Two Paths

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 153428/153428 K (Java/Others)
Total Submission(s): 2139    Accepted Submission(s): 834


Problem Description


You are given a undirected graph with n nodes (numbered from 1 to n) and m edges. Alice and Bob are now trying to play a game.
Both of them will take different route from 1 to n (not necessary simple).
Alice always moves first and she is so clever that take one of the shortest path from 1 to n.
Now is the Bob's turn. Help Bob to take possible shortest route from 1 to n.
There's neither multiple edges nor self-loops.
Two paths S and T are considered different if and only if there is an integer i, so that the i-th edge of S is not the same as the i-th edge of T or one of them doesn't exist.

 


Input


The first line of input contains an integer T(1 <= T <= 15), the number of test cases.
The first line of each test case contains 2 integers n, m (2 <= n, m <= 100000), number of nodes and number of edges. Each of the next m lines contains 3 integers a, b, w (1 <= a, b <= n, 1 <= w <= 1000000000), this means that there's an edge between node a and node b and its length is w.
It is guaranteed that there is at least one path from 1 to n.
Sum of n over all test cases is less than 250000 and sum of m over all test cases is less than 350000.

 


Output


For each test case print length of valid shortest path in one line.

 


Sample Input

2 3 3 1 2 1 2 3 4 1 3 3 2 1 1 2 1

 


Sample Output

Hint

给定多张无向图，求出每张图中的从s到t的次短路

Input
第一行一个数T，表示数据组数
后面给出T张无向图

Output
对每一张图，给出其次短路

裸的次短路问题
G[i]忘清空了，WA了好多次，
难受。
很难受。

#include<bits/stdc++.h>
#include<vector>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> P;
const ll INF  = 1e18;
const int MAXN = 2e5+7;
struct edge{
        ll to,cost;
        edge(){};
        edge(ll _to, ll _cost)
        {
                to = _to;
                cost = _cost;
        }
};

vector<edge> G[MAXN];
int n,m;
ll dist[MAXN];
ll dist2[MAXN];

void slove()
{
        priority_queue<P, vector<P>, greater<P> >que;
        fill(dist, dist + n + 1, INF);
        fill(dist2,dist2+ n + 1, INF);
        dist[0] = 0;
        que.push(P(0,0));
        while(!que.empty())
        {
                P p = que.top(); que.pop();
                ll v = p.second, d = p.first;
                if(dist2[v] < d)        continue;
                for(int i = 0; i < G[v].size(); ++i )
                {
                        edge &e = G[v][i];
                        ll d2 = d + e.cost;
                        if(dist[e.to] > d2)
                        {
                                swap(dist[e.to], d2);
                                que.push(P(dist[e.to], e.to));
                        }
                        if(dist2[e.to] > d2 && dist[e.to] < d2)
                        {
                                dist2[e.to] = d2;
                                que.push(P(dist2[e.to],e.to));
                        }
                }
        }
        printf("%lld\n",dist2[n-1]);
}
int main()
{
        int t;
        scanf("%d",&t);
        while(t--)
        {
                scanf("%d %d",&n,&m);
                ll x,y,z;
                for(int i=0;i<=n;i++)
                        G[i].clear();
                for(int i=0;i<m;i++)
                {
                        scanf("%lld %lld %lld",&x,&y,&z);
                        G[x-1].push_back(edge(y-1, z));
                        G[y-1].push_back(edge(x-1, z));
                }
                slove();
        }
        return 0;
}