{"id":73900,"date":"2026-02-08T16:17:31","date_gmt":"2026-02-08T08:17:31","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/73900.html"},"modified":"2026-02-08T16:17:31","modified_gmt":"2026-02-08T08:17:31","slug":"%e6%b4%9b%e8%b0%b7p2349-%e9%87%91%e5%ad%97%e5%a1%94%e9%a2%98%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/73900.html","title":{"rendered":"\u6d1b\u8c37P2349 \u91d1\u5b57\u5854\u9898\u89e3"},"content":{"rendered":"

\u6d1b\u8c37P2349 \u91d1\u5b57\u5854\u9898\u89e3<\/h2>\n

\u9898\u76ee\u4f20\u9001\u95e8 – Luogu （\u6700\u8fd1\u597d\u50cf\u53c8\u62d6\u66f4\u4e86\u2026\u2026）<\/p>\n

\u5e9f\u8bdd<\/h3>\n

\u6211\u7684\u7cbe\u795e\u72b6\u6001： \u4eca\u5929\u66f4\u65b0\u6ca1\u6709？ \u597d\u50cf\u66f4\u4e86，\u53c8\u597d\u50cf\u6ca1\u66f4，\u660e\u5929\u518d\u8bf4\u5427<\/p>\n

\u9898\u76ee\u5927\u610f<\/h3>\n

\u6709\u4e00\u4e2a\u65e0\u5411\u56fe，\u4ece <\/p>\n

1 <\/p>\n

1 <\/p>\n

<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u8282\u70b9\u5f00\u59cb，\u8dd1\u5230\u7b2c <\/p>\n

n <\/p>\n

n <\/p>\n

<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span> \u8282\u70b9，\u73b0\u5728\u89e6\u53d1\u4e86\u70df\u96fe，\u4f1a\u8ba9\u56fe\u4e2d\u4e00\u6761\u8fb9\u7684\u8fb9\u6743\u7ffb\u500d，\u627e\u51fa\u6700\u574f\u60c5\u51b5\u4e0b\u7684\u6700\u77ed\u8def<\/p>\n

\u601d\u8def<\/h3>\n

\u8003\u8651\u4f7f\u7528\u7f8e\u4e3d\u8ff7\u4eba\u7684 <\/p>\n

S <\/p>\n

P <\/p>\n

F <\/p>\n

A <\/p>\n

SPFA <\/p>\n

<\/span><\/span>SPF<\/span>A<\/span><\/span><\/span><\/span><\/span> \u7b97\u6cd5， <\/p>\n

n <\/p>\n

\u2264 <\/p>\n

100 <\/p>\n

, <\/p>\n

m <\/p>\n

\u2264 <\/p>\n

1000 <\/p>\n

n\\\\le 100 , m \\\\le1 000 <\/p>\n

<\/span><\/span>n<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>100<\/span>,<\/span><\/span>m<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1000<\/span><\/span><\/span><\/span><\/span> \u7684\u6570\u636e\u91cf\u5e94\u8be5\u4e0d\u4f1a\u7206<\/p>\n

\u6211\u4eec\u53ef\u4ee5\u7206\u6539\u4e00\u4e0b <\/p>\n

S <\/p>\n

P <\/p>\n

F <\/p>\n

A <\/p>\n

SPFA <\/p>\n

<\/span><\/span>SPF<\/span>A<\/span><\/span><\/span><\/span><\/span> \u7684\u677e\u5f1b\u6761\u4ef6，\u5728 <\/p>\n

