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.
InputLine 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.
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
NO YES
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.
#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
struct node
{
int u,v,w;
} eage[6000];
const int INF=0x3f3f3f3f;
int dis[6000];
int num;
int n,m,w;
void Add(int s,int e,int t)
{
num++;
eage[num].u=s;
eage[num].v=e;
eage[num].w=t;
}
int Bellman()//该算法用于图中有负权值的题目
{
int i,j;
int flag;
for(i=0; i<=n; i++)
{
dis[i]=INF;
}
dis[1]=0;
flag=0;
for(i=1; i<=n; i++)
{
for(j=1; j<=num; j++)
{
if(dis[eage[j].v]>dis[eage[j].u]+eage[j].w)
{
dis[eage[j].v]=dis[eage[j].u]+eage[j].w;
}
}
}
for(i=1; i<=num; i++)
{
if(dis[eage[i].v]>dis[eage[i].u]+eage[i].w)
return 1;
}
return 0;
}
int main()
{
int t;
while(~scanf("%d",&t))
{
while(t--)
{
scanf("%d%d%d",&n,&m,&w);
num=0;
while(m--)
{
int s,e,t;
scanf("%d%d%d",&s,&e,&t);
Add(s,e,t);
Add(e,s,t);
}
while(w--)
{
int s,e,t;
scanf("%d%d%d",&s,&e,&t);
Add(s,e,-t);
}
if(Bellman())printf("YES\n");
else printf("NO\n");
}
}
return 0;
}
探讨了在一个包含特殊路径和虫洞的农场模型中,是否存在一种路径使得从起点出发后能够回到过去的时间点。通过贝尔曼-福特算法检测负权重环来判断是否可以实现时间旅行。
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