黑暗城堡（算法竞赛进阶指南，最短路径生成树）

一.题目链接：

黑暗城堡

二.题目大意：

求最短路径生成树的方案数

三.分析：

模板题，好水啊...

四.代码实现：

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

const int M = (int)1e3;
const int inf = 0x3f3f3f3f;
const int mod = INT_MAX;

int n, m;

int cnt;
int head[M + 5];
struct node
{
    int v, w, nx;
}Edge[M * M + 5];

bool vis[M + 5];
int dis[M + 5];

int num[M + 5];

void init()
{
    cnt = 0;
    for(int i = 1; i <= n; ++i)
    {
        vis[i] = 0;
        head[i] = -1;
        dis[i] = inf;
        num[i] = 0;
    }
}

void add(int u, int v, int w)
{
    Edge[cnt].v = v;
    Edge[cnt].w = w;
    Edge[cnt].nx = head[u];
    head[u] = cnt++;
}

priority_queue < pair<int, int> > q;

void dijkstra(int s)
{
    dis[s] = 0;
    q.push(make_pair(-dis[s], s));
    while(!q.empty())
    {
        int u = q.top().second;
        q.pop();
        if(vis[u])  continue;
        vis[u] = 1;
        for(int i = head[u]; ~i; i = Edge[i].nx)
        {
            int v = Edge[i].v;
            if(dis[v] > dis[u] + Edge[i].w)
            {
                dis[v] = dis[u] + Edge[i].w;
                q.push(make_pair(-dis[v], v));
            }
        }
    }
}

int main()
{
    scanf("%d %d", &n, &m);
    init();
    for(int i = 0, u, v, w; i < m; ++i)
    {
        scanf("%d %d %d", &u, &v, &w);
        add(u, v, w), add(v, u, w);
    }
    dijkstra(1);
    for(int i = 1; i <= n; ++i)
    {
        for(int j = head[i]; ~j; j = Edge[j].nx)
        {
            int v = Edge[j].v;
            if(dis[v] == dis[i] + Edge[j].w)
                num[v]++;
        }
    }
    ll ans = 1;
    for(int i = 1; i <= n; ++i)
    {
        if(num[i])  ans = ans * num[i] % mod;
    }
    printf("%lld\n", ans);
    return 0;
}