POJ 3255 （次短路）

Roadblocks

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 8425		Accepted: 3044

Description

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.

The countryside consists of R (1 ≤ R ≤ 100,000) bidirectional roads, each linking two of the N (1 ≤ N ≤ 5000) intersections, conveniently numbered 1..N. Bessie starts at intersection 1, and her friend (the destination) is at intersection N.

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).

Input

Line 1: Two space-separated integers:  N and  R 
Lines 2.. R+1: Each line contains three space-separated integers:  A,  B, and  D that describe a road that connects intersections  A and  B and has length  D (1 ≤  D ≤ 5000)

Output

Line 1: The length of the second shortest path between node 1 and node  N

Sample Input

4 4
1 2 100
2 4 200
2 3 250
3 4 100

Sample Output

450

Hint

Two routes: 1 -> 2 -> 4 (length 100+200=300) and 1 -> 2 -> 3 -> 4 (length 100+250+100=450)

题意：求次短路。

分析：

只需要在最短路基础上稍稍修改即可。我们要分别记录和更新最短路和次短路并加入到队列中。可以在每次更新最短路时把把原先的最短路记录下来，如果它比最新的次短路短则更新次短路。或者比最短路长的也需要与次短路比较，看是否可以更新。

code:

#include<stdio.h>
#include<queue>
#include<vector>
#include<algorithm>
using namespace std;
#define INF 1e9
struct Edge{int to, cost;};
typedef pair<int,int> P;
vector<Edge> G[5010];
int n, dis[5010], dis2[5010];
void dijkstra(int s)
{
    priority_queue<P, vector<P>, greater<P> > q;
    for(int i=1; i<=n; i++)
        dis[i] = dis2[i] = INF;
    dis[0] = 0;
    q.push(P(s,0));
    while(!q.empty())
    {
        P p = q.top(); q.pop();
        int v = p.first, x = p.second;
        for(int i=0; i<G[v].size(); i++)
        {
            Edge e = G[v][i];
            int d2 = x+e.cost;
            if(d2 < dis[e.to])
            {
                swap(dis[e.to], d2);
                q.push(P(e.to,dis[e.to]));
            }
            if(d2 < dis2[e.to])
            {
                dis2[e.to] = d2;
                q.push(P(e.to,dis2[e.to]));
            }
        }
    }
}
int main()
{
    int m;

    scanf("%d%d", &n,&m);
    for(int i=1; i<=n; i++) G[i].clear();
    for(int i=1; i<=m; i++)
    {
        int a, b, d;
        scanf("%d%d%d", &a,&b,&d);
        Edge e;
        e.to = b; e.cost = d;
        G[a].push_back(e);
        e.to = a;
        G[b].push_back(e);
    }
    dijkstra(1);
    printf("%d\n", dis2[n]);
    return 0;
}