POJ - 3259 Wormholes(多種方法求負權迴路)+譯文
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 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).
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.
t譯文:農夫約翰在探索他的許多農場,發現了一些驚人的蟲洞。蟲洞是很奇特的,因為它是一個單向通道,可讓你進入蟲洞的前達到目的地!他的N(1≤N≤500)個農場被編號為1..N,之間有M(1≤M≤2500)條路徑,W(1≤W≤200)個蟲洞。作為一個狂熱的時間旅行FJ的愛好者,他要做到以下幾點:開始在一個區域,通過一些路徑和蟲洞旅行,他要回到最開時出發的那個區域出發前的時間。也許他就能遇到自己了:)。為了幫助FJ找出這是否是可以或不可以,他會為你提供F個農場的完整的對映到(1≤F≤5)。所有的路徑所花時間都不大於10000秒,所有的蟲洞都不大於萬秒的時間回溯。
輸入
第1行:一個整數F表示接下來會有F個農場說明。
每個農場第一行:分別是三個空格隔開的整數:N,M和W
第2行到M+1行:三個空格分開的數字(S,E,T)描述,分別為:需要T秒走過S和E之間的雙向路徑。兩個區域可能由一個以上的路徑來連線。
第M +2到M+ W+1行:三個空格分開的數字(S,E,T)描述蟲洞,描述單向路徑,S到E且回溯T秒。
輸出
F行,每行代表一個農場
每個農場單獨的一行,” YES”表示能滿足要求,”NO”表示不能滿足要求。
NO
YES
哈哈,要想回到原點。。。蟲洞可以讓 你回到過去,就相當於一個負權。。。然後判斷是否存在負環,即走走走。。。然後又走回去了,,,
方法一:Bellmand---Ford
#include<stdio.h>
#define INF 0x3f3f3f3f
int dis[10000],bak[10000],u[10000],v[10000],t[10000],check,flag,n,m,w;
int main()
{
int f;
scanf("%d",&f);
while(f--)
{
scanf("%d%d%d",&n,&m,&w);
for(int i=1;i<=m;i++)
scanf("%d%d%d",&u[i],&v[i],&t[i]);
for(int i=m+1;i<=m+w;i++)
{
scanf("%d%d%d",&u[i],&v[i],&t[i]); //蟲洞時間是負的·且單向
t[i]=-t[i];
}
for(int i=1;i<=n;i++)
dis[i]=INF;
dis[1]=0;
for(int k=1;k<n;k++)
{
for(int i=1;i<=n;i++)bak[i]=dis[i]; //將dis陣列備份,可省時,提前跳出迴圈
for(int i=1;i<=m;i++)
{
if(dis[v[i]]>dis[u[i]]+t[i]) //農場兩個方向都要判斷
dis[v[i]]=dis[u[i]]+t[i];
if(dis[u[i]]>dis[v[i]]+t[i])
dis[u[i]]=dis[v[i]]+t[i];
}
for(int i=m+1;i<=m+w;i++)
{
if(dis[v[i]]>dis[u[i]]+t[i]) //注意!!!!!!!!!!!!!從v[i]-u[i]是正的,方向別弄錯了。。
dis[v[i]]=dis[u[i]]+t[i];
}
check=0;
for(int i=1;i<=n;i++)
if(bak[i]!=dis[i])
{
check=1;
break;
}
if(check==0)break;
}
flag=0;
for(int i=1;i<=m;i++) //蟲洞不用判斷,因為本身就是負的,判斷m就好了.加上也行。
if(dis[v[i]]>dis[u[i]]+t[i])flag=1;
if(flag)
printf("YES\n");
else printf("NO\n");
}
return 0;
}
方法二(floyd):
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>
using namespace std;
int map[505][505],n,m,k,num=0;
int floyd()
{
int i,j,k,f=0;
for(k=1;k<=n;k++)
for(i=1;i<=n;i++){
for(j=1;j<=n;j++)
{
int t=map[i][k]+map[k][j];
if(map[i][j]>t)map[i][j]=t;
/*map[i][j]=min(map[i][j],map[i][k]+map[k][j]);*/ //注意這裡,用錯了會超時!!!!不用min就跑了1688ms,,,,
}
if(map[i][i]<0)return 1;
}
return f;
}
int main()
{
int t;
scanf("%d",&t);
while(t--)
{
int i,j,a,b,c;
scanf("%d%d%d",&n,&m,&k);
memset(map,0x3f3f3f3f,sizeof(map));
for(i=1;i<=n;i++)map[i][i]=0;
for(i=1;i<=m;i++)
{
scanf("%d%d%d",&a,&b,&c);
if(c<map[a][b])map[a][b]=map[b][a]=c;
}
for(i=1;i<=k;i++)
{
scanf("%d%d%d",&a,&b,&c);
map[a][b]=-c;
}
num++;
int f=floyd();
if(!f)printf("NO\n");
else printf("YES\n");
}
return 0;
}
轉載自:https://blog.csdn.net/zitian246/article/details/76082393