{"id":149,"date":"2020-11-19T04:42:00","date_gmt":"2020-11-19T04:42:00","guid":{"rendered":"https:\/\/imwarming.com\/?p=149"},"modified":"2020-11-19T04:42:00","modified_gmt":"2020-11-19T04:42:00","slug":"%e6%9c%80%e7%9f%ad%e8%b7%af","status":"publish","type":"post","link":"https:\/\/imwarming.com\/?p=149","title":{"rendered":"\u6700\u77ed\u8def"},"content":{"rendered":"

bellman ford\u4e0d\u5e38\u7528\u4e0b\u9762\u6709\u5b83\u7684\u4f18\u5316spfa<\/p>\n

\n
for<\/span> (int<\/span> i = 0<\/span>; i < n; i++) {\n    <\/span>for<\/span> (int<\/span> j = 0<\/span>; j < m; j++) {\n        d[v[i]] <\/span>= min(d[v[i]], d[u[i]] + w[i]);\n    }\n}<\/span><\/pre>\n<\/div>\n
dijkstra<\/p>\n
\n
d[s] = 0<\/span>;\/\/<\/span>\u81ea\u5df1\u5230\u81ea\u5df10<\/span>\nfor<\/span> (int<\/span> i = 0<\/span>; i < n; i++) {\n    <\/span>int<\/span> t = -1<\/span>;\n    <\/span>for<\/span> (int<\/span> j = 0<\/span>; j < n; j++) {\n        <\/span>if<\/span> (!v[j]) {\n            <\/span>if<\/span> (t == -1<\/span> || d[j] < d[t]) {\n                t <\/span>= j;\n            }\n        }\n    }\n    v[t] <\/span>= 1<\/span>;\n    <\/span>for<\/span> (each edge e of t) {\n        relax(e);<\/span>\/\/<\/span>\u677e\u5f1b<\/span>\n    }\n}<\/span><\/pre>\n<\/div>\n
floyd<\/p>\n
\n
for<\/span> (int<\/span> k = 0<\/span>; k < n; k++) {\n    <\/span>for<\/span> (int<\/span> i = 0<\/span>; i < n; i++) {\n        <\/span>for<\/span> (int<\/span> j = 0<\/span>; j < n; j++) {\n            f[i][j] <\/span>= min(f[i][j], f[i][k]+f[k][j])\n        }\n    }\n}<\/span><\/pre>\n<\/div>\n
spfa(\u6d1b\u8c37\u5927\u4f6c\u4ee3\u7801)<\/p>\n
\n
void<\/span> spfa()\n{\n  queue<\/span><int<\/span>> q; \/\/<\/span>spfa\u7528\u961f\u5217\uff0c\u8fd9\u91cc\u7528\u4e86stl\u7684\u6807\u51c6\u961f\u5217<\/span>\n  for<\/span>(int<\/span> i=1<\/span>; i<=n; i++) \n  {\n    dis[i]<\/span>=inf; \/\/<\/span>\u5e26\u6743\u56fe\u521d\u59cb\u5316<\/span>\n    vis[i]=0<\/span>; \/\/<\/span>\u8bb0\u5f55\u70b9i\u662f\u5426\u5728\u961f\u5217\u4e2d\uff0c\u540cdijkstra\u7b97\u6cd5\u4e2d\u7684visited\u6570\u7ec4<\/span>\n  }\n  q.push(s); dis[s]<\/span>=0<\/span>; vis[s]=1<\/span>; \/\/<\/span>\u7b2c\u4e00\u4e2a\u9876\u70b9\u5165\u961f\uff0c\u8fdb\u884c\u6807\u8bb0<\/span>\n  while<\/span>(!q.empty())\n  {\n    <\/span>int<\/span> u=q.front(); \/\/<\/span>\u53d6\u51fa\u961f\u9996<\/span>\n    q.pop(); vis[u]=0<\/span>; \/\/<\/span>\u51fa\u961f\u6807\u8bb0<\/span>\n    for<\/span>(int<\/span> i=head[u]; i; i=edge[i].next) \/\/<\/span>\u90bb\u63a5\u8868\u904d\u5386\uff0c\u4e0d\u591a\u89e3\u91ca\u4e86\uff08\u4e5f\u53ef\u7528vector\u4ee3\u66ff\uff09<\/span>\n    {\n      <\/span>int<\/span> v=edge[i].to; \n      <\/span>if<\/span>(dis[v]>dis[u]+edge[i].dis) \/\/<\/span>\u5982\u679c\u6709\u6700\u77ed\u8def\u5c31\u66f4\u6539<\/span>\n      {\n        dis[v]<\/span>=dis[u]+edge[i].dis;\n        <\/span>if<\/span>(vis[v]==0<\/span>) \/\/<\/span>\u672a\u5165\u961f\u5219\u5165\u961f<\/span>\n        {\n          vis[v]<\/span>=1<\/span>; \/\/<\/span>\u6807\u8bb0\u5165\u961f<\/span>\n          q.push(v);\n        }\n      }\n    }\n  }\n}<\/span><\/pre>\n<\/div>\n
