{"id":154,"date":"2025-01-12T12:56:00","date_gmt":"2025-01-12T04:56:00","guid":{"rendered":"http:\/\/150.230.63.147\/blog\/?p=154"},"modified":"2025-01-12T12:56:00","modified_gmt":"2025-01-12T04:56:00","slug":"b-jzzhu-and-cities-%e8%a7%a3%e6%9e%90%e6%80%9d%e7%b6%ad%e3%80%81%e6%9c%80%e7%9f%ad%e8%b7%af","status":"publish","type":"post","link":"https:\/\/blog.seekrealthing.net\/blog\/?p=154","title":{"rendered":"B. Jzzhu and Cities \u89e3\u6790(\u601d\u7dad\u3001\u6700\u77ed\u8def)"},"content":{"rendered":"\n

Codeforce 449 B. Jzzhu and Cities \u89e3\u6790(\u601d\u7dad\u3001\u6700\u77ed\u8def)<\/h1>\n

\u4eca\u5929\u6211\u5011\u4f86\u770b\u770bCF449B
\n\u984c\u76ee\u9023\u7d50<\/a><\/p>\n

\n

\u984c\u76ee<\/strong>
\n\u7565\uff0c\u8acb\u76f4\u63a5\u770b\u539f\u984c\u3002<\/p>\n<\/blockquote>\n

\u524d\u8a00<\/h3>\n

\u9019\u984c\u8b93\u6211\u5c0dDijkstra\u7684\u904b\u4f5c\u6709\u66f4\u6df1\u4e00\u6b65\u7684\u4e86\u89e3\u3002<\/p>\n

\u60f3\u6cd5<\/h3>\n

\u89c0\u5bdf\u5230\uff0c\u5982\u679c\u60f3\u8981\u6574\u500b\u6700\u77ed\u8def\u5f91\u6a39\u4e0d\u8b8a\uff0c\u5c31\u4ee3\u8868\u8aaa\uff0c\u5c0d\u65bc$1\\rightarrow i$\u7684\u706b\u8eca\u8def\u7dda\uff0c\u9577\u5ea6$y$\uff0c\u5982\u679c\u5230$i$\u7684\u6700\u77ed\u8def\u5f91\u5c0f\u65bc$y$\uff0c\u9019\u500b\u706b\u8eca\u8def\u5f91\u5c31\u53ef\u4ee5\u62ff\u6389\u3002\u5982\u679c\u6700\u77ed\u8def\u5f91\u525b\u597d\u7b49\u65bc$y$\uff0c\u5c31\u8981\u770b\u770b\uff0c\u662f\u4e0d\u662f\u6709\u4e0d\u662f\u9019\u689d\u706b\u8eca\u8def\u5f91\u7684\u53e6\u4e00\u689d\u8def\u5f91\u53ef\u4ee5\u4ee5\u6700\u77ed\u8def\u5f91\u5230\u9054$i$\uff0c\u5982\u679c\u6709\u7684\u8a71\u5c31\u53ef\u4ee5\u6368\u53bb\u9019\u689d\u706b\u8eca\u8def\u5f91\u3002
\n\u7531\u65bc\u9019\u984c\u7684$n\\le1e5$\uff0c\u57fa\u672c\u4e0a\u6211\u5011\u80fd\u60f3\u5230\u7684\uff0c\u8907\u96dc\u5ea6\u5920\u4f4e\u7684\u6700\u77ed\u8def\u5f91\u7b97\u6cd5\u53ea\u6709Dijkstra\u53ef\u4ee5\u52dd\u4efb\u4e86\u3002\u56e0\u6b64\u4ee5\u4e0b\u6211\u5011\u4f86\u8a73\u7d30\u6558\u8ff0\u5728\u9019\u984c\u8a72\u5982\u4f55\u4f7f\u7528Dijkstra\u3002
\n\u4e3b\u8981\u6bd4\u8f03\u6703\u8b93\u4eba\u4e0d\u77e5\u9053\u8a72\u5982\u4f55\u4e0b\u624b\u7684\uff0c\u61c9\u8a72\u662f\u5982\u4f55\u5224\u65b7\u6709\u6c92\u6709\u591a\u65bc\u4e00\u689d\u7684\u6700\u77ed\u8def\u5f91\u3002Dijkstra\u7684\u4f5c\u6cd5\u662f\uff0c\u6bcf\u6b21\u627e\u51fa\u548c\u6700\u77ed\u8def\u5f91\u6a39\u76f8\u9130\u7684\uff0c\u8ddd\u96e2\u9ede$1$\u6700\u8fd1\u7684\u9ede(\u7528priority_queue)\uff0c\u4e26\u4e14\u9023\u4e0a\u53bb\u3002\u4e5f\u5c31\u662f\u8aaa\uff0c\u5728\u628a\u4e00\u500b\u9edepush\u9032priority_queue\u4e4b\u524d\uff0c\u6211\u5011\u6703\u5148\u770b\u770b\u9019\u500b\u9ede\u662f\u5426\u5df2\u7d93\u5728\u6a39\u4e0a\u4e86\u3002
\n\u4e26\u4e14\u6ce8\u610f\u5230\uff0c\u6211\u5011\u5c0d\u65bc\u5716\u4e0a\u7684\u6bcf\u4e00\u689d\u908a<\/strong>\u90fd\u6703\u8003\u616e\u5230\uff0c\u4e26\u4e14\u8003\u616e\u4e00\u689d\u908a($u\\rightarrow v$)\u6642\uff0c\u6211\u5011\u5fc5\u5b9a\u5df2\u7d93\u77e5\u9053\u9ede$1$\u5230\u9ede$u$\u7684\u6700\u77ed\u8def\u5f91\u4e86\u3002\u4e5f\u5c31\u662f\u8aaa\uff0c\u5982\u679c$1\\rightarrow v$\u7684\u6700\u77ed\u8def\u6709\u5169\u689d\uff0c\u90a3\u9ebc\u6211\u5011\u53ea\u8981\u5728\u6aa2\u67e5\u6bcf\u689d\u908a\u8981\u4e0d\u8981\u653e\u9032priority_queue\u4e4b\u6642\uff0c\u518d\u6aa2\u67e5\u4e00\u4e0b\u662f\u5426\u76ee\u524d\u5230$v$\u7684\u6700\u77ed\u8def\u5f91\u662f\u706b\u8eca\u8def\u7dda\uff0c\u4e26\u4e14\u53e6\u4e00\u689d\u8def\u5f91\u9577\u5ea6(\u5c0f\u65bc)\u7b49\u65bc\u706b\u8eca\u9435\u8ecc\u9577\u5ea6\uff0c\u5982\u679c\u662f\u7684\u8a71\u5373\u53ef\u62cb\u68c4\u6389\u9019\u689d\u706b\u8eca\u9435\u8ecc\u3002<\/p>\n

