ZOJ1406，POJ1251

题意：求连接所有村子的最短路

prim+邻接矩阵

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
using namespace std;
#define inf 999999
#define N 30
int n,dis[N],vis[N],g[N][N];

int prim(int root)
{
    for(int i=1; i<=n; i++)
    dis[i]= g[i][root],vis[i]= 0;
    dis[root]= 0;
    vis[root]=1;
    int cost= 0;
    for(int T=1; T<=n-1; T++)
    {
        int mindis= inf,idx= -1;
        for(int i=1; i<=n; i++)
        {
            if( vis[i]==0 )
            {
                if( mindis>dis[i] )
                {
                    mindis= dis[i];
                    idx= i;
                }
            }
        }
        cost+=mindis;
        if( idx==-1 ) return -1;
        vis[idx]= 1;
        for(int i=1; i<=n; i++)
        {
            if( vis[i]==0 )
            {
                if( dis[i]>g[i][idx] )
                dis[i]= g[i][idx];
            }
        }
    }
    return cost;
} 

int main()
{
    char op1[2],op2[2];
    int co,w;
    while(scanf("%d",&n)&&n)
    {
        for(int i=0; i<=N; i++)
        for(int j=0; j<=N; j++)
        {
            if(i==j) g[i][j] = 0;
            else g[i][j] = inf;
        }
        for(int i=1; i<=n-1; i++)
        {
            scanf("%s%d",op1,&co);
            for(int j=1; j<=co; j++)
            {
                scanf("%s%d",op2,&w);
                int u = op1[0]-'A'+1;
                int v = op2[0]-'A'+1;
                g[u][v] = g[v][u] = min(g[u][v],w);
            }
        }
        int ans=prim(1);
        printf("%d
",ans);
    }
    return 0;
}

prim+优先队列

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<queue>
using namespace std;
#define M 200
#define N 30
const int inf= 999999;
int n,size;
typedef pair<int,int>mp;

int head[N];
int dis[N];
int vis[N];

struct Edge
{
    int v,w,next;
    Edge(){}
    Edge(int V,int W,int NEXT):v(V),w(W),next(NEXT){}
}edge[M];

void Init()
{
    memset(head,-1,sizeof(head));
    size = 0;
}

void InsertEdge(int u,int v,int w)
{
    edge[size] = Edge(v,w,head[u]);
    head[u] = size++;
    edge[size] = Edge(u,w,head[v]);
    head[v] =size++;
}

int prim(int s)
{
    int cost= 0;
    int times = 0;
    for(int i=1; i<=n; i++)
    {
        vis[i] = 0;
        dis[i] = inf;
    }
    mp p(0,s);

    priority_queue< mp,vector<mp>,greater<mp> > Q;
    Q.push(mp(0,s));
    while(!Q.empty()&&times<n)
    {
        do
        {
            p = Q.top();
            Q.pop();
        }while(vis[p.second]==1&&!Q.empty());
        if(vis[p.second]==0)
        {
            cost += p.first;
            vis[p.second] = 1;
            times ++;
            for(int i = head[p.second]; i!=-1; i=edge[i].next)
            {
                int v = edge[i].v;
                if(vis[v]==0)
                {
                    if(edge[i].w < dis[v])
                    {
                        dis[v] = edge[i].w;
                        Q.push(mp(dis[v],v));
                    }
                }
            }
        }
    }
    if(times<n) 
    return -1;
    return cost;
} 
int main()
{
    char op1[2],op2[2];
    int co,w;
    while(scanf("%d",&n)&&n)
    {
        Init();
        for(int i=1; i<=n-1; i++)
        {
            scanf("%s%d",op1,&co);
            for(int j=1; j<=co; j++)
            {
                scanf("%s%d",op2,&w);
                int u = op1[0]-'A'+1;
                int v = op2[0]-'A'+1;
                int flag = 0;
                for(int k=head[u]; k!=-1; k=edge[k].next)
                {//重边的情况
                    if(v == edge[j].v)
                    {
                        if(w < edge[j].w)
                        edge[j].w = w;
                        flag = 1;
                        break;
                    }
                }
                if(flag) continue;
                InsertEdge(u,v,w);
            }
        }
        int ans=prim(1);
        printf("%d
",ans);
    }
    return 0;
}

kruskal

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

#define N 30
#define M 100
int n,m,father[N],rank[N],sum;
struct Edge
{
    int u;
    int v;
    int w;
}edge[M];

bool cmp(Edge a,Edge b)
{
    return a.w < b.w ;
}

void Init()
{
    for(int i=0; i<=n; i++)
    {
        father[i] = i;
        rank[i] = 1;
    }
}

int find(int x)
{
    if(father[x] != x)
    {
        father[x] = find(father[x]);
    }
    return father[x];
}

void merge(int x,int y)
{
    int xf = find(x);
    int yf = find(y);
    if(rank[x] > rank[y])
    {
        rank[xf] += rank[yf];
        father[yf] = xf;
    }
    else
    {
        rank[yf] += rank[xf];
        father[xf] = yf;
    }
}

void Kruskal()
{
    int num = 0;
    for(int i=0; i<m; i++)
    {
        int u = edge[i].u;
        int v = edge[i].v;
        if(find(u) != find(v))
        {
            num++;
            sum += edge[i].w;
            merge(u,v);
        }
        if(num==n-1) break;
    }
}

int main()
{
    char op1[2],op2[2];
    int co,w,cnt;
    while(scanf("%d",&n)&&n)
    {
        Init();
        cnt = 0;
        for(int i=1; i<n; i++)
        {
            scanf("%s%d",op1,&co);
            for(int j=1; j<=co; j++)
            {
                scanf("%s%d",op2,&w);
                int u = op1[0]-'A'+1;
                int v = op2[0]-'A'+1;
                edge[cnt].u = u ; edge[cnt].v = v ; edge[cnt].w = w;
                cnt++;
            }
        }
        m = cnt;
        sort(edge,edge+m,cmp);
        sum = 0;
        Kruskal();
        printf("%d
",sum);
    }
    return 0;
}