A Walk Through the Forest（最短路径+DFS）

A Walk Through the Forest

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 123 Accepted Submission(s): 59 

Problem Description

Jimmy experiences a lot of stress at work these days, especially since his accident made working difficult. To relax after a hard day, he likes to walk home. To make things even nicer, his office is on one side of a forest, and his house is on the other. A nice walk through the forest, seeing the birds and chipmunks is quite enjoyable. 
The forest is beautiful, and Jimmy wants to take a different route everyday. He also wants to get home before dark, so he always takes a path to make progress towards his house. He considers taking a path from A to B to be progress if there exists a route from B to his home that is shorter than any possible route from A. Calculate how many different routes through the forest Jimmy might take. 

 

Input

Input contains several test cases followed by a line containing 0. Jimmy has numbered each intersection or joining of paths starting with 1. His office is numbered 1, and his house is numbered 2. The first line of each test case gives the number of intersections N, 1 < N ≤ 1000, and the number of paths M. The following M lines each contain a pair of intersections a b and an integer distance 1 ≤ d ≤ 1000000 indicating a path of length d between intersection a and a different intersection b. Jimmy may walk a path any direction he chooses. There is at most one path between any pair of intersections. 

 

Output

For each test case, output a single integer indicating the number of different routes through the forest. You may assume that this number does not exceed 2147483647

 

Sample Input

5 61 3 21 4 23 4 31 5 124 2 345 2 247 81 3 11 4 13 7 17 4 17 5 16 7 15 2 16 2 10

 

Sample Output

24

#include <stdio.h>#include <iostream>#include <queue>#include <vector>#include <cmath>#include <algorithm>#include <string.h>#define INF 0x3fffffff#define MAX_N 5005#define MAX_E 5005#define MAX_V 50005using namespace std;typedef long long ll;typedef pair<int, int> pp;struct edge {    int to;    int w;};edge e;int u, v, w;int V, E;int N, M, R;vector<edge> G[MAX_V];int d[MAX_V];int ans[MAX_V];int vis[MAX_V];void dijkstra(int s) {    priority_queue<pp, vector<pp>, greater<pp> > q;    fill(d, d+V+1, INF);    d[s] = 0;    q.push(pp(0, s));    while (q.size()) {        pp p = q.top();        q.pop();        int v = p.second;        int w = p.first;        if (d[v] < w) continue;        for (int i = 0; i < G[v].size(); i++) {            edge e = G[v][i];            if (d[e.to] > d[v] + e.w) {                d[e.to] = d[v] + e.w;                q.push(pp(d[e.to], e.to));            }        }    }}int dfs(int v) {    int sum = 0;    if (ans[v] != -1) return ans[v];    // 1到达2    if (v == 2) return 1;    for (int i = 0; i < G[v].size(); i++) {        edge e = G[v][i];        // 如果a,b之间有路，且你选择要走这条路，那么必须保证a到终点的所有路都小于b到终点的一条路        if (d[v] > d[ e.to ]) {            sum += dfs(e.to);        }    }    return ans[v] = sum;}int main(void){  //  freopen("in.txt", "r", stdin);    while (~scanf("%d%d", &V, &E)) {        if (V == 0) break;        memset(G, 0, sizeof(G));        for (int i = 0; i < E; i++) {            scanf("%d%d%d", &u, &v, &e.w);            e.to = v;            G[u].push_back(e);            e.to = u;            G[v].push_back(e);        }        // 得到顶点2到其他顶点的最短距离        dijkstra(2);        memset(ans, -1, sizeof(ans));        printf("%d\n", dfs(1));    }    return 0;}