次短路

蔚落 2022-05-30 11:27 161阅读 0赞

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      原创： 
     <a href="http://blog.csdn.net/SunMoonVocano/article/details/79514213" rel="nofollow">点击打开链接</a> 
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     <br> 
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    <div style="text-align:center;font-family:Arial, Helvetica, sans-serif;font-size:18pt;font-weight:bold;color:#0000FF;">
      Roadblocks 
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        <td><strong>Time Limit:</strong>&nbsp;2000MS</td> 
        <td>&nbsp;</td> 
        <td><strong>Memory Limit:</strong>&nbsp;65536K</td> 
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       <tr> 
        <td><strong>Total Submissions:</strong>&nbsp;17713</td> 
        <td>&nbsp;</td> 
        <td><strong>Accepted:</strong>&nbsp;6211</td> 
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    </div><p style="font-family:Arial, Helvetica, sans-serif;font-size:18pt;font-weight:bold;color:#0000FF;">Description</p> 
    <div style="font-family:'Times New Roman', Times, serif;font-size:12pt;"> 
     <p>Bessie has moved to a small farm and sometimes enjoys returning to visit one of her best friends. She does not want to get to her old home too quickly, because she likes the scenery along the way. She has decided to take the second-shortest rather than the shortest path. She knows there must be some second-shortest path.</p> 
     <p>The countryside consists of&nbsp;<em>R</em>&nbsp;(1 ≤&nbsp;<em>R</em>&nbsp;≤ 100,000) bidirectional roads, each linking two of the N (1 ≤&nbsp;<em>N</em>&nbsp;≤ 5000) intersections, conveniently numbered 1..<em>N</em>. Bessie starts at intersection 1, and her friend (the destination) is at intersection&nbsp;<em>N</em>.</p> 
     <p>The second-shortest path may share roads with any of the shortest paths, and it may backtrack i.e., use the same road or intersection more than once. The second-shortest path is the shortest path whose length is longer than the shortest path(s) (i.e., if two or more shortest paths exist, the second-shortest path is the one whose length is longer than those but no longer than any other path).</p> 
    </div><p style="font-family:Arial, Helvetica, sans-serif;font-size:18pt;font-weight:bold;color:#0000FF;">Input</p> 
    <div style="font-family:'Times New Roman', Times, serif;font-size:12pt;">
      Line 1: Two space-separated integers:&nbsp; 
     <em>N</em>&nbsp;and&nbsp; 
     <em>R</em>&nbsp; 
     <br>Lines 2.. 
     <em>R</em>+1: Each line contains three space-separated integers:&nbsp; 
     <em>A</em>,&nbsp; 
     <em>B</em>, and&nbsp; 
     <em>D</em>&nbsp;that describe a road that connects intersections&nbsp; 
     <em>A</em>&nbsp;and&nbsp; 
     <em>B</em>&nbsp;and has length&nbsp; 
     <em>D</em>&nbsp;(1 ≤&nbsp; 
     <em>D</em>&nbsp;≤ 5000) 
    </div><p style="font-family:Arial, Helvetica, sans-serif;font-size:18pt;font-weight:bold;color:#0000FF;">Output</p> 
    <div style="font-family:'Times New Roman', Times, serif;font-size:12pt;">
      Line 1: The length of the second shortest path between node 1 and node&nbsp; 
     <em>N</em> 
    </div><p style="font-family:Arial, Helvetica, sans-serif;font-size:18pt;font-weight:bold;color:#0000FF;">Sample Input</p><pre style="font-family:'Courier New', Courier, monospace;font-size:12pt;">4 4
1 2 100
2 4 200
2 3 250
3 4 100</pre><p style="font-family:Arial, Helvetica, sans-serif;font-size:18pt;font-weight:bold;color:#0000FF;">Sample Output</p><pre style="font-family:'Courier New', Courier, monospace;font-size:12pt;">450</pre><p style="font-family:Arial, Helvetica, sans-serif;font-size:18pt;font-weight:bold;color:#0000FF;">Hint</p> 
    <div style="font-family:'Times New Roman', Times, serif;font-size:12pt;">
      Two routes: 1 -&gt; 2 -&gt; 4 (length 100+200=300) and 1 -&gt; 2 -&gt; 3 -&gt; 4 (length 100+250+100=450) 
    </div><p style="font-family:Arial, Helvetica, sans-serif;font-size:18pt;font-weight:bold;color:#0000FF;">Source</p> 
    <div style="font-family:'Times New Roman', Times, serif;font-size:12pt;"> 
     <a href="http://poj.org/searchproblem?field=source&amp;key=USACO+2006+November+Gold" rel="nofollow">USACO 2006 November Gold</a> 
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\[[Submit][]\]   \[Go Back\]   \[[Status][]\]   \[[Discuss][]\]

#include<iostream>
    #include<cstdio>
    #include<cstring>
    #include<algorithm>
    #include<queue>
    using namespace std;
    
    const int maxn=5e3+10;
    const int INF=0x3f3f3f3f;
    
    struct node1{
        int v, w, next;
    }side[100*maxn];
    
    struct node2{
        int x, d, t;
        bool operator < (const node2& tmp) const {
            return d>tmp.d;
        }
    };
    
    int vis[2][maxn], cnt, dis[2][maxn], head[maxn];
    
    void Dijkstra(){
        memset(dis, 0x3f, sizeof(dis));
        dis[0][1]=0;
        priority_queue <node2> pq;
        pq.push((node2){1, 0, 0});
        while(!pq.empty()){
            node2 tmp=pq.top();
            pq.pop();
    
            if(vis[tmp.t][tmp.x]) continue;
            vis[tmp.t][tmp.x]=1;
    
            for(int i=head[tmp.x]; i!=-1; i=side[i].next)
            {
                    int v=side[i].v, w=side[i].w;
    
                    if(dis[0][v]> tmp.d +w)//次短路永远更新慢于最短路
                    {
                        dis[1][v]=dis[0][v];
                        pq.push((node2){v, dis[0][v], 1});
                        dis[0][v]= tmp.d +w;
                        pq.push((node2){v, tmp.d +w, 0});
                    }
                    else if(dis[0][v] < tmp.d + w && dis[1][v] > tmp.d + w)//只要大于最短路，次短路可以随意更新。
                    {
                        dis[1][v]=tmp.d + w;
                        pq.push((node2){v, tmp.d+w, 1});
                    }
            }
        }
    
    }
    
    void add(int u, int v, int w){
        side[cnt].v=v;
        side[cnt].w=w;
        side[cnt].next=head[u];
        head[u]=cnt++;
    }
    
    int main(){
        int n, r;
        scanf("%d%d", &n, &r);
    
        for(int i=1; i<=n; i++)
            head[i]=-1;
    
        int u, v, w;
        for(int i=1; i<=r; i++)
        {
            scanf("%d%d%d", &u, &v, &w);
            add(u, v, w);
            add(v, u, w);
        }
        Dijkstra();
    
        printf("%d\n", dis[1][n]);
        return 0;
    }

[Submit]: http://poj.org/submit?problem_id=3255
[Status]: http://poj.org/problemstatus?problem_id=3255
[Discuss]: http://poj.org/bbs?problem_id=3255