首页 > 代码库 > POJ1734/Floyd求最小环
POJ1734/Floyd求最小环
Sightseeing trip
Time Limit: 1000MS | Memory Limit: 65536K | |||
Total Submissions: 6647 | Accepted: 2538 | Special Judge |
Description
There is a travel agency in Adelton town on Zanzibar island. It has decided to offer its clients, besides many other attractions, sightseeing the town. To earn as much as possible from this attraction, the agency has accepted a shrewd decision: it is necessary to find the shortest route which begins and ends at the same place. Your task is to write a program which finds such a route.
In the town there are N crossing points numbered from 1 to N and M two-way roads numbered from 1 to M. Two crossing points can be connected by multiple roads, but no road connects a crossing point with itself. Each sightseeing route is a sequence of road numbers y_1, ..., y_k, k>2. The road y_i (1<=i<=k-1) connects crossing points x_i and x_{i+1}, the road y_k connects crossing points x_k and x_1. All the numbers x_1,...,x_k should be different.The length of the sightseeing route is the sum of the lengths of all roads on the sightseeing route, i.e. L(y_1)+L(y_2)+...+L(y_k) where L(y_i) is the length of the road y_i (1<=i<=k). Your program has to find such a sightseeing route, the length of which is minimal, or to specify that it is not possible,because there is no sightseeing route in the town.
In the town there are N crossing points numbered from 1 to N and M two-way roads numbered from 1 to M. Two crossing points can be connected by multiple roads, but no road connects a crossing point with itself. Each sightseeing route is a sequence of road numbers y_1, ..., y_k, k>2. The road y_i (1<=i<=k-1) connects crossing points x_i and x_{i+1}, the road y_k connects crossing points x_k and x_1. All the numbers x_1,...,x_k should be different.The length of the sightseeing route is the sum of the lengths of all roads on the sightseeing route, i.e. L(y_1)+L(y_2)+...+L(y_k) where L(y_i) is the length of the road y_i (1<=i<=k). Your program has to find such a sightseeing route, the length of which is minimal, or to specify that it is not possible,because there is no sightseeing route in the town.
Input
The first line of input contains two positive integers: the number of crossing points N<=100 and the number of roads M<=10000. Each of the next M lines describes one road. It contains 3 positive integers: the number of its first crossing point, the number of the second one, and the length of the road (a positive integer less than 500).
Output
There is only one line in output. It contains either a string ‘No solution.‘ in case there isn‘t any sightseeing route, or it contains the numbers of all crossing points on the shortest sightseeing route in the order how to pass them (i.e. the numbers x_1 to x_k from our definition of a sightseeing route), separated by single spaces. If there are multiple sightseeing routes of the minimal length, you can output any one of them.
Sample Input
5 7 1 4 1 1 3 300 3 1 10 1 2 16 2 3 100 2 5 15 5 3 20
Sample Output
1 3 5 2
Source
CEOI 1999
#include<cstdio> #include<iostream> #include<algorithm> using namespace std; const int MAXN=105; const int INF=1e6;//改成1e9就不对了 int dis[MAXN][MAXN],mp[MAXN][MAXN]; int R[MAXN][MAXN],path[MAXN]; int N,M,len; int u,v,w; int cnt=0; void Init() { for(int i=0;i<=N;i++) for(int j=0;j<=N;j++) dis[i][j]=INF,R[i][j]=0; cnt=0; } void Path(int s,int t) { if(R[s][t]) { Path(s,R[s][t]); Path(R[s][t],t); } else path[++cnt]=t; } void Floyd() { len=INF; for(int k=1;k<=N;k++) {
//判断负环 for(int i=1;i<k;i++) for(int j=i+1;j<k;j++) { if(len>dis[i][j]+mp[i][k]+mp[k][j]) { len=dis[i][j]+mp[i][k]+mp[k][j]; cnt=0; path[++cnt]=i; Path(i,j); path[++cnt]=k; } } //求最短路 for(int i=1;i<=N;i++) for(int j=1;j<=N;j++) { if(dis[i][j]>dis[i][k]+dis[k][j]) { dis[i][j]=dis[i][k]+dis[k][j]; R[i][j]=k; } } } } int main () { while(~scanf("%d%d",&N,&M)) { Init(); for(int i=1;i<=M;i++) { scanf("%d%d%d",&u,&v,&w); if(dis[u][v]>w)//记录重边 { dis[u][v]=w; dis[v][u]=w; } } for(int i=1;i<=N;i++) for(int j=1;j<=N;j++) mp[i][j]=dis[i][j];//mp判断环的时候要用到 Floyd(); if(len==INF) printf("No solution.\n"); else { for(int i=1;i<=cnt;i++) { if(i!=cnt) printf("%d ",path[i]); else printf("%d\n",path[i]); } } } return 0; }
POJ1734/Floyd求最小环
声明:以上内容来自用户投稿及互联网公开渠道收集整理发布,本网站不拥有所有权,未作人工编辑处理,也不承担相关法律责任,若内容有误或涉及侵权可进行投诉: 投诉/举报 工作人员会在5个工作日内联系你,一经查实,本站将立刻删除涉嫌侵权内容。