UVA10917 A walk trough the Forest （最短路，dp）

求出家到其他点的最短路径，题目的条件变成了u->v不是回头路等价于d[u]>d[v]。

然后根据这个条件建DAG图，跑dp统计方案数，dp[u] = sum(dp[v])。

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

const int maxn = 1001, maxm = 2002;
struct Edge
{
    int v,w,nxt;
};

#define PB push_back
vector<Edge> edges;
vector<int> G[maxn];
int head[maxn];
int d[maxn];

void addEdge(int u,int v,int w)
{
    edges.PB({v,w,head[u]});
    head[u] = edges.size()-1;
}

void init()
{
    memset(head,-1,sizeof(head));
    edges.clear();
}

typedef pair<int,int> Node;
#define fi first
#define se second
void dijkstra(int s = 1)
{
    memset(d,0x3f,sizeof(d));
    priority_queue<Node,vector<Node>,greater<Node> > q;
    q.push(Node(d[s] = 0,s));
    while(q.size()){
        Node x = q.top(); q.pop();
        int u = x.se;
        if(x.fi != d[u]) continue;
        for(int i = head[u]; ~i ; i = edges[i].nxt){
            Edge &e = edges[i];
            if(d[e.v] > d[u]+e.w){
                d[e.v] = d[u]+e.w;
                q.push(Node(d[e.v],e.v));
            }
        }
    }
}

int dp[maxn];
int dfs(int u)
{
    int &ans = dp[u];
    if(~ans) return ans;
    if(u == 1) return ans = 1;
    ans = 0;
    for(int i = 0; i < (int)G[u].size(); i++){
        ans += dfs(G[u][i]);
    }
    return ans;
}

void rebuild(int n)
{
    for(int i = 0; i < n; i++) G[i].clear();
    for(int u = 0; u < n; u++){
        for(int i = head[u]; ~i; i = edges[i].nxt){
            int v = edges[i].v;
            if(d[v] < d[u]) G[u].PB(v);
        }
    }
}

int main()
{
    //freopen("in.txt","r",stdin);
    int n,m;
    while(scanf("%d%d",&n,&m),n){
        init();
        while(m--){
            int u,v,w; scanf("%d%d%d",&u,&v,&w); u--;v--;
            addEdge(u,v,w); addEdge(v,u,w);
        }
        dijkstra();
        rebuild(n);
        memset(dp,-1,sizeof(dp));
        printf("%d
",dfs(0));
    }
    return 0;
}