\u7a0b\u5f0f\u78bc:<\/h3>\n
const int _n=1e5+10;  \nconst ll inf=1e18;  \nint t,n,m,k,u,v,x,s,y,ans,train[_n];  \nll dis[_n];  \nstruct WE{int to,w;};  \nstruct W{ll f,t,w;  \nbool operator<(const W& rhs)const{return w>rhs.w;}};  \nvector<WE> G[_n];  \npriority_queue<W> pq;  \nmain(void) {ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);  \n  cin>>n>>m>>k;rep(i,0,m){cin>>u>>v>>x;G[u].pb({v,x}),G[v].pb({u,x});}  \n  rep(i,0,k){  \n    cin>>s>>y;  \n    if(!train[s])train[s]=y;  \n    else if(train[s])ans++,train[s]=min(train[s],y);  \n  }rep(i,1,n+1)dis[i]=inf;  \n  rep(i,2,n+1)if(train[i])pq.push({0,i,train[i]});  \n  pq.push({0,1,0});while(!pq.empty()){  \n    W now=pq.top();pq.pop();if(dis[now.t]!=inf)continue;  \n    dis[now.t]=now.w;  \n    for(WE& u:G[now.t]){  \n      if(dis[u.to]==inf)pq.push({now.t,u.to,dis[now.t]+u.w});  \n      if(train[u.to] and dis[now.t]+u.w<=train[u.to])ans++,train[u.to]=0;  \n    }  \n  }cout<<ans<<'\\n';  \n  return 0;  \n}  \n<\/code><\/pre>\n
\u6a19\u982d\u3001\u6a21\u677f\u8acb\u9edeSubmission\u770b(\u4e8b\u5be6\u4e0apriority_queue\u7528WE\u9019\u500bstruct\u5c31\u5920\u4e86\uff0c\u4e0d\u7528\u591a\u5b58\u4e00\u500bf)
\nSubmission<\/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":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[3],"tags":[10,9,8,37],"class_list":["post-154","post","type-post","status-publish","format-standard","hentry","category-ojcode","tag-codeforce","tag-ojcode","tag-8","tag-37"],"jetpack_publicize_connections":[],"yoast_head":"\nB. Jzzhu and Cities \u89e3\u6790(\u601d\u7dad\u3001\u6700\u77ed\u8def) - Logic Formatting<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blog.seekrealthing.net\/blog\/?p=154\" \/>\n<meta property=\"og:locale\" content=\"zh_TW\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"B. Jzzhu and Cities \u89e3\u6790(\u601d\u7dad\u3001\u6700\u77ed\u8def) - Logic Formatting\" \/>\n<meta property=\"og:url\" content=\"https:\/\/blog.seekrealthing.net\/blog\/?p=154\" \/>\n<meta property=\"og:site_name\" content=\"Logic Formatting\" \/>\n<meta property=\"article:published_time\" content=\"2025-01-12T04:56:00+00:00\" \/>\n<meta name=\"author\" content=\"jeff\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005:\" \/>\n\t<meta name=\"twitter:data1\" content=\"jeff\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9810\u4f30\u95b1\u8b80\u6642\u9593\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 \u5206\u9418\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/?p=154#article\",\"isPartOf\":{\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/?p=154\"},\"author\":{\"name\":\"jeff\",\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/#\/schema\/person\/233e80a0fee3d4706f067f2e88c0b454\"},\"headline\":\"B. Jzzhu and Cities \u89e3\u6790(\u601d\u7dad\u3001\u6700\u77ed\u8def)\",\"datePublished\":\"2025-01-12T04:56:00+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/?p=154\"},\"wordCount\":46,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/#organization\"},\"keywords\":[\"codeforce\",\"ojcode\",\"\u601d\u7dad\",\"\u6700\u77ed\u8def\"],\"articleSection\":[\"ojcode\"],\"inLanguage\":\"zh-TW\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/blog.seekrealthing.net\/blog\/?p=154#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/?p=154\",\"url\":\"https:\/\/blog.seekrealthing.net\/blog\/?p=154\",\"name\":\"B. Jzzhu and Cities \u89e3\u6790(\u601d\u7dad\u3001\u6700\u77ed\u8def) - Logic