POJ 3259 Wormholes(Bellman-Ford)
题目网址:http://poj.org/problem?id=3259
题目:
Time Limit: 2000MS | Memory Limit: 65536K | |
Total Submissions: 52198 | Accepted: 19426 |
Description
While exploring his many farms, Farmer John has discovered a number of amazing wormholes. A wormhole is very peculiar because it is a one-way path that delivers you to its destination at a time that is BEFORE you entered the wormhole! Each of FJ's farms comprises N (1 ≤ N ≤ 500) fields conveniently numbered 1..N, M (1 ≤ M ≤ 2500) paths, and W (1 ≤ W ≤ 200) wormholes.
As FJ is an avid time-traveling fan, he wants to do the following: start at some field, travel through some paths and wormholes, and return to the starting field a time before his initial departure. Perhaps he will be able to meet himself :) .
To help FJ find out whether this is possible or not, he will supply you with complete maps to F (1 ≤ F ≤ 5) of his farms. No paths will take longer than 10,000 seconds to travel and no wormhole can bring FJ back in time by more than 10,000 seconds.
Input
Line 1 of each farm: Three space-separated integers respectively: N, M, and W
Lines 2..M+1 of each farm: Three space-separated numbers (S, E, T) that describe, respectively: a bidirectional path between S and E that requires T seconds to traverse. Two fields might be connected by more than one path.
Lines M+2..M+W+1 of each farm: Three space-separated numbers (S, E, T) that describe, respectively: A one way path from S to E that also moves the traveler back T seconds.
Output
Sample Input
2
3 3 1
1 2 2
1 3 4
2 3 1
3 1 3
3 2 1
1 2 3
2 3 4
3 1 8
Sample Output
NO
YES
Hint
For farm 2, FJ could travel back in time by the cycle 1->2->3->1, arriving back at his starting location 1 second before he leaves. He could start from anywhere on the cycle to accomplish this.
我们根本不需要关心他所处的起点的具体位置,我们只需要判断是否有负权环即可,所以将所有的dist[i]都初始化为无穷大。有负权环的话就输出YES,没有的话就输出NO。很自然地就会想到Bellman-Ford算法。判断第n次循环,是否还会松弛,如果还需要就说明有负权环。 这道题需要注意的一点是:虫洞是单向边,路径是双向边。
#include <cstdio>
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
const int inf = ;
struct node{
int v,u,w;
};
vector<node>v;
int n,m,w;
int dist[];
node x;
bool relax(int j){//松弛操作
if(dist[v[j].u]>dist[v[j].v]+v[j].w){
dist[v[j].u]=dist[v[j].v]+v[j].w;
return true;
}
return false;
}
bool bellman_ford(){
for (int i=; i<=n; i++) {
dist[i]=inf;
}
for (int i=; i<n-; i++) {
int flag=;
for (int j=; j<v.size(); j++) {
if(relax(j)) flag=;
}
if(!flag) return false;
}
for (int j=; j<v.size(); j++) {//核心
if(relax(j)) return true;
}
return false;
}
int main(){
int t;
cin>>t;
while (t--) {
int ok=;
v.clear();
cin>>n>>m>>w;
for (int i=; i<m; i++) {
cin>>x.v>>x.u>>x.w;
v.push_back(x);
swap(x.v, x.u);
v.push_back(x);
}
for (int i=; i<w; i++) {
cin>>x.v>>x.u>>x.w;
x.w=-x.w;
v.push_back(x);
}
if (bellman_ford()) printf("YES\n");
else printf("NO\n");
}
return ;
}
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