\u4f8b : luogu p3371<\/a> \u9884\u5907\u77e5\u8bc6: \u94fe\u5f0f\u524d\u5411\u661f<\/a><\/p>\n
\n
#include<bits\/stdc++.h>\nusing<\/span> namespace<\/span> std;\ntypedef <\/span>long<\/span> long<\/span> ll;\n<\/span>const<\/span> int<\/span> maxn = 1e4 + 5<\/span>;\n<\/span>const<\/span> int<\/span> maxm = 5e5 + 5<\/span>;\n<\/span>const<\/span> ll inf = 2147483647<\/span>;\n<\/span>struct<\/span> edge{\n    <\/span>int<\/span> next,to,w;\n}e[maxm];\n<\/span>int<\/span> head[maxn], cnt, n, m, s, vis[maxn], dis[maxn];\/\/<\/span>head\u521d\u59cb\u5316\u4e3a0<\/span>\npriority_queue<int<\/span>, vector< pair<int<\/span>, int<\/span>> >, greater< pair<int<\/span>, int<\/span>> > >q;\/\/<\/span>\u6700\u5c0f\u5806\uff0cdijkstra\u627e\u6700\u77ed\u8ddd\u79bb\u7684<\/span>\n\ninline <\/span>void<\/span> add(int<\/span> u, int<\/span> v, int<\/span> w){\/\/<\/span>\u94fe\u5f0f\u5411\u524d\u661f<\/span>\n    e[cnt].w = w;\/\/<\/span>\u5b58\u6743\u91cd<\/span>\n    e[cnt].to = v;\n    e[cnt].next <\/span>= head[u];\n    head[u] <\/span>= cnt++;\n}\n\n<\/span>void<\/span> dijkstra(){\n    q.push(make_pair(<\/span>0<\/span>, s));\/\/<\/span>\u8d77\u70b9s\u8fdb\u53bb<\/span>\n    while<\/span>(!q.empty()){\/\/<\/span>\u7a7a\u4e86\u5c31\u5168\u641e\u597d\u4e86<\/span>\n        int<\/span> now = q.top().second;\/\/<\/span>\u5f53\u524d\u70b9<\/span>\n        q.pop();\/\/<\/span>\u6ca1\u7528\u4e86\u5f39\u51fa<\/span>\n        if<\/span>(!vis[now]){\/\/<\/span>\u8981\u6ca1\u6807\u8bb0<\/span>\n            vis[now] = 1<\/span>;\/\/<\/span>\u6807\u8bb0\u4e86<\/span>\n            for<\/span>(int<\/span> i = head[now]; i; i = e[i].next){\/\/<\/span>\u628a\u4e0enow\u6709\u8054\u7cfb\u7684\u90fd\u5faa\u73af\uff0ci = 0\u5c31\u6ca1\u4e86\uff0chead\u521d\u59cb\u5316\u5c31\u662f0<\/span>\n                int<\/span> v = e[i].to;\n                <\/span>if<\/span>(dis[v] > dis[now] + e[i].w){\n                    dis[v] <\/span>= dis[now] + e[i].w;\n                    q.push(make_pair(dis[v], v));<\/span>\/\/<\/span>\u53d1\u73b0\u5b83\u53d8\u5c0f\u4e86\u5c31\u63a8\u8fdb\u53bb<\/span>\n                }\n            }\n        }\n    }\n}\n\n<\/span>int<\/span> main(){\n    <\/span>\/\/<\/span>ios_base::sync_with_stdio(0);\n    <\/span>\/\/<\/span>cin.tie(); cout.tie();<\/span>\n    cin>>n>>m>>s;\n    <\/span>int<\/span> x, y, z;\n    <\/span>for<\/span>(int<\/span> i = 1<\/span>; i <= m; i++){\n        cin<\/span>>>x>>y>>z;\n        add(x, y, z);<\/span>\/\/<\/span>\u94fe\u5f0f\u5411\u524d\u661f<\/span>\n    }\n    <\/span>for<\/span>(int<\/span> i = 1<\/span>; i <= n; i++)\n        dis[i] <\/span>= inf;\/\/<\/span>\u521d\u59cb\u5316<\/span>\n    dis[s] = 0<\/span>;\/\/<\/span>\u81ea\u5df1<\/span>\n    dijkstra();\n    <\/span>for<\/span>(int<\/span> i = 1<\/span>; i <= n; i++){\n        cout<\/span><<dis[i]<<'<\/span> '<\/span>;\n    }\n    <\/span>return<\/span> 0<\/span>;\n}<\/span><\/pre>\n<\/div>\n
