POJ 3259 Wormholes （bellman_ford算法判负环）

Wormholes

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

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.

Source

USACO 2006 December Gold

题意：John有个n个农场，所有农场之间有m条路，每条路都有通过所需的时间。有一天，他在农场转悠，竟然发现了w个虫洞（估计这孩子小学物理学的不错~~~），每个虫洞然都有倒退的时间，他就想利用这些虫洞回到以前。问他能不能实现这个神奇之旅。

解析：就是单纯的判断是否有负环，因为如果有负环的话，就代表着回到原点的时间在出发之前，这就会到的以前。不过要特别注意路是双向的，但是虫洞确是单向的！！！级的数组一定要开的足够大，不然就RE，因为路是双向的，所以存路就需要2*MAX_E，再加上MAX_W个虫洞，总共就需要开到 2*MAX_E + MAX_W 才可以。

PS：bellman_ford算法判断负环有两种方法，但是两者的实质都是一样的，不用纠结的，如果直接就只是判断有无负环，还是版本二好写一点。

AC代码：

判负环版本一：

#include <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;
#define INF 1234567
#define MAX_V 505
#define MAX_E 5205

struct edge{ int s, e, w; };
edge es[MAX_E];
int d[MAX_V];
int E, V;

bool Bellman_ford(int s){
    for(int i=1; i<=V; i++) d[i] = (i==s) ? 0 : INF;
    for(int i=0; i<V-1; i++){
        int flag = 0;
        for(int j=0; j<E; j++){
            edge now = es[j];
            if(d[now.e] > d[now.s] + now.w){
                d[now.e] = d[now.s] + now.w;
                flag = 1;
            }
        }
        if(flag == 0) break;
    }

    for(int i=0; i<E; i++){                 //判负环
        edge now = es[i];
        if(d[now.e] > d[now.s] + now.w)
            return true;
    }
    return false;
}

int main(){
//    freopen("in.txt", "r", stdin);
    int t, n, m, w, s, e, time;
    scanf("%d", &t);
    while(t--){
        scanf("%d%d%d", &n, &m, &w);
        V = n;                             //顶点数
        E = 0;                             //边数
        for(int i=0; i<m; i++){            //路是双向的
            scanf("%d%d%d", &s, &e, &time);
            es[E].s = s;
            es[E].e = e;
            es[E++].w = time;
            es[E].s = e;
            es[E].e = s;
            es[E++].w = time;
        }
        for(int i=0; i<w; i++){          //虫洞是单向！！！
            scanf("%d%d%d", &s, &e, &time);
            es[E].s = s;
            es[E].e = e;
            es[E++].w = -time;
        }
        printf("%s\n", flag ? "YES" : "NO");
    }
    return 0;
}

判负环版本二：

#include <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;
#define INF 1234567
#define MAX_V 505
#define MAX_E 5205

struct edge{ int s, e, w; };
edge es[MAX_E];
int d[MAX_V];
int E, V;

bool Bellman_ford(int s){
    for(int i=1; i<=V; i++) d[i] = (i==s) ? 0 : INF;
    for(int i=0; i<V; i++){
        for(int j=0; j<E; j++){
            edge now = es[j];
            if(d[now.e] > d[now.s] + now.w){
                d[now.e] = d[now.s] + now.w;
                if(i == V-1) return true;
            }
        }
    }
    return false;
}

int main(){
//    freopen("in.txt", "r", stdin);
    int t, n, m, w, s, e, time;
    scanf("%d", &t);
    while(t--){
        scanf("%d%d%d", &n, &m, &w);
        V = n;
        E = 0;
        for(int i=0; i<m; i++){            //路是双向的
            scanf("%d%d%d", &s, &e, &time);
            es[E].s = s;
            es[E].e = e;
            es[E++].w = time;
            es[E].s = e;
            es[E].e = s;
            es[E++].w = time;
        }
        for(int i=0; i<w; i++){          //虫洞是单向！！！
            scanf("%d%d%d", &s, &e, &time);
            es[E].s = s;
            es[E].e = e;
            es[E++].w = -time;
        }
        printf("%s\n", Bellman_ford(1) ? "YES" : "NO");
    }
    return 0;
}

小编福利：如果想求出来所有的负环的话，只需要把将版本二中的d数组全部初始化为0即可~~~