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  • UVa 10917

    题目链接:https://onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&category=0&problem=1858&mosmsg=Submission+received+with+ID+26582881

    转化题意后就是如果一个点 (B) 到终点的最短路小于 (A) 到终点的最短路,则 (A->B) 可以通过。

    从终点求一遍最短路,新图是 (DAG),记忆化搜索统计路径即可

    #include<bits/stdc++.h>
    using namespace std;
    typedef long long ll;
    typedef pair<int, int> pii;
    
    const int maxn = 1010;
    const int INF = 0x3f3f3f3f;
    
    int n, m; 
    int h[maxn], cnt = 0;
    struct E{
    	int to, cost, next;
    }e[maxn * maxn * 2];
    void add(int u, int v, int w){
    	e[++cnt].to = v;
    	e[cnt].cost = w;
    	e[cnt].next = h[u];
    	h[u] = cnt;
    }
    
    int d[maxn];
    void dij(int S){
    	memset(d, 0x3f, sizeof(d));
    	priority_queue<pii, vector<pii>, greater<pii> > q;
    	d[S] = 0;
    	q.push(pii(0, S));
    	
    	while(!q.empty()){
    		pii p = q.top(); q.pop();
    		int u = p.second;
    		
    		if(p.first != d[u]) continue;
    		
    		for(int i = h[u] ; i != -1 ; i = e[i].next){
    			int v = e[i].to;
    			if(d[v] > d[u] + e[i].cost){
    				d[v] = d[u] + e[i].cost;
    				q.push(pii(d[v], v));
    			}
    		}
    	}
    }
    
    int dp[maxn];
    int DP(int u){
    	if(dp[u] > 0) return dp[u];
    	
    	for(int i = h[u] ; i != -1 ; i = e[i].next){
    		int v = e[i].to;
    		if(d[u] > d[v]) dp[u] += DP(v);
    	}
    	return dp[u];
    }
    
    ll read(){ ll s = 0, f = 1; char ch = getchar(); while(ch < '0' || ch > '9'){ if(ch == '-') f = -1; ch = getchar(); } while(ch >= '0' && ch <= '9'){ s = s * 10 + ch - '0'; ch = getchar(); } return s * f; }
    
    int main(){
    	while(scanf("%d", &n) == 1 && n){
    		memset(h, -1, sizeof(h)); cnt = 0;
    		scanf("%d", &m);
    		int u, v, w;
    		for(int i = 1 ; i <= m ; ++i){
    			scanf("%d%d%d", &u, &v, &w);
    			add(u, v, w), add(v, u, w);
    		}
    		
    		dij(2);
    		
    		memset(dp, 0, sizeof(dp));
    		dp[2] = 1;
    		DP(1);
    		printf("%d
    ", dp[1]);
    	}
    	return 0;
    }
    
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  • 原文地址:https://www.cnblogs.com/tuchen/p/15025685.html
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