d <\/p>\n

i <\/p>\n

s <\/p>\n

u <\/p>\n

+ <\/p>\n

w <\/p>\n

+ <\/p>\n

max <\/p>\n

\u2061 <\/p>\n

{ <\/p>\n

m <\/p>\n

e <\/p>\n

u <\/p>\n

, <\/p>\n

w <\/p>\n

} <\/p>\n

< <\/p>\n

d <\/p>\n

i <\/p>\n

s <\/p>\n

v <\/p>\n

+ <\/p>\n

m <\/p>\n

e <\/p>\n

v <\/p>\n

dis_u+w+\\\\max\\\\{me_u,w\\\\}<dis_v+me_v <\/p>\n

<\/span><\/span>d<\/span>i<\/span>s<\/span><\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>w<\/span><\/span>+<\/span><\/span><\/span><\/span>max<\/span>{<\/span>m<\/span>e<\/span><\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>w<\/span>}<\/span><\/span><<\/span><\/span><\/span><\/span>d<\/span>i<\/span>s<\/span><\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>m<\/span>e<\/span><\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u65f6\u8fdb\u884c\u677e\u5f1b，\u540c\u65f6\u7ef4\u62a4\u6700\u77ed\u8def\u6570\u7ec4 <\/p>\n

m <\/p>\n

e <\/p>\n

me <\/p>\n

<\/span><\/span>m<\/span>e<\/span><\/span><\/span><\/span><\/span> ： <\/p>\n

m <\/p>\n

e <\/p>\n

v <\/p>\n

= <\/p>\n

m <\/p>\n

a <\/p>\n

x <\/p>\n

{ <\/p>\n

m <\/p>\n

e <\/p>\n

u <\/p>\n

, <\/p>\n

w <\/p>\n

} <\/p>\n

me_v=max\\\\{me_u,w\\\\} <\/p>\n

<\/span><\/span>m<\/span>e<\/span><\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>ma<\/span>x<\/span>{<\/span>m<\/span>e<\/span><\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>w<\/span>}<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u6700\u540e\u8f93\u51fa <\/p>\n

d <\/p>\n

i <\/p>\n

s <\/p>\n

n <\/p>\n

+ <\/p>\n

m <\/p>\n

e <\/p>\n

n <\/p>\n

dis_n+me_n <\/p>\n

<\/span><\/span>d<\/span>i<\/span>s<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>m<\/span>e<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5b9e\u73b0<\/h3>\n

\u9996\u5148\u5bf9 <\/p>\n

v <\/p>\n

i <\/p>\n

s <\/p>\n

vis <\/p>\n

<\/span><\/span>v<\/span>i<\/span>s<\/span><\/span><\/span><\/span><\/span> （\u7528\u4e8e\u4f18\u5316）， <\/p>\n

d <\/p>\n

i <\/p>\n

s <\/p>\n

dis <\/p>\n

<\/span><\/span>d<\/span>i<\/span>s<\/span><\/span><\/span><\/span><\/span> ， <\/p>\n

m <\/p>\n

e <\/p>\n

me <\/p>\n

<\/span><\/span>m<\/span>e<\/span><\/span><\/span><\/span><\/span> \u4e09\u4e2a\u6570\u7ec4\u521d\u59cb\u5316：<\/p>\n

memset<\/span>(<\/span>vis,<\/span>0<\/span>,<\/span>sizeof<\/span> vis)<\/span>;<\/span>
\nmemset<\/span>(<\/span>dis,<\/span>0x3f<\/span>,<\/span>sizeof<\/span> dis)<\/span>;<\/span>
\nmemset<\/span>(<\/span>me,<\/span>63<\/span>,<\/span>sizeof<\/span> me)<\/span>;<\/span><\/p>\n

\u7136\u540e\u8dd1 SPFA ，\u6ce8\u610f\u4fee\u6539\u677e\u5f1b\u6761\u4ef6：<\/p>\n

