poj1751 Highways 最小生成树(小组赛A)
来源:互联网 发布:录音人声放大软件 编辑:程序博客网 时间:2024/04/30 23:56
链接:http://poj.org/problem?id=1751
Highways
Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 13584 Accepted: 3954 Special Judge
Description
The island nation of Flatopia is perfectly flat. Unfortunately, Flatopia has a very poor system of public highways. The Flatopian government is aware of this problem and has already constructed a number of highways connecting some of the most important towns. However, there are still some towns that you can't reach via a highway. It is necessary to build more highways so that it will be possible to drive between any pair of towns without leaving the highway system.
Flatopian towns are numbered from 1 to N and town i has a position given by the Cartesian coordinates (xi, yi). Each highway connects exaclty two towns. All highways (both the original ones and the ones that are to be built) follow straight lines, and thus their length is equal to Cartesian distance between towns. All highways can be used in both directions. Highways can freely cross each other, but a driver can only switch between highways at a town that is located at the end of both highways.
The Flatopian government wants to minimize the cost of building new highways. However, they want to guarantee that every town is highway-reachable from every other town. Since Flatopia is so flat, the cost of a highway is always proportional to its length. Thus, the least expensive highway system will be the one that minimizes the total highways length.
Flatopian towns are numbered from 1 to N and town i has a position given by the Cartesian coordinates (xi, yi). Each highway connects exaclty two towns. All highways (both the original ones and the ones that are to be built) follow straight lines, and thus their length is equal to Cartesian distance between towns. All highways can be used in both directions. Highways can freely cross each other, but a driver can only switch between highways at a town that is located at the end of both highways.
The Flatopian government wants to minimize the cost of building new highways. However, they want to guarantee that every town is highway-reachable from every other town. Since Flatopia is so flat, the cost of a highway is always proportional to its length. Thus, the least expensive highway system will be the one that minimizes the total highways length.
Input
The input consists of two parts. The first part describes all towns in the country, and the second part describes all of the highways that have already been built.
The first line of the input file contains a single integer N (1 <= N <= 750), representing the number of towns. The next N lines each contain two integers, xi and yi separated by a space. These values give the coordinates of ith town (for i from 1 to N). Coordinates will have an absolute value no greater than 10000. Every town has a unique location.
The next line contains a single integer M (0 <= M <= 1000), representing the number of existing highways. The next M lines each contain a pair of integers separated by a space. These two integers give a pair of town numbers which are already connected by a highway. Each pair of towns is connected by at most one highway.
The first line of the input file contains a single integer N (1 <= N <= 750), representing the number of towns. The next N lines each contain two integers, xi and yi separated by a space. These values give the coordinates of ith town (for i from 1 to N). Coordinates will have an absolute value no greater than 10000. Every town has a unique location.
The next line contains a single integer M (0 <= M <= 1000), representing the number of existing highways. The next M lines each contain a pair of integers separated by a space. These two integers give a pair of town numbers which are already connected by a highway. Each pair of towns is connected by at most one highway.
Output
Write to the output a single line for each new highway that should be built in order to connect all towns with minimal possible total length of new highways. Each highway should be presented by printing town numbers that this highway connects, separated by a space.
If no new highways need to be built (all towns are already connected), then the output file should be created but it should be empty.
If no new highways need to be built (all towns are already connected), then the output file should be created but it should be empty.
Sample Input
91 50 0 3 24 55 10 45 21 25 331 39 71 2
Sample Output
1 63 74 95 78 3题意:有N个城市的坐标(x,y),城市之间有公路,现在有m个条公路是完整的,连接两个城市,问要使得任意两个城市连通并且路的总距离最短,如何建路,输出路径
思路:最小生成树的题,相当于它已经给你一些已经加到里面的边,让你加入其它边,使得所加入边的权和最小。
Prim算法
#include <iostream>#include <cstdio>#include <cstdlib>#include <cmath>#include <algorithm>#include <climits>#include <cstring>#include <string>#include <set>#include <map>#include <queue>#include <stack>#include <vector>#include <list>#include<functional>#define mod 1000000007#define inf 0x3f3f3f3f#define pi acos(-1.0)using namespace std;typedef long long ll;const int N=10005;const int M=15005;int n,m,k,edg[N][N],x[N],y[N],lowcost[N],pre[N];void Prim() { for(int i=1;i<=n;i++){ lowcost[i]=edg[1][i]; pre[i]=1; } lowcost[1]=-1; for(int i=1;i<n;i++){ int minn=inf; for(int j=1;j<=n;j++){ if(lowcost[j]!=-1&&lowcost[j]<minn){ minn=lowcost[j]; k=j; } } if(lowcost[k]!=0)printf("%d %d\n",pre[k],k); lowcost[k]=-1; for(int j=1;j<=n;j++){ if(edg[j][k]<lowcost[j]){ lowcost[j]=edg[j][k]; pre[j]=k; } } }}int main() { while(~scanf("%d",&n)) { for(int i=1; i<=n; i++) { scanf("%d%d",&x[i],&y[i]); for(int j=1; j<i; j++) edg[i][j]=edg[j][i]=(x[i]-x[j])*(x[i]-x[j])+(y[i]-y[j])*(y[i]-y[j]); edg[i][i]=inf; } scanf("%d",&m); for(int i=0; i<m; i++) { int ita,itb; scanf("%d%d",&ita,&itb); edg[ita][itb]=edg[itb][ita]=0; } Prim(); } return 0;}
0 0
- poj1751 Highways 最小生成树(小组赛A)
- poj1751 Highways(最小生成树)
- poj1751 highways 最小生成树记录路径
- POJ1751 Highways(最小生成树)(prim)
- POJ1751 Highways(最小生成树,Kruskal模板题)
- poj1751-最小生成树
- POJ1751->最小生成树
- poj1751——Highways(部分确定的最小生成树)
- 最小生成树Highways
- poj1751 Highways
- POJ1751 Highways
- POJ1751 Highways
- POJ1751 Highways
- poj1751 Highways
- 2485highways{最小生成树}
- Highways(最小生成树)
- poj2485 Highways(最小生成树)
- 1751 Highways【最小生成树】
- 正数求和
- Java学习笔记--解析JDK与IDE(Linux下Java环境变量的配置)
- ADB命令简单使用技巧(Android)
- C语言学习第二章
- javascript 小知识整理
- poj1751 Highways 最小生成树(小组赛A)
- js生成多html节点
- log4j,self4j
- Trailing Zero解题思路及java代码实现
- php disk_free_space与disk_total_space实例介绍
- hduoj1677
- typeid
- 建makefile
- Hadoop 启动脚本分析