最小生成树两种算法。kruskal和prim

测试数据：
8
0 2 8 1 0 0 0 0
2 0 6 0 1 0 0 0
8 6 0 7 5 1 2 0
1 0 7 0 0 0 9 0
0 1 5 0 0 3 0 8
0 0 1 0 3 0 4 6
0 0 2 9 0 4 0 3
0 0 0 0 8 6 3 0

8个点，矩阵m[i][j]代表i与j的距离。
kruskal
所有边按长度从小到大排序，如果边的两点连在一起，那么就不添加边，如果不连在一起，就添加边。用并查集维护是否连在一起。

/***********************************************\
 |Author: YMC
 |Created Time: 2014-5-9 18:25:59
 |File Name: kruskal.cpp
 |Description: 
\***********************************************/
#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <string>
#include <cstring>
#include <algorithm>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <stack>
using namespace std;
#define N 100
#define inf 1<<29
struct seg{
    int x,y,c;
}se[1000];
int n;
int ma[N][N];
int fa[N];
int cnt;
void init(int n){
    for(int i=1;i<=n;++i) fa[i] = i;
}
int find(int x){
    return fa[x] = fa[x] == x ? x : find(fa[x]);        //路径优化，可以使查询速度稳定在O(n) 
}
void merge(int x,int y){
    int a = find(x);
    int b = find(y);
    fa[a] = b;
}
bool judge(int x,int y){
    if(find(x) == find(y)) return true;
    else return false;
}
bool cmp(seg a,seg b){
    return a.c < b.c;
}
int kruskal()
{
    sort(se,se+cnt,cmp);    //边排序 
    init(n);        //并查集初始化 
    int cas = 0;
    int ans = 0;
    for(int i=0;i<cnt;++i){
        int x = se[i].x;
        int y = se[i].y;
        int c = se[i].c;
        if(!judge(x,y)){
            //cout<<x<<" "<<y<<endl;
            ans += c;
            cas ++;
            if(cas == n-1) return ans;
        }
    }
}
int main() {
    freopen("input.txt","r",stdin);
    scanf("%d",&n);
    cnt = 0; 
    for(int i=1;i<=n;++i){          //输入 
        for(int j=1;j<=n;++j)
        {
            scanf("%d",&ma[i][j]);
            if(ma[i][j] == 0) ma[i][j] = inf;
        }
    }
    for(int i=1;i<n;++i){       //放入边 
        for(int j=i+1;j<=n;++j){
            seg tp;
            tp.x = i;
            tp.y = j;
            tp.c = ma[i][j];
            se[cnt ++] = tp;
        }
    }
    printf("%d\n",kruskal());       //输出最小生成树长度 
    return 0;

}

prim
类似dijstra,从一个点开始找，每次找到与当前连在一起的点的最短的距离的那个点，然后添加那条当前最短的边。

/***********************************************\
 |Author: YMC
 |Created Time: 2014-5-9 18:13:44
 |File Name: prim.cpp
 |Description: 
\***********************************************/
#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <string>
#include <cstring>
#include <algorithm>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <stack>

using namespace std;
#define N 100
#define inf 1<<29
int n;
int ma[N][N];
int dis[N];
bool vis[N];
int prim()
{
    for(int i=1;i<=n;++i) dis[i] = inf;
    memset(vis,false,sizeof(vis));
    dis[1] = 0;
    vis[1] = true;
    for(int i=2;i<=n;++i) dis[i] = ma[1][i];
    int ans = 0;
    for(int ii = 2;ii<=n;++ii){
        int minn = inf;
        int pos = -1;
        for(int i=2;i<=n;++i){
            if(!vis[i] && minn > dis[i]){
                minn = dis[i];
                pos = i;
             }
        }
        dis[pos] = minn;
        vis[pos] = true;
        ans += minn;
        for(int i=1;i<=n;++i){
            if(!vis[i] && dis[i]>ma[pos][i]){
                dis[i] = ma[pos][i];
            }
        }
    }
    return ans;
}
int main() {
    freopen("input.txt","r",stdin);
    scanf("%d",&n); 
    for(int i=1;i<=n;++i){
        for(int j=1;j<=n;++j)
        {
            scanf("%d",&ma[i][j]);
            if(ma[i][j] == 0) ma[i][j] = inf;
        }
    }
    printf("%d\n",prim());
    return 0;

}