while<\/span>(<\/span>!<\/span>q.<\/span>empty<\/span>(<\/span>)<\/span>)<\/span>{<\/span>
\n int<\/span> u=<\/span>q.<\/span>front<\/span>(<\/span>)<\/span>;<\/span>
\n q.<\/span>pop<\/span>(<\/span>)<\/span>;<\/span>
\n vis[<\/span>u]<\/span>=<\/span>0<\/span>;<\/span>
\n for<\/span>(<\/span>auto<\/span> it:<\/span>e[<\/span>u]<\/span>)<\/span>{<\/span>
\n int<\/span> v=<\/span>it.<\/span>first,<\/span>w=<\/span>it.<\/span>second;<\/span>
\n if<\/span>(<\/span>dis[<\/span>u]<\/span>+<\/span>w+<\/span>max<\/span>(<\/span>me[<\/span>u]<\/span>,<\/span>w)<\/span><<\/span>dis[<\/span>v]<\/span>+<\/span>me[<\/span>v]<\/span>)<\/span>{<\/span>
\n dis[<\/span>v]<\/span>=<\/span>dis[<\/span>u]<\/span>+<\/span>w;<\/span>
\n me[<\/span>v]<\/span>=<\/span>max<\/span>(<\/span>me[<\/span>u]<\/span>,<\/span>w)<\/span>;<\/span>
\n if<\/span>(<\/span>!<\/span>vis[<\/span>v]<\/span>)<\/span>q.<\/span>push<\/span>(<\/span>v)<\/span>,<\/span>vis[<\/span>v]<\/span>=<\/span>1<\/span>;<\/span>
\n }<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

\u8bb0\u5f97\u5efa\u56fe\u65f6\u5efa\u65e0\u5411\u56fe<\/p>\n

AC\u4ee3\u7801<\/h3>\n

#<\/span>include<\/span><bits\/stdc++.h><\/span><\/span>
\n#<\/span>define<\/span> int<\/span> long<\/span> long<\/span><\/span><\/span>
\nusing<\/span> namespace<\/span> std;<\/span>
\nvector<<\/span>pair<<\/span>int<\/span>,<\/span>int<\/span>>><\/span>e[<\/span>110<\/span>]<\/span>;<\/span>
\nint<\/span> vis[<\/span>110<\/span>]<\/span>,<\/span>dis[<\/span>110<\/span>]<\/span>,<\/span>me[<\/span>110<\/span>]<\/span>;<\/span>
\nvoid<\/span> solve<\/span>(<\/span>int<\/span> s)<\/span>{<\/span>
\nmemset<\/span>(<\/span>vis,<\/span>0<\/span>,<\/span>sizeof<\/span> vis)<\/span>;<\/span>
\nmemset<\/span>(<\/span>dis,<\/span>0x3f<\/span>,<\/span>sizeof<\/span> dis)<\/span>;<\/span>
\nmemset<\/span>(<\/span>me,<\/span>63<\/span>,<\/span>sizeof<\/span> me)<\/span>;<\/span>
\nqueue<<\/span>int<\/span>><\/span>q;<\/span>
\nq.<\/span>push<\/span>(<\/span>s)<\/span>;<\/span>
\ndis[<\/span>s]<\/span>=<\/span>0<\/span>;<\/span>
\nvis[<\/span>s]<\/span>=<\/span>1<\/span>;<\/span>
\nme[<\/span>s]<\/span>=<\/span>0<\/span>;<\/span>
\nwhile<\/span>(<\/span>!<\/span>q.<\/span>empty<\/span>(<\/span>)<\/span>)<\/span>{<\/span>
\nint<\/span> u=<\/span>q.<\/span>front<\/span>(<\/span>)<\/span>;<\/span>
\nq.<\/span>pop<\/span>(<\/span>)<\/span>;<\/span>
\nvis[<\/span>u]<\/span>=<\/span>0<\/span>;<\/span>
\nfor<\/span>(<\/span>auto<\/span> it:<\/span>e[<\/span>u]<\/span>)<\/span>{<\/span>
\nint<\/span> v=<\/span>it.<\/span>first,<\/span>w=<\/span>it.<\/span>second;<\/span>
\nif<\/span>(<\/span>dis[<\/span>u]<\/span>+<\/span>w+<\/span>max<\/span>(<\/span>me[<\/span>u]<\/span>,<\/span>w)<\/span><<\/span>dis[<\/span>v]<\/span>+<\/span>me[<\/span>v]<\/span>)<\/span>{<\/span>
\ndis[<\/span>v]<\/span>=<\/span>dis[<\/span>u]<\/span>+<\/span>w;<\/span>
\nme[<\/span>v]<\/span>=<\/span>max<\/span>(<\/span>me[<\/span>u]<\/span>,<\/span>w)<\/span>;<\/span>
\nif<\/span>(<\/span>!<\/span>vis[<\/span>v]<\/span>)<\/span>q.<\/span>push<\/span>(<\/span>v)<\/span>,<\/span>vis[<\/span>v]<\/span>=<\/span>1<\/span>;<\/span>
\n}<\/span>
\n}<\/span>
\n}<\/span>
\n}<\/span>
\nsigned<\/span> main<\/span>(<\/span>)<\/span>{<\/span>
\nint<\/span> n,<\/span>m;<\/span>
\ncin>><\/span>n>><\/span>m;<\/span>
\nfor<\/span>(<\/span>int<\/span> i=<\/span>1<\/span>;<\/span>i<=<\/span>m;<\/span>i++<\/span>)<\/span>{<\/span>
\nint<\/span> u,<\/span>v,<\/span>w;<\/span>
\ncin>><\/span>u>><\/span>v>><\/span>w;<\/span>
\ne[<\/span>u]<\/span>.<\/span>push_back<\/span>(<\/span>{<\/span>v,<\/span>w}<\/span>)<\/span>;<\/span>
\ne[<\/span>v]<\/span>.<\/span>push_back<\/span>(<\/span>{<\/span>u,<\/span>w}<\/span>)<\/span>;<\/span>
\n}<\/span>
\nsolve<\/span>(<\/span>1<\/span>)<\/span>;<\/span>
\ncout<<<\/span>dis[<\/span>n]<\/span>+<\/span>me[<\/span>n]<\/span>;<\/span>
\nreturn<\/span> 0<\/span>;<\/span>
\n}<\/span><\/p>\n

