Wormholes(最短路)

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探讨了在一个包含特殊虫洞的农场中，是否存在一条路径使得旅行者能够回到起点的同时时间倒流到出发之前。通过两种算法SPFA和Floyd解决此问题。

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Wormholes

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 52936		Accepted: 19732

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 toF (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

spfa

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <queue>
#define inf 0x3f3f3f3f
using namespace std;

int dis[505], vis[505], first[505], num[505], next[8005], u[8005], v[8005], w[8005], sum; //注意边的数目要开到二倍
int spfa(int n);
void add(int x, int y, int z)
{
    u[sum] = x, v[sum] = y, w[sum] = z;
    next[sum] = first[x];
    first[x] = sum;
    sum++;
}
int main()
{
    int f, x, y, z, n, m, k;
    scanf("%d", &f);
    while(f--)
    {
        scanf("%d %d %d", &n, &m, &k);
        for(int i = 1; i <= n; i++)
        {
            num[i] = 0;
            vis[i] = 0;
            first[i] = -1;
            dis[i] = inf;
        }
        sum = 1;
        for(int i = 1; i <= m; i++)
            {
                scanf("%d %d %d", &x, &y, &z);
                add(x, y, z);
                add(y, x, z);
            }
        for(int i = 1; i <= k; i++)
            {
                scanf("%d %d %d", &x, &y, &z);
                add(x, y, -z);
            }
        if(spfa(n))
                printf("YES\n");
        else
                printf("NO\n");
    }
    return 0;
}
int spfa(int n)
{
    int k;
    queue<int>q;
    dis[1] = 0;
    vis[1] = 1;
    num[1]++;
    q.push(1);
    while(q.size() > 0)
        {
            k = first[q.front()];
            vis[q.front()] = 0;
            q.pop();
            while(k != -1)
            {
                if(dis[v[k]] > dis[u[k]] + w[k])
                    {
                        dis[v[k]] = dis[u[k]] + w[k];
                        if(vis[v[k]] == 0)
                            {
                                q.push(v[k]);
                                vis[v[k]] = 1;
                                num[v[k]]++;
                                if(num[v[k]] > n)
                                    return 1;
                            }
                    }
                k = next[k];
            }
        }
    return 0;
}

floyd

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#define inf 0x3f3f3f3f
using namespace std;

int maps[550][550];
int main()
{
    int f, n, m, w, x, y, z;
    scanf("%d", &f);
    while(f--)
    {
        bool flag = 0;
        scanf("%d %d %d", &n , &m , &w);
        memset(maps,0x3f3f3f3f,sizeof(maps));
            for(int i=1;i<=n;i++)maps[i][i]=0;
        for(int i = 1; i <= m; i++)
            {
                scanf("%d %d %d", &x, &y, &z);
                if(z < maps[x][y])maps[x][y]=maps[y][x]=z;
            }
        for(int i = 1; i <= w; i++)
            {
                scanf("%d %d %d", &x, &y, &z);
                maps[x][y] = min(maps[x][y], -z);
            }
        for(int k = 1; k <= n; k++)
               {
                for(int i = 1; i <= n; i++)
                    {
                    for(int j = 1; j <= n; j++)
                           {
                            int t = maps[i][k] + maps[k][j];
                            if(maps[i][j] > t)
                            maps[i][j] = t;
                           }
                    if(maps[i][i] < 0)
                        flag = 1;
                    }
                    if(flag)
                        break;
               }
        if(flag)
                printf("YES\n");
        else
                printf("NO\n");
    }
    return 0;
}