    return BFS(newStart, target , color);\n}\n\nint main() {\n    cin.sync_with_stdio(0);\n    cin.tie(0);\n    while (cin &gt;&gt; N && N != 0) {\n        MAP.clear();\n        walk.clear();\n        int M;\n        cin &gt;&gt; M;\n        for (int i = 0; i&lt;M; i++) {\n            int a, b;\n            cin &gt;&gt; a &gt;&gt; b;\n            MAP[a].push_back(b);\n            MAP[b].push_back(a);\n        }\n        bool ok = true;\n        for (int i = 0; i&lt;N; i++) {\n            if (walk[i] &gt; 0) continue;\n            vector&lt;int&gt;start;\n            start.push_back(i);\n            if (!BFS(start, i , 1)) {\n                cout &lt;&lt; &quot;NOT BICOLORABLE.\\n&quot;;\n                ok = false;\n                break;\n            }\n        }\n        if (ok) cout &lt;&lt; &quot;BICOLORABLE.\\n&quot;;\n    }\n}\n\n\/\/ZeroJudge D768\n\/\/Dr. SeanXD<\/code><\/pre><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u540c\u984c\uff1aUVa 10004 &#8211; Bicoloring 1976 \u5e74\uff0c\u5728\u96fb\u8166\u5354\u52a9\u4e4b\u4e0b\u8b49\u660e\u4e86 4 \u8272\u5730\u5716 [&hellip;]<\/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":[18],"tags":[30,14,20,8,11,34,9],"class_list":["post-1181","post","type-post","status-publish","format-standard","hentry","category-uva","tag-bfs","tag-map","tag-20","tag-8","tag-11","tag-34","tag-9"],"blocksy_meta":[],"_links":{"self":[{"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/posts\/1181","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=1181"}],"version-history":[{"count":2,"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/posts\/1181\/revisions"}],"predecessor-version":[{"id":1183,"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/posts\/1181\/revisions\/1183"}],"wp:attachment":[{"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/media?parent=1181"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/categories?post=1181"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/seanxd.com\/zh\/wp-json\/wp\/v2\/tags?post=1181"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}