Formatting\",\"isPartOf\":{\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/#website\"},\"datePublished\":\"2025-01-12T04:56:00+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/?p=154#breadcrumb\"},\"inLanguage\":\"zh-TW\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/blog.seekrealthing.net\/blog\/?p=154\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/?p=154#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u9996\u9801\",\"item\":\"https:\/\/blog.seekrealthing.net\/blog\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"B. Jzzhu and Cities \u89e3\u6790(\u601d\u7dad\u3001\u6700\u77ed\u8def)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/#website\",\"url\":\"https:\/\/blog.seekrealthing.net\/blog\/\",\"name\":\"Logic Formatting\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/blog.seekrealthing.net\/blog\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"zh-TW\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/#organization\",\"name\":\"Logic Formatting\",\"url\":\"https:\/\/blog.seekrealthing.net\/blog\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-TW\",\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/blog.seekrealthing.net\/blog\/wp-content\/uploads\/2025\/02\/android-chrome-512x512-1.png\",\"contentUrl\":\"https:\/\/blog.seekrealthing.net\/blog\/wp-content\/uploads\/2025\/02\/android-chrome-512x512-1.png\",\"width\":512,\"height\":512,\"caption\":\"Logic Formatting\"},\"image\":{\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/#\/schema\/person\/233e80a0fee3d4706f067f2e88c0b454\",\"name\":\"jeff\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-TW\",\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f9b571b28c252728386f0002b35d9cb9a9028f740b0f9ca5ad678e7eb21c4857?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f9b571b28c252728386f0002b35d9cb9a9028f740b0f9ca5ad678e7eb21c4857?s=96&d=mm&r=g\",\"caption\":\"jeff\"},\"sameAs\":[\"http:\/\/150.230.63.147\/blog\"],\"url\":\"https:\/\/blog.seekrealthing.net\/blog\/?author=1\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"B. Jzzhu and Cities \u89e3\u6790(\u601d\u7dad\u3001\u6700\u77ed\u8def) - Logic Formatting","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/blog.seekrealthing.net\/blog\/?p=154","og_locale":"zh_TW","og_type":"article","og_title":"B. Jzzhu and Cities \u89e3\u6790(\u601d\u7dad\u3001\u6700\u77ed\u8def) - Logic Formatting","og_url":"https:\/\/blog.seekrealthing.net\/blog\/?p=154","og_site_name":"Logic Formatting","article_published_time":"2025-01-12T04:56:00+00:00","author":"jeff","twitter_card":"summary_large_image","twitter_misc":{"\u4f5c\u8005:":"jeff","\u9810\u4f30\u95b1\u8b80\u6642\u9593":"1 \u5206\u9418"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/blog.seekrealthing.net\/blog\/?p=154#article","isPartOf":{"@id":"https:\/\/blog.seekrealthing.net\/blog\/?p=154"},"author":{"name":"jeff","@id":"https:\/\/blog.seekrealthing.net\/blog\/#\/schema\/person\/233e80a0fee3d4706f067f2e88c0b454"},"headline":"B. Jzzhu and Cities \u89e3\u6790(\u601d\u7dad\u3001\u6700\u77ed\u8def)","datePublished":"2025-01-12T04:56:00+00:00","mainEntityOfPage":{"@id":"https:\/\/blog.seekrealthing.net\/blog\/?p=154"},"wordCount":46,"commentCount":0,"publisher":{"@id":"https:\/\/blog.seekrealthing.net\/blog\/#organization"},"keywords":["codeforce","ojcode","\u601d\u7dad","\u6700\u77ed\u8def"],"articleSection":["ojcode"],"inLanguage":"zh-TW","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/blog.seekrealthing.net\/blog\/?p=154#respond"]}]},{"@type":"WebPage","@id":"https:\/\/blog.seekrealthing.net\/blog\/?p=154","url":"https:\/\/blog.seekrealthing.net\/blog\/?p=154","name":"B. Jzzhu