Wormholes

SPFA算法解决时间旅行问题
本文探讨了如何使用SPFA算法解决一个有趣的时间旅行问题,即在一个包含特殊路径(wormholes)的农场中,判断是否存在一条路径使得从起点出发并返回起点时,时间倒流到出发前。通过构建图模型并应用SPFA算法,我们能够检测是否存在负权环,从而判断是否可以实现时间旅行。

题目

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..NM (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, FF farm descriptions follow. 
Line 1 of each farm: Three space-separated integers respectively: NM, and W 
Lines 2.. M+1 of each farm: Three space-separated numbers ( SET) 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.. MW+1 of each farm: Three space-separated numbers ( SET) that describe, respectively: A one way path from S to E that also moves the traveler backT seconds.

Output

Lines 1.. F: For each farm, output "YES" if FJ can achieve his goal, otherwise output "NO" (do not include the quotes).

样例

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.

最短路中的求负边,其实可以用BF的,但是考虑到更加长远,还是学习使用了SPFA!

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <vector>
#include <string.h>
#include <string>
typedef long long ll;
#define INF 0x3f3f3f3f
using namespace std;
#define maxn 1010
struct Edge{
	int v;
	int cost;
	Edge(int v, int cost) :v(v), cost(cost) {}
};

vector<Edge>E[maxn];
void addedge(int u, int v, int w) {
	E[u].push_back(Edge(v, w));
}
bool vis[maxn];
int cnt[maxn];
int dist[maxn];
bool spfa(int start, int n) {
	memset(vis, false, sizeof(vis));
	for (int i = 1; i <= n; ++i)dist[i] = INF;
	dist[start] = 0;
	vis[start] = true;
	queue<int> q;
	while (!q.empty())q.pop();
	q.push(start);
	memset(cnt, 0, sizeof(cnt));
	cnt[start] = 1;
	while (!q.empty()) {
		int u = q.front();
		q.pop();
		vis[u] = false;
		for (int i = 0; i < E[u].size(); ++i) {
			int v = E[u][i].v;
			if (dist[v] > dist[u] + E[u][i].cost) {
				dist[v] = dist[u] + E[u][i].cost;
				if (!vis[v]) {
					vis[v] = true;
					q.push(v);
					if (++cnt[v] > n)
						return false;
				}
			}
		}
	}
	return true;
}

int main()
{
	int T;
	int N, M, W;
	int a, b, c;
	scanf("%d", &T);
	while (T--) {
		scanf("%d%d%d", &N, &M, &W);
		for (int i = 1; i <= N + 1; ++i)E[i].clear();
		while (M--) {
			scanf("%d%d%d", &a, &b, &c);
			addedge(a, b, c);
			addedge(b, a, c);
		}
		while (W--) {
			scanf("%d%d%d", &a, &b, &c);
			addedge(a, b, -c);
		}
		for (int i = 1; i <= N; ++i)addedge(N + 1, i, 0);
		if (!spfa(N + 1, N + 1))printf("YES\n");
		else printf("NO\n");
	}
	return 0;
}

 

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