poj1258 Agri-Net（Prime || Kruskal）

题目链接

http://poj.org/problem?id=1258

题意

有n个农场，现在要在n个农场之间铺设光纤使得n个农场连接起来，求铺设光纤的最短距离。

思路

最小生成树问题，使用Prime算法或者Kruskal算法解决。

代码

Prime算法：

#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;

const int INF = 0x7fffffff;
const int N = 100 + 10;
int map[N][N];
int dist[N];
int n;

void prime()
{
    int min_edge, min_node;
    for (int i = 0; i < n; i++)
        dist[i] = INF;
    int ans = 0;
    int now = 0;
    for (int i = 0; i < n - 1; i++)
    {
        dist[now] = -1;
        min_edge = INF;
        for (int j = 0; j < n; j++)
        {
            if (j != now && dist[j] >= 0)
            {
                if (map[now][j]>0)
                    dist[j] = min(dist[j], map[now][j]);
                if (dist[j] < min_edge)
                {
                    min_edge = dist[j];    //min_edge存储与当前结点相连的最短的边
                    min_node = j;
                }
            }
        }
        ans += min_edge;
        now = min_node;
    }
    printf("%d\n", ans);
}

int main()
{
    //freopen("poj1258.txt", "r", stdin);
    while (scanf("%d", &n) == 1)
    {
        memset(map, 0, sizeof(map));    //注意初始化
        for (int i = 0; i < n; i++)
            for (int j = 0; j < n; j++)
                cin >> map[i][j];
        prime();
    }
    return 0;
}

Kruskal算法：

#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdio>
#include <vector>
using namespace std;

struct Edge
{
    int a, b, dist;

    Edge() {}
    Edge(int a, int b, int d) :a(a), b(b), dist(d) {}
};

bool cmp(Edge e1, Edge e2)
{
    return e1.dist < e2.dist;
}

const int N = 100 + 10;
vector<Edge> v;
int p[N];
int map[N][N];
int n;

int find_root(int x)
{
    if (p[x] == -1)
        return x;
    else return find_root(p[x]);
}

void kruskal()
{
    memset(p, -1, sizeof(p));
    sort(v.begin(), v.end(), cmp);    //将边按边长从短到长排序
    int ans = 0;
    for (int i = 0; i < v.size(); i++)
    {
        int ra = find_root(v[i].a);
        int rb = find_root(v[i].b);
        if (ra != rb)
        {
            ans += v[i].dist;
            p[ra] = rb;
        }
    }
    printf("%d\n", ans);
}

int main()
{
    //freopen("poj1258.txt", "r", stdin);
    while (scanf("%d", &n) == 1)
    {
        v.clear();    //注意初始化
        for (int i = 0; i < n; i++)
            for (int j = 0; j < n; j++)
                cin >> map[i][j];
        for (int i = 0; i < n; i++)
            for (int j = 0; j < n; j++)
                if (i < j) v.push_back(Edge(i, j, map[i][j]));
        kruskal();
    }
    return 0;
}