POJ3255:Roadblocks(次短路 SPFA+A星)

给出1～N 个点 的距离， 求从1号到N号的次短路， 直接用k短路来做了，，dj会TLE， 用spfa就过了

题目：

I - Roadblocks

Time Limit:2000MS     Memory Limit:65536KB     64bit IO Format:%I64d & %I64u

Submit Status

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 lengthD (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)

 

 

代码：

#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;

#define MAXN 5000+10


int N,R;

#define MP(a,b) make_pair(a,b)
#define INF 100000000

#define pii pair<int,int>
vector<pii> G[MAXN];
struct pri
{ 
    bool operator () (const pair<int,int> &p1,const pair<int,int>&p2)
    {
        return p1.second< p2.second;
    }
};

int d[MAXN];
void dj(int s)
{
    for(int i = 1;i<=N;i++) 
    {
        d[i]= INF;
        d[i] = INF;
    }
    d[s]=0;
    d[s]=0;
    
    priority_queue<pii,vector<pii>,pri> q;
    q.push( MP(s,d[s]) );
    while(!q.empty())
    {   
        int u = q.top().first;
        q.pop();

        int size = G[u].size();

        for(int i=0;i<size;i++)
        {
            int v,w;
            v = G[u][i].first;
            w = G[u][i].second;

            if( d[v] > d[u]+w )
            {
                d[v]=d[u]+w;
                q.push(MP(v,d[v]));

            }
        }
    }

}
/*
void spfa(int src)
{
    
    for(int i=1;i<=N;i++)
    {
        d[i] = INF;
    }
    d[src]=0;
    queue<int> q;
    q.push(src);
    int a,next;
    int vis[MAXN]={0};
    while(!q.empty())
    {
        a = q.front();
        q.pop();
        vis[a] = 0;
        int len = G[a].size();
        for(int i=0;i<len;i++)
        {
            next = G[a][i].first;
            if( d[next]> d[a]+G[a][i].second )
            {
                d[next] = d[a]+G[a][i].second;
                if( !vis[next] )
                {
                    q.push(next);
                    vis[next]=1;
                }
            }
        }
    }
}
*/
struct node{

    int now,g,h,f;
    bool operator < (const node& x) const
    {
        if( f == x.f )
        {
            return x.g<g;
        }
        else
        {
            return x.f<f;
        }
    }
};
void astar(int src,int to)
{
    priority_queue<node> q;
    node a, next;

    a.now = src;
    a.g = 0;
    a.f = d[src]+a.g;
    q.push(a);
    int cnt = 0;
    while(!q.empty())
    {
        a = q.top();
        q.pop();
        if( a.now == to )
        {
            cnt++;
            if( cnt == 2 )
            {
                cout<<a.g<<endl;
                return;
            }
        }
        int size = G[a.now].size();
        for(int i=0;i<size;i++)
        {
            next.now = G[a.now][i].first;
            next.g = a.g + G[a.now][i].second;
            next.f = next.g+d[next.now];
            q.push(next);
        }
    }
}

int main()
{

    cin>>N>>R;

    for(int i=0;i<R;i++)
    {
        int f,t,w;
        cin>>f>>t>>w;

        G[f].push_back( MP(t,w) );
        G[t].push_back( MP(f,w) );
    }
    
    dj(N);    
//    spfa(N);
    astar(1,N);
    return 0;
}