\u4f8b \uff1aluogu p1821<\/a> \u6b63\u53cd\u4e24\u6b21\u6700\u77ed\u8def\uff08\u5927\u4f6c\u4ee3\u7801\uff09<\/p>\n
\n
#include<iostream>\n#include<\/span><cstdio>\n#include<\/span><cstring>\n#include<\/span><queue>\n#include<\/span><vector>\nusing<\/span> namespace<\/span> std;\n<\/span>struct<\/span> edge\n{\n    <\/span>int<\/span> u,v;    \n};\n\nvector<\/span><edge> g[3<\/span>][1001<\/span>];\/\/<\/span>\u52a8\u6001\u6570\u7ec4\u5b58\u8fb9<\/span>\n\nqueue<\/span><int<\/span>> q;\/\/<\/span>\u961f\u5217\uff08stl\u5927\u6cd5\u597d\uff09<\/span>\n\nint<\/span> n,m,f[3<\/span>][1001<\/span>],l,ans;\n<\/span>bool<\/span> vis[1001<\/span>];\n\n<\/span>void<\/span> spfa(int<\/span> k)\/\/<\/span>k=1\u65f6\u6b63\u5411\u56fe\uff0ck=2\u65f6\u53cd\u5411\u56fe<\/span>\n{\n    memset(vis,<\/span>0<\/span>,sizeof<\/span>(vis));\/\/<\/span>\u521d\u59cb\u5316false<\/span>\n    vis[l]=true<\/span>;\n    f[k][l]<\/span>=0<\/span>;\n    q.push(l);\n    <\/span>while<\/span>(!q.empty())\n    {\n        <\/span>int<\/span> news=q.front();\n        q.pop();\n        vis[news]<\/span>=false<\/span>;\n        <\/span>for<\/span>(int<\/span> i=0<\/span>;i<g[k][news].size();i++)\n        {\n            <\/span>int<\/span> v=g[k][news][i].v,u=g[k][news][i].u;\n            <\/span>if<\/span>(f[k][v]>f[k][news]+u)\n            {\n                f[k][v]<\/span>=f[k][news]+u;\n                <\/span>if<\/span>(!vis[v])\n                {\n                    vis[v]<\/span>=true<\/span>;\n                    q.push(v);\n                }\n            }\n        }\n    }\n}\n\n<\/span>int<\/span> main()\n{\n    scanf(<\/span>\"<\/span>%d%d%d<\/span>\"<\/span>,&n,&m,&l);\n    memset(f,<\/span>0x3f3f3f<\/span>,sizeof<\/span>(f));\n    <\/span>for<\/span>(int<\/span> a=1<\/span>;a<=m;a++)\n    {\n        <\/span>int<\/span> x,y,z;\n        scanf(<\/span>\"<\/span>%d%d%d<\/span>\"<\/span>,&x,&y,&z);\n        edge cmp;\n        cmp.v<\/span>=y;\n        cmp.u<\/span>=z;\n        g[<\/span>1<\/span>][x].push_back(cmp);\/\/<\/span>\u6b63\u5411\u5efa\u56fe<\/span>\n        cmp.v=x;\n        g[<\/span>2<\/span>][y].push_back(cmp);\/\/<\/span>\u53cd\u5411\u5efa\u56fe<\/span>\n    }\n    spfa(<\/span>1<\/span>);\/\/<\/span>\u8dd1\u6b63\u5411\u56fe<\/span>\n    spfa(2<\/span>);\/\/<\/span>\u8dd1\u53cd\u5411\u56fe<\/span>\n    for<\/span>(int<\/span> a=1<\/span>;a<=n;a++)\n    {\n        <\/span>if<\/span>(a==l)\n        {\n            <\/span>continue<\/span>;\n        }\n        ans<\/span>=max(f[1<\/span>][a]+f[2<\/span>][a],ans);\/\/<\/span>\u627e\u6700\u957f\u7684<\/span>\n    }\n    printf(<\/span>\"<\/span>%dn<\/span>\"<\/span>,ans);\n    <\/span>return<\/span> 0<\/span>;\n}<\/span><\/pre>\n<\/div>\n
\u6b63\u5411\u5efa\u5c31\u662f\u6c42\u5404\u70b9\u5230\u7ec8\u70b9\u6700\u77ed\u8def\uff0c\u53cd\u5411\u5efa\u6c42\u7ec8\u70b9\u5230\u5404\u70b9\u6700\u77ed\u8def<\/p>\n","protected":false},"excerpt":{"rendered":"
