{"id":188,"date":"2025-02-07T20:47:30","date_gmt":"2025-02-07T12:47:30","guid":{"rendered":"https:\/\/blog.seekrealthing.net\/blog\/?p=188"},"modified":"2025-02-07T20:47:33","modified_gmt":"2025-02-07T12:47:33","slug":"d-monitor-%e8%a7%a3%e6%9e%90%e6%80%9d%e7%b6%ad%e3%80%81%e5%89%8d%e7%b6%b4%e5%92%8c%e3%80%81%e4%ba%8c%e5%88%86%e6%90%9c","status":"publish","type":"post","link":"https:\/\/blog.seekrealthing.net\/blog\/?p=188","title":{"rendered":"D. Monitor \u89e3\u6790(\u601d\u7dad\u3001\u524d\u7db4\u548c\u3001\u4e8c\u5206\u641c)"},"content":{"rendered":"\n<div class=\"wp-block-jetpack-markdown\"><p>\u4eca\u5929\u6211\u5011\u4f86\u770b\u770bCF846D\n<a href=\"https:\/\/codeforces.com\/contest\/846\/problem\/D\">\u984c\u76ee\u9023\u7d50<\/a><\/p>\n<h3>\u984c\u76ee\u63cf\u8ff0<\/h3>\n<p>Luba \u6700\u8fd1\u8cb7\u4e86\u4e00\u500b\u986f\u793a\u5668\uff0c\u5176\u986f\u793a\u5668\u53ef\u4ee5\u770b\u4f5c\u4e00\u500b $n \\times m$ \u7684\u77e9\u9663\u3002\u96a8\u8457\u6642\u9593\u7684\u63a8\u79fb\uff0c\u90e8\u5206\u50cf\u7d20\u6703\u505c\u6b62\u5de5\u4f5c\u3002\u7576\u5b58\u5728\u4e00\u500b\u5927\u5c0f\u70ba $k \\times k$ \u7684\u6b63\u65b9\u5f62\u5340\u57df\uff0c\u5176\u5167\u6240\u6709\u50cf\u7d20\u5747\u505c\u6b62\u5de5\u4f5c\u6642\uff0cLuba \u8a8d\u70ba\u986f\u793a\u5668\u5df2\u7d93\u300c\u58de\u6389\u300d\u3002<\/p>\n<hr>\n<h3><strong>\u8f38\u5165\u683c\u5f0f<\/strong><\/h3>\n<ul>\n<li>\u7b2c\u4e00\u884c\u5305\u542b\u56db\u500b\u6574\u6578\uff1a$n$, $m$, $k$, $q$<br>\n\u5176\u4e2d\uff1a\n<ul>\n<li>$1 \\le n, m \\le 500$<\/li>\n<li>$1 \\le k \\le \\min(n, m)$<\/li>\n<li>$0 \\le q \\le n \\cdot m$<\/li>\n<\/ul>\n<\/li>\n<li>\u63a5\u4e0b\u4f86 $q$ \u884c\uff0c\u6bcf\u884c\u5305\u542b\u4e09\u500b\u6574\u6578\uff1a$x_i$, $y_i$, $t_i$<br>\n\u8868\u793a\u4f4d\u65bc\u7b2c $x_i$ \u884c\u3001\u7b2c $y_i$ \u5217\u7684\u50cf\u7d20\u5728\u6642\u523b $t_i$ \u505c\u6b62\u5de5\u4f5c\uff0c\u5176\u4e2d\n<ul>\n<li>$1 \\le x_i \\le n$<\/li>\n<li>$1 \\le y_i \\le m$<\/li>\n<li>$0 \\le t_i \\le 10^9$<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr>\n<h3><strong>\u8f38\u51fa\u683c\u5f0f<\/strong><\/h3>\n<p>\u8f38\u51fa\u4e00\u500b\u6574\u6578\uff0c\u8868\u793a\u986f\u793a\u5668\u7b2c\u4e00\u6b21\u300c\u58de\u6389\u300d\u7684\u6700\u5c0f\u6642\u523b\uff08\u5373\u51fa\u73fe\u5168\u58de\u7684 $k \\times k$ \u6b63\u65b9\u5f62\u7684\u6642\u523b\uff09\uff0c\u5982\u679c\u5373\u4f7f\u6240\u6709 $q$ \u500b\u50cf\u7d20\u90fd\u505c\u6b62\u5de5\u4f5c\u5f8c\u4ecd\u4e0d\u5b58\u5728\u9019\u6a23\u7684\u6b63\u65b9\u5f62\uff0c\u5247\u8f38\u51fa $-1$\u3002<\/p>\n<h2>\u524d\u8a00<\/h2>\n<p>\u6211\u6709\u60f3\u5230\u8981\u4e8c\u5206\u641c\u87a2\u5e55\u6700\u65e9\u58de$k\\times k$\u65b9\u584a\u7684\u6642\u9593\uff0c\u4f46\u662f\u5c45\u7136\u5728\u6700\u7c21\u55ae\u7684\uff0c\u8981\u600e\u9ebc\u5feb\u901f\u7b97\u51fa\u4e00\u500b$k\\times k$\u65b9\u584a\u6709\u6c92\u6709\u5168\u90fd\u58de\u6389\u90a3\u908a\u5361\u4f4f\u4e86<\/p>\n<h3>\u60f3\u6cd5<\/h3>\n<p>\u7531\u65bc\u53ea\u6703\u6709$500\\times500$\u500b\u58de\u6389\u7684pixel\uff0c\u6240\u4ee5\u6211\u5011\u4e0d\u7528\u88ab\u6642\u9593$t\\le10^9$\u5687\u5230\uff0c\u53ea\u8981\u628a\u58de\u6389\u7684pixel\u7528\u6642\u9593\u6392\u5e8f\u5c31\u597d\u3002<br>\n\u6ce8\u610f\u5230\u6642\u9593$t$\u5982\u679c\u96fb\u8996\u5df2\u7d93\u58de\u6389\u4e86\uff0c\u5c0d\u65bc\u6642\u9593$t\u2019&gt;t$\u662f\u4e00\u5b9a\u6703\u58de\u6389\u7684\uff0c\u90a3\u9ebc\u6211\u5011\u5c31\u6709\u55ae\u8abf\u6027\uff0c\u53ef\u4ee5\u53bb\u4e8c\u5206\u641c\u6700\u65e9\u58de\u6389\u7684\u6642\u9593\uff0c\u9019\u90e8\u5206\u4e8c\u5206\u641c\u7684\u8907\u96dc\u5ea6\u662f$O(\\lg q)$<br>\n\u90a3\u9ebc\u6211\u5011\u53ea\u8981\u60f3\u60f3\u770b\uff0c\u5c0d\u65bc\u67d0\u500b\u6642\u9593$t$\uff0c\u6211\u5011\u8981\u600e\u9ebc\u77e5\u9053\u87a2\u5e55\u6709\u6c92\u6709$k\\times k$\u7684\u58de\u6389\u7684\u5340\u57df\u3002<br>\n\u53ef\u4ee5\u5c0d\u6bcf\u500b\u9ede$(x,y)$\uff0c\u7dad\u8b77\u5f9e\u87a2\u5e55$(1,1)$\u5230$(x,y)$\u6709\u591a\u5c11\u500b\u58de\u9ede\u3002\u90a3\u9ebc\u5c0d\u65bc\u4efb\u4f55\u65b9\u5f62\u5340\u57df\uff0c\u6211\u5011\u90fd\u53ef\u4ee5\u5229\u7528\u9019\u500b\u8cc7\u8a0a\u53bb\u5f97\u5230\u65b9\u5f62\u5340\u57df\u88e1\u6709\u591a\u5c11\u58de\u9ede\u3002\u53ea\u8981\u6211\u5c0d\u6240\u6709$k\\times k$\u5340\u57df\u53bb\u770b\u58de\u9ede\u6578\u91cf\u662f\u4e0d\u662f$k^2$\u5373\u53ef\u3002<br>\n\u8981\u7dad\u8b77\u9019\u500b\u6578\u91cf\u5c31\u662f\u7c21\u55ae\u7684\u5229\u7528dp\u601d\u60f3\uff1a<br>\n$$\ncnt[i][j] = cnt[i &#8211; 1][j] + cnt[i][j &#8211; 1] &#8211; cnt[i &#8211; 1][j &#8211; 1] + (tv[i][j]\u5728\u6b64\u6642\u5df2\u7d93\u58de\u6389\u4e86\u55ce ? 