POJ 1258 Agri-Net（最小生成树）

最新推荐文章于 2019-08-24 23:34:37 发布

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最新推荐文章于 2019-08-24 23:34:37 发布

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原文链接：http://www.cnblogs.com/syhandll/p/4675888.html

本文探讨了如何使用最小生成树算法解决农民约翰的互联网连接问题，通过优化光纤线路布局，确保所有农场都能高效互联，同时降低整体成本。

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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

Sample Output

Kruskal算法（运用并查集思想）：
#include<stdio.h>
#include<stdlib.h>
#define N 20010
int f[N], n;
struct node
{
    int s, e, d;
}no[N];
void Init()
{
    int i;
    for (i = 0; i <= n; i++)
        f[i] = i;
}
int cmp(const void *a, const void *b)
{
    node *s1 = (node *)a, *s2 = (node *)b;
    return s1->d - s2->d;
}
int Find(int x)
{
    if (f[x] != x)
        f[x] = Find(f[x]);
    return f[x];
}
int main ()
{
    int k, a, ans, i, j, ns, ne;
    while (scanf("%d", &n) != EOF)
    {
        ans = 0;
        k = 0;
        Init();
        for (i = 1; i <= n; i++)
        {
            for(j = 1; j <= n; j++)
            {
                scanf("%d", &a);
                no[k].s = i;
                no[k].e = j;
                no[k].d = a;
                k++;
            }
        }
        qsort(no, k, sizeof(no[0]), cmp);
        for (i = 0; i < k; i++)
        {
            ns = Find(no[i].s);
            ne = Find(no[i].e);
            if (ns != ne)
            {
                f[ns] = ne;
                ans += no[i].d;
            }
        }
        printf("%d\n", ans);
    }
    return 0;
}

Prim算法：
#include<stdio.h>
#include<string.h>
#define INF 0x3f3f3f3f
#define N 110
int Map[N][N], dist[N], visit[N], n, ans;
void Prim()
{
    int i, j, Min, idex;
    memset(visit, 0, sizeof(visit));
    visit[1] = 1;
    for (i = 1; i <= n; i++)
        dist[i] = Map[1][i];
    for (i = 1; i < n; i++)
    {
        Min = INF;
        for (j = 1; j <= n; j++)
        {
            if (dist[j] < Min && !visit[j])
            {
                Min = dist[j];
                idex = j;
            }
        }
        visit[idex] = 1;
        ans += Min; //统计最小权值
        for (j = 1; j <= n; j++)
        {
            if (!visit[j] && dist[j] > Map[idex][j])
                dist[j] = Map[idex][j];
        }
    }
}
int main ()
{
    int i, j;
    while (scanf("%d", &n) != EOF)
    {
        ans = 0;
        for (i = 1; i <= n; i++)
        {
            for (j = 1; j <= n; j++)
                scanf("%d", &Map[i][j]);
        }
        Prim(); //假设每次将结点1先加入最小生成树，直到n个结点全部加入
        printf("%d\n", ans);
    }
    return 0;
}