POJ 1258, Agri-Net

本文深入探讨了在给定多个农场间连接成本的情况下,如何利用最小生成树算法找到连接所有农场所需的最少光纤长度。通过具体实例,展示了算法的实现过程,包括初始化、选择最小边、更新连接状态等关键步骤。

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Time Limit: 1000MS  Memory Limit: 10000K
Total Submissions: 11276  Accepted: 4707


Description
Farmer John has been elected mayor of his town! One of his campaign promises was to bring internet connectivity to all farms in the area. He needs your help, of course.
Farmer John ordered a high speed connection for his farm and is going to share his connectivity with the other farmers. To minimize cost, he wants to lay the minimum amount of optical fiber to connect his farm to all the other farms.
Given a list of how much fiber it takes to connect each pair of farms, you must find the minimum amount of fiber needed to connect them all together. Each farm must connect to some other farm such that a packet can flow from any one farm to any other farm.
The distance between any two farms will not exceed 100,000.

 

Input
The input includes several cases. For each case, the first line contains the number of farms, N (3 <= N <= 100). The following lines contain the N x N conectivity matrix, where each element shows the distance from on farm to another. Logically, they are N lines of N space-separated integers. Physically, they are limited in length to 80 characters, so some lines continue onto others. Of course, the diagonal will be 0, since the distance from farm i to itself is not interesting for this problem.

 

Output
For each case, output a single integer length that is the sum of the minimum length of fiber required to connect the entire set of farms.

 

Sample Input
4
0 4 9 21
4 0 8 17
9 8 0 16
21 17 16 0

 

Sample Output
28

 

Source
USACO 102


// POJ1258.cpp : Defines the entry point for the console application.
//

#include 
<iostream>
#include 
<numeric>
using namespace std;

int main(int argc, char* argv[])
{
    
int N;
    
int d[101][101];
    
bool used[101];
    
int l[101];
    
while (cin >> N && N != 0)
    {
        
for (int i = 0; i < N; ++i)
            
for (int j = 0; j < N; ++j)
                cin 
>>d[i][j];

        
for (int i = 0; i < N; ++i) l[i] = d[0][i];
        used[
0= true;
        memset(used, 
0sizeof(used));

        
for (int i = 0; i < N; ++i)
        {
            
int len = 100000;
            
int pos = 0;
            
            
for (int j = 0; j < N; ++j)
                
if (used[j] == false && l[j] < len)
                {
                    len 
= l[j];
                    pos 
= j;
                };

            used[pos] 
= true;

            
for (int j = 0; j < N; ++j)
                
if (used[j] == false && l[j] > d[pos][j]) l[j] = d[pos][j];
        }

        cout 
<< accumulate(&l[0], &l[N], 0<<endl;
    }
    
return 0;
}

转载于:https://www.cnblogs.com/asuran/archive/2009/10/01/1577158.html

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