poj3259 Wormholes

Wormholes

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 29805		Accepted: 10779

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: 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

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.

Source

USACO 2006 December Gold

解题：Bellman-Ford 算法模板题。存在负环即可以看见自己，虫洞？你懂的！

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <cstdlib>
 5 #include <vector>
 6 #include <climits>
 7 #include <algorithm>
 8 #include <cmath>
 9 #define LL long long
10 using namespace std;
11 const int INF = INT_MAX>>1;
12 int cnt,dis[600];
13 struct ARC {
14     int u,v,w;
15 } arc[6000];
16 bool bf(int n) {
17     int i,j;
18     for(i = 2; i <= n; i++)
19         dis[i] = INF;
20     dis[1] = 0;
21     for(i = 1; i < n; i++) {
22         for(j = 0; j < cnt; j++) {
23             if(dis[arc[j].v] > dis[arc[j].u]+arc[j].w) {
24                 dis[arc[j].v] = dis[arc[j].u] + arc[j].w;
25             }
26         }
27     }
28     for(j = 0; j < cnt; j++) {
29         if(dis[arc[j].v] > dis[arc[j].u]+arc[j].w) return false;
30     }
31     return true;
32 }
33 int main() {
34     int kase,n,m,k,u,v,w,i;
35     scanf("%d",&kase);
36     while(kase--) {
37         scanf("%d %d %d",&n,&m,&k);
38         cnt = 0;
39         while(m--) {
40             scanf("%d %d %d",&u,&v,&w);
41             arc[cnt++] = (ARC) {u,v,w};
42             arc[cnt++] = (ARC) {v,u,w};
43         }
44         while(k--) {
45             scanf("%d %d %d",&u,&v,&w);
46             arc[cnt++] = (ARC) {u,v,-w};
47         }
48         bf(n)?puts("NO"):puts("YES");
49     }
50     return 0;
51 }

View Code

解法2：SPFA算法，邻接表存储图。不过此题貌似效果不明显，还没裸的Bellman-Ford快！

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <cstdlib>
 5 #include <vector>
 6 #include <climits>
 7 #include <algorithm>
 8 #include <cmath>
 9 #include <queue>
10 #define LL long long
11 using namespace std;
12 const int maxn = 510;
13 const int INF = INT_MAX>>2;
14 int n;
15 struct arc {
16     int w,to;
17 };
18 vector<arc>e[maxn];
19 bool used[maxn];
20 int num[maxn],d[maxn];
21 bool spfa(int x) {
22     int i,j,temp;
23     memset(num,0,sizeof(num));
24     memset(used,false,sizeof(used));
25     for(i = 1; i <= n; i++)
26         d[i] = INF;
27     d[x] = 0;
28     queue<int>q;
29     while(!q.empty()) q.pop();
30     used[x] = true;
31     num[x]++;
32     q.push(x);
33     while(!q.empty()) {
34         temp = q.front();
35         q.pop();
36         used[temp] = false;
37         for(i = 0; i < e[temp].size(); i++) {
38             j = e[temp][i].to;
39             if(d[j] > e[temp][i].w+d[temp]) {
40                 d[j] = e[temp][i].w + d[temp];
41                 if(!used[j]) {
42                     num[j]++;
43                     used[j] = true;
44                     if(num[j] >= n) return true;
45                     q.push(j);
46                 }
47             }
48         }
49     }
50     return false;
51 }
52 int main() {
53     int kase,i,u,v,w,m,k;
54     scanf("%d",&kase);
55     while(kase--) {
56         for(i = 0; i < maxn; i++)
57             e[i].clear();
58         scanf("%d %d %d",&n,&m,&k);
59         while(m--) {
60             scanf("%d %d %d",&u,&v,&w);
61             e[u].push_back((arc) {w,v});
62             e[v].push_back((arc {w,u}));
63         }
64         while(k--) {
65             scanf("%d %d %d",&u,&v,&w);
66             e[u].push_back((arc) {-w,v});
67         }
68         spfa(1)?puts("YES"):puts("NO");
69     }
70 }

View Code