and Cities \u89e3\u6790(\u601d\u7dad\u3001\u6700\u77ed\u8def) - Logic Formatting","isPartOf":{"@id":"https:\/\/blog.seekrealthing.net\/blog\/#website"},"datePublished":"2025-01-12T04:56:00+00:00","breadcrumb":{"@id":"https:\/\/blog.seekrealthing.net\/blog\/?p=154#breadcrumb"},"inLanguage":"zh-TW","potentialAction":[{"@type":"ReadAction","target":["https:\/\/blog.seekrealthing.net\/blog\/?p=154"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/blog.seekrealthing.net\/blog\/?p=154#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u9996\u9801","item":"https:\/\/blog.seekrealthing.net\/blog"},{"@type":"ListItem","position":2,"name":"B. Jzzhu and Cities \u89e3\u6790(\u601d\u7dad\u3001\u6700\u77ed\u8def)"}]},{"@type":"WebSite","@id":"https:\/\/blog.seekrealthing.net\/blog\/#website","url":"https:\/\/blog.seekrealthing.net\/blog\/","name":"Logic Formatting","description":"","publisher":{"@id":"https:\/\/blog.seekrealthing.net\/blog\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/blog.seekrealthing.net\/blog\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"zh-TW"},{"@type":"Organization","@id":"https:\/\/blog.seekrealthing.net\/blog\/#organization","name":"Logic Formatting","url":"https:\/\/blog.seekrealthing.net\/blog\/","logo":{"@type":"ImageObject","inLanguage":"zh-TW","@id":"https:\/\/blog.seekrealthing.net\/blog\/#\/schema\/logo\/image\/","url":"https:\/\/blog.seekrealthing.net\/blog\/wp-content\/uploads\/2025\/02\/android-chrome-512x512-1.png","contentUrl":"https:\/\/blog.seekrealthing.net\/blog\/wp-content\/uploads\/2025\/02\/android-chrome-512x512-1.png","width":512,"height":512,"caption":"Logic Formatting"},"image":{"@id":"https:\/\/blog.seekrealthing.net\/blog\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/blog.seekrealthing.net\/blog\/#\/schema\/person\/233e80a0fee3d4706f067f2e88c0b454","name":"jeff","image":{"@type":"ImageObject","inLanguage":"zh-TW","@id":"https:\/\/blog.seekrealthing.net\/blog\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f9b571b28c252728386f0002b35d9cb9a9028f740b0f9ca5ad678e7eb21c4857?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f9b571b28c252728386f0002b35d9cb9a9028f740b0f9ca5ad678e7eb21c4857?s=96&d=mm&r=g","caption":"jeff"},"sameAs":["http:\/\/150.230.63.147\/blog"],"url":"https:\/\/blog.seekrealthing.net\/blog\/?author=1"}]}},"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/blog.seekrealthing.net\/blog\/index.php?rest_route=\/wp\/v2\/posts\/154","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.seekrealthing.net\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.seekrealthing.net\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.seekrealthing.net\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.seekrealthing.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=154"}],"version-history":[{"count":1,"href":"https:\/\/blog.seekrealthing.net\/blog\/index.php?rest_route=\/wp\/v2\/posts\/154\/revisions"}],"predecessor-version":[{"id":155,"href":"https:\/\/blog.seekrealthing.net\/blog\/index.php?rest_route=\/wp\/v2\/posts\/154\/revisions\/155"}],"wp:attachment":[{"href":"https:\/\/blog.seekrealthing.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=154"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.seekrealthing.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=154"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.seekrealthing.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=154"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}