AC\u8bb0\u5f55<\/p>\n

\u5927\u5bb6\u518d\u89c1，\u8bb0\u5f97👍+\u2764\ufe0f<\/h3>\n","protected":false},"excerpt":{"rendered":"

\u6d1b\u8c37P2349 \u91d1\u5b57\u5854\u9898\u89e3
\n\u9898\u76ee\u4f20\u9001\u95e8 – Luogu （\u6700\u8fd1\u597d\u50cf\u53c8\u62d6\u66f4\u4e86\u2026\u2026）
\n\u5e9f\u8bdd
\n\u6211\u7684\u7cbe\u795e\u72b6\u6001： \u4eca\u5929\u66f4\u65b0\u6ca1\u6709？ \u597d\u50cf\u66f4\u4e86，\u53c8\u597d\u50cf\u6ca1\u66f4，\u660e\u5929\u518d\u8bf4\u5427
\n\u9898\u76ee\u5927\u610f
\n\u6709\u4e00\u4e2a\u65e0\u5411\u56fe，\u4ece 1 1 1 \u8282\u70b9\u5f00\u59cb，\u8dd1\u5230\u7b2c n n n \u8282\u70b9，\u73b0\u5728\u89e6\u53d1\u4e86\u70df\u96fe，\u4f1a\u8ba9\u56fe\u4e2d\u4e00\u6761\u8fb9\u7684\u8fb9\u6743\u7ffb\u500d，\u627e\u51fa\u6700\u574f\u60c5\u51b5\u4e0b\u7684\u6700\u77ed\u8def
\n\u601d\u8def
\n\u8003\u8651\u4f7f<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[55,1984,427],"topic":[],"class_list":["post-73900","post","type-post","status-publish","format-standard","hentry","category-server","tag-c","tag-1984","tag-427"],"yoast_head":"\n\u6d1b\u8c37P2349 \u91d1\u5b57\u5854\u9898\u89e3 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/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:\/\/www.wsisp.com\/helps\/73900.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u6d1b\u8c37P2349 \u91d1\u5b57\u5854\u9898\u89e3 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u6d1b\u8c37P2349 \u91d1\u5b57\u5854\u9898\u89e3 \u9898\u76ee\u4f20\u9001\u95e8 - 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