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SPFA  +　A*

#include <cstdio>
#include <queue>
#include <cstring>
#include <algorithm>
using namespace std;

struct node {
	int v, dis, f, next;
	friend bool operator <(node a, node b){
		return a.f>b.f;
	}
};

const int INF = 1e9;
const int maxn = 1005;
const int maxm = 100005;
node edge[maxm], edgef[maxm];
int head[maxn], e, headf[maxn], dis[maxn], n, m, s, t, k;
void Add(int u, int v, int dis){
	edge[e].v = v;
	edge[e].dis = dis;
	edge[e].next = head[u];
	head[u] = e;

	edgef[e].v = u;
	edgef[e].dis = dis;
	edgef[e].next = headf[v];
	headf[v] = e++;
}

void init(){
	int i, u, v, dis;
	memset(head, -1, sizeof head );
	memset(headf, -1, sizeof headf );
	e = 0;
	for(i=1; i<=m; ++i){
		scanf("%d%d%d", &u, &v, &dis);
		Add(u, v, dis);
	}
}

int cnt[maxn], vis[maxn];

void SPFA(int s, int t){
	int u, v, i, j;
	queue<int> q;
	memset(vis, 0, sizeof vis );
	memset(cnt, 0, sizeof cnt );
	for(i=0; i<=n; ++i) dis[i] = INF;
	vis[s]=1; dis[s]=0; q.push(s);
	while(!q.empty()){
		u = q.front();
		q.pop();
		vis[u] = 0;
		cnt[u]++;
		if(cnt[u]>=n) return ;
		for(j=headf[u];~j;j=edgef[j].next)
			if(dis[v=edgef[j].v]>dis[u]+edgef[j].dis){
				dis[v] = dis[u] + edgef[j].dis;
				if(!vis[v]) vis[v]=1,q.push(v);
			}
	}
}

int A_STAR(int s, int t, int k){
	int cnt=0, i;
	node e, next;
	priority_queue<node> q;
	if(s==t) k++;
	if(dis[s]==INF) return -1;
	e.v = s; e.dis = 0; e.f = dis[s]; q.push(e);
	while(!q.empty()){
		e = q.top();
		q.pop();
		if(e.v==t&&++cnt==k) return e.dis;
		for(i=head[e.v]; ~i; i=edge[i].next){
			next.v = edge[i].v;
			next.dis = e.dis + edge[i].dis;
			next.f = next.dis + dis[next.v];
			q.push(next);
		}
	}
	return -1;
}

void solve(){
	scanf("%d%d%d", &s, &t, &k);
	SPFA(t, s);
	printf("%d\n", A_STAR(s, t, k));
}

int main(){
	while(~scanf("%d%d", &n, &m)){
		init();
		solve();
	}
	return 0;
}

参考链接：

http://www.cnblogs.com/vongang/archive/2012/07/17/2594737.html

http://yzmduncan.iteye.com/blog/1162759

http://ycool.com/post/krb8pah

poj2449 Remmarguts' Date，第K短路