bellman ford\u4e0d\u5e38\u7528\u4e0b\u9762\u6709\u5b83\u7684\u4f18\u5316spfa for (int i = 0; i <  […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-149","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"yoast_head":"\n\u6700\u77ed\u8def - imwarming<\/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:\/\/imwarming.com\/?p=149\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u6700\u77ed\u8def - imwarming\" \/>\n<meta property=\"og:description\" content=\"bellman ford\u4e0d\u5e38\u7528\u4e0b\u9762\u6709\u5b83\u7684\u4f18\u5316spfa for (int i = 0; i < […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/imwarming.com\/?p=149\" \/>\n<meta property=\"og:site_name\" content=\"imwarming\" \/>\n<meta property=\"article:published_time\" content=\"2020-11-19T04:42:00+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"warming\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebSite\",\"@id\":\"https:\/\/imwarming.com\/#website\",\"url\":\"https:\/\/imwarming.com\/\",\"name\":\"imwarming\",\"description\":\"\u6c38\u8fdc\u5e74\u8f7b\uff0c\u6c38\u8fdc\u70ed\u6cea\u76c8\u7736\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/imwarming.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"zh-Hans\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/imwarming.com\/?p=149#webpage\",\"url\":\"https:\/\/imwarming.com\/?p=149\",\"name\":\"\u6700\u77ed\u8def - imwarming\",\"isPartOf\":{\"@id\":\"https:\/\/imwarming.com\/#website\"},\"datePublished\":\"2020-11-19T04:42:00+00:00\",\"dateModified\":\"2020-11-19T04:42:00+00:00\",\"author\":{\"@id\":\"https:\/\/imwarming.com\/#\/schema\/person\/9d76869a558bac6dd0d6d58f420ee8ea\"},\"breadcrumb\":{\"@id\":\"https:\/\/imwarming.com\/?p=149#breadcrumb\"},\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/imwarming.com\/?p=149\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/imwarming.com\/?p=149#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u9996\u9875\",\"item\":\"https:\/\/imwarming.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u6700\u77ed\u8def\"}]},{\"@type\":\"Person\",\"@id\":\"https:\/\/imwarming.com\/#\/schema\/person\/9d76869a558bac6dd0d6d58f420ee8ea\",\"name\":\"warming\",\"image\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/imwarming.com\/#personlogo\",\"inLanguage\":\"zh-Hans\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/c4a913eed88f7601b76bbf2b103472621195b6fa2f742af89b5ea185b60e7cff?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/c4a913eed88f7601b76bbf2b103472621195b6fa2f742af89b5ea185b60e7cff?s=96&d=mm&r=g\",\"caption\":\"warming\"},\"sameAs\":[\"https:\/\/imwarming.com\"],\"url\":\"https:\/\/imwarming.com\/?author=1\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u6700\u77ed\u8def - imwarming","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:\/\/imwarming.com\/?p=149","og_locale":"zh_CN","og_type":"article","og_title":"\u6700\u77ed\u8def - imwarming","og_description":"bellman ford\u4e0d\u5e38\u7528\u4e0b\u9762\u6709\u5b83\u7684\u4f18\u5316spfa for (int i = 0; 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