1 : 0)\n$$\n\u6ce8\u610f\u5230\uff0c\u5982\u679c\u8981\u5feb\u901f\u5224\u65b7\u4e00\u500b\u9ede$(i,j)$\u5728\u6642\u9593$time$\u6709\u6c92\u6709\u58de\u6389\uff0c\u53ea\u8981\u4e8b\u5148\u7dad\u8b77\u4e00\u500b\u9663\u5217$tv[n][m]$\uff0c\u5982\u679c\u6709\u58de\u9ede\uff0c\u5c31\u5728$tv[i][j]$\u5beb\u4e0a\u58de\u6389\u7684\u6642\u9593\u9ede\u5373\u53ef\u3002<\/p>\n<h3>\u7a0b\u5f0f\u78bc:<\/h3>\n<pre><code class=\"language-cpp\">const int _n = 500 + 10;\nint n, m, k, q, tv[_n][_n], cnt[_n][_n];\nstruct Query {\n  int x, y, t;\n  bool operator&lt;(const auto&amp; rhs) const {\n    return t &lt; rhs.t;\n  }\n};\nvector&lt;Query&gt; qs;\nbool hasKxK(int qsIdx) {\n  int time = qs[qsIdx].t;\n  memset(cnt, 0, sizeof(cnt));\n  cnt[0][0] = tv[0][0] &lt;= time ? 1 : 0;\n  rep(i, 1, n + 1) {\n    cnt[i][0] = cnt[i - 1][0] + (tv[i][0] &lt;= time ? 1 : 0);\n  }\n  rep(j, 1, m + 1) {\n    cnt[0][j] = cnt[0][j - 1] + (tv[0][j] &lt;= time ? 1 : 0);\n  }\n  rep(i, 1, n + 1) {\n    rep(j, 1, m + 1) {\n      cnt[i][j] = cnt[i - 1][j] + cnt[i][j - 1] - cnt[i - 1][j - 1] + (tv[i][j] &lt;= time ? 1 : 0);\n    }\n  }\n  rep(i, k, n + 1) {\n    rep(j, k, m + 1) {\n      int cntInKxK = cnt[i][j] - cnt[i - k][j] - cnt[i][j - k] + cnt[i - k][j - k];\n      if (cntInKxK == k * k) return true;\n    }\n  }\n  return false;\n}\nmain(void) {\n  ios_base::sync_with_stdio(0);\n  cin.tie(0);\n  cout.tie(0);\n  cin &gt;&gt; n &gt;&gt; m &gt;&gt; k &gt;&gt; q;\n  rep(i, 0, n + 1) rep(j, 0, m + 1) {\n    tv[i][j] = 0x7f7f7f7f;\n  }\n  rep(i, 0, q) {\n    int x, y, t;\n    cin &gt;&gt; x &gt;&gt; y &gt;&gt; t;\n    qs.pb(Query{x, y, t});\n    tv[x][y] = t;\n  }\n  sort(all(qs));\n  int MAXB = (int)log2(qs.size()) + 2;\n  int tmp = -1;\n  per(i, 0, MAXB) {\n    if ((tmp + (1 &lt;&lt; i)) &lt; qs.size() and !hasKxK(tmp + (1 &lt;&lt; i))) {\n      tmp = tmp + (1 &lt;&lt; i);\n    }\n  }\n  if (tmp == qs.size() - 1) {\n    cout &lt;&lt; -1 &lt;&lt; '\\n';\n  } else {\n    cout &lt;&lt; qs[tmp + 1].t &lt;&lt; '\\n';\n  }\n\n  return 0;\n}\n<\/code><\/pre>\n<p>\u6a19\u982d\u3001\u6a21\u677f\u8acb\u9edeSubmission\u770b\n<a href=\"https:\/\/codeforces.com\/contest\/846\/submission\/304817381\">Submission<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[3],"tags":[10,9,29,25,8],"class_list":["post-188","post","type-post","status-publish","format-standard","hentry","category-ojcode","tag-codeforce","tag-ojcode","tag-29","tag-25","tag-8"],"jetpack_publicize_connections":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>D. 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