POJ3259 Wormholes(Bellman-ford 负环)
2015-03-15 14:09
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Wormholes
Time Limit: 2000MS | Memory Limit: 65536K | |
Total Submissions: 33194 | Accepted: 12085 |
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: A single integer, F. F farm descriptions follow.
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
Lines 1..F: For each farm, output "YES" if FJ can achieve his goal, otherwise output "NO" (do not include the quotes).
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 1, FJ cannot travel back in time.
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.
解题思路:
还是运用bellman-ford算法,求负环。代码如下:
#include<iostream> #include<cstring> #include<cstdio> using namespace std; const int maxn = 10000; //开了5002 RE,索性爆炸点开个10000. #define inf 100000000 int all; //表示边数 int n,m,w; //分别表示顶点数,邻接边,虫洞个数 int cnt; struct point { int start; int end; int seconds; } a[maxn]; int dis[maxn]; bool bellman() { int i,j; bool flag; memset(dis,inf,sizeof(dis)); dis[0] = 0; for(i=1; i<n; i++) //因为0这个点已经初始化,所以从1这个点开始 { flag = false; for(j=0; j< all; j++) //all为总的边数,包含虫洞 { if(dis[a[j].start] > dis[a[j].end] + a[j].seconds) { dis[a[j].start] = dis[a[j].end] + a[j].seconds; flag = true; } } if(!flag) { break; } } for(j=0; j<all; j++) { if(dis[a[j].start] > dis[a[j].end] + a[j].seconds) { dis[a[j].start] = dis[a[j].end] + a[j].seconds; return true; //存在负环 } } return false; //不存在负环,也就是回不去 } int main() { int F,i; int num1,num2,seconds; //freopen("111","r",stdin); cin>>F; while(F--) { all = 0; cin>>n>>m>>w; for(i=0; i<m; i++) //普通的道路 { cin>>num1>>num2>>seconds; a[all].start = num1; a[all].end = num2; a[all++].seconds = seconds; a[all].start = num2; a[all].end = num1; a[all++].seconds = seconds; } for(i=0; i<w; i++) { cin>>num1>>num2>>seconds; a[all].start = num1; a[all].end = num2; a[all++].seconds = -seconds; } if(bellman()) { cout<<"YES"<<endl; } else { cout<<"NO"<<endl; } } return 0; }
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