MST& Prime算法& Kruskal算法

hdu1301–MST板题

prime + 邻接矩阵
O(n^2)

//
//  main.cpp
//  MST板题_hdu1301
//
//  Created by 陈冉飞 on 2019/9/23.
//  Copyright © 2019 陈冉飞. All rights reserved.
//

#include <iostream>
using namespace std;
#define maxn 30
int mp[maxn][maxn],n,m,l,d[maxn],vis[maxn];     //mp[][]邻接矩阵储存
char s[10],t[10];
#define INF 0x3f3f3f
#include <cstring>
#define cl(a,b) memset(a,b,sizeof(a))

int prime(){
    for (int i = 0; i < n; i++) d[i] = mp[0][i];
    d[0] = 0;vis[0] = 1;
    int ans = 0;
    for (int i = 1; i < n; i++) {
        int v = -1,tem = INF;
        for (int j = 0; j < n; j++)
            if (!vis[j] && d[j] < tem) {
                v = j;tem = d[j];
            }
        vis[v] = 1;ans += tem;
        for (int j = 1; j < n; j++)
            if (!vis[j] && mp[v][j] < d[j]) d[j] = mp[v][j];
    }
    return ans;
}

int main(int argc, const char * argv[]) {
    while (~scanf("%d",&n) && n) {
        //init
        cl(mp, 0);cl(vis, 0);cl(d, 0);
        for (int i = 0; i < n; i++)
            for (int j = 0; j < n; j++)
                if (i == j) mp[i][j] = 0;
                else mp[i][j] = INF;
        for (int e = 0; e < n-1; e++) {
            scanf("%s%d",s,&m);
            while (m--) {
                scanf("%s%d",t,&l);
                if (mp[s[0]-'A'][t[0]-'A'] > l) mp[s[0]-'A'][t[0]-'A'] = mp[t[0]-'A'][s[0]-'A'] = l;
            }
        }
//        for (int i = 0; i < n; i++){
//            for (int j = 0; j < n; j++)
//                printf("%d ",mp[i][j]);
//            printf("\n");
//        }
        cout<<prime()<<endl;
    }
    return 0;
}

kruskal + 邻接表
O(m*logn)

//
//  main.cpp
//  MST板题hdu1301_Kruskal实现
//
//  Created by 陈冉飞 on 2019/9/25.
//  Copyright © 2019 陈冉飞. All rights reserved.
//

#include <iostream>
using namespace std;
#include <cstring>
#define cl(a,b) memset(a,b,sizeof(a))
#define maxn 30
#include <algorithm>

struct node{
    int s,e,w;
}edge[maxn<<4];   //邻接表储存图中的结构
int fa[maxn],n,m,l,cnt;
char s[10],t[10];

bool cmp(node x,node y){return x.w < y.w;}

int findfa(int x){
    if (x != fa[x]) fa[x] = findfa(fa[x]);
    return fa[x];
}

int kruskal(){
    sort(edge,edge+cnt,cmp);
    int ans = 0;
    //遍历所有的边
    for (int i = 0; i < cnt; i++)
        if (findfa(edge[i].s) != findfa(edge[i].e)) {
            ans += edge[i].w;
            fa[findfa(edge[i].s)] = findfa(edge[i].e);
        }
    return ans;
}

int main(int argc, const char * argv[]) {
    while (~scanf("%d",&n) && n) {
        //init
        cnt = 0;cl(fa,0);
        for (int i = 0; i < n; i++) fa[i] = i;
        for (int e = 0; e < n-1; e++) {
            scanf("%s%d",s,&m);
            while (m--) {
                scanf("%s%d",t,&l);
                edge[cnt].s = s[0]-'A';
                edge[cnt].e = t[0]-'A';
                edge[cnt++].w = l;
            }
        }
//        for (int i = 0; i < cnt; i++) cout<<i<<" "<<edge[i].s<<" "<<edge[i].e<<" "<<edge[i].w<<endl;
        cout<<kruskal()<<endl;
    }
    return 0;
}

Poj1679