最小生成树专题

poj2421,poj2560,poj1789

这些都是一些比较基础的最小生成树的题目，在这里我分别用两种方法来实现--kruskal以及prim(其中prim是建哥写的,kruskal是我写的).

//poj2421 kruskal
#include <iostream>
#include<cstdio>
#include<algorithm>
using namespace std;
#define INF 0x3f3f3f3f
int n,m;
int a[105][105],d;
int p[105],xa,yb;
int sum,res;
typedef struct Node
{
    int value;
    int l;
    int r;
};
Node edges[105*105];
int find_set(int x)
{
    if(x!=p[x])
        p[x]=find_set(p[x]);
    return p[x];
}
bool cmp(Node e1,Node e2)
{
    return e1.value<e2.value;
}
int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
    {
        p[i]=i;
    }
    int sym=0,mm=0,m=0;
    for(int i=1;i<=n;i++)
    {
        for(int j=1;j<=n;j++)
        {
            scanf("%d",&d);
            a[i][j]=a[j][i]=d;

        }
    }
    scanf("%d",&mm);
    for(int i=0;i<mm;i++)
    {
        scanf("%d%d",&xa,&yb);
        a[xa][yb]=0;

    }
    for(int i=1;i<n;i++)
    {
        for(int j=i+1;j<=n;j++)
        {
            edges[m].l=i;
            edges[m].r=j;
            edges[m].value=a[i][j];
            m++;
        }
    }
    sort(edges,edges+m,cmp);
    for(int i=0;i<m;i++)
    {
        int fx=find_set(edges[i].l);
        int fy=find_set(edges[i].r);
        if(fx!=fy)
        {
            sum+=edges[i].value;
            p[fy]=fx;
        }

    }
    printf("%d\n",sum);

  return 0;
}

//poj2421 prim
#include <stdio.h>
#include <string.h>

#define INF 0x3f3f3f3f

int maps[305][305];
bool vis[305];
int dis[305];
int n;

int Prim()
{
    memset(vis,false,sizeof(vis));
    for(int i=1; i<=n; i++)
        dis[i] = INF;
    int ans=0;
    dis[1] = 0;
    for(int i=1; i<=n; i++)
    {
        int tmp = INF,k=0;
        for(int j=1; j<=n; j++)
        {
            if(!vis[j]&&dis[j]<tmp)
            {
                tmp = dis[j];
                k=j;
            }
        }

        vis[k] = true;
        ans+=tmp;
        for(int i=1; i<=n; i++)
        {
            if(!vis[i]&&dis[i]>maps[k][i])
                dis[i] = maps[k][i];
        }
    }
    return ans;
}

int main()
{
    while(scanf("%d",&n),n)
    {
        for(int i=0; i<=n; i++)
        {
            for(int j=0; j<=n; j++)
                if(i==j)
                    maps[i][j]=0;
                else maps[i][j] = INF;
        }
        for(int i=0; i<n-1; i++)
        {
            int t;
            char a[2],b[2];
            scanf("%s%d",a,&t);
            for(int j=0; j<t; j++)
            {
                int dist;
                scanf("%s%d",b,&dist);
                maps[a[0]-'A'+1][b[0]-'A'+1] = maps[b[0]-'A'+1][a[0]-'A'+1] = dist;
            }
        }
        printf("%d\n",Prim());
    }
    return 0;
}

//poj2560 kruskal

#include<iostream>
#include<cstdio>
#include<cmath>
#include<algorithm>
using namespace std;
int t;
typedef struct Node
{
    double x;
    double y;
};
typedef struct Edge
{
    int l;
    int r;
    double value;
};
Edge edges[105*105];
Node node[105];
int p[105],n;
double sum;
bool cmp(Edge e1,Edge e2)
{
    return e1.value<e2.value;
}
int find_set(int x)
{
    if(x!=p[x])
        p[x]=find_set(p[x]);
    return p[x];
}
int main()
{
    sum=0;
    scanf("%d",&n);

    for(int i=1;i<=n;i++)
    {
        scanf("%lf%lf",&node[i].x,&node[i].y);
        p[i]=i;
    }
    int m=0;
   for(int i=1;i<=n;i++)
   {
       for(int j=1;j<=n;j++)
       {
            double d=sqrt((node[i].x-node[j].x)*(node[i].x-node[j].x)+(node[i].y-node[j].y)*(node[i].y-node[j].y));
            edges[m].l=i;
            edges[m].r=j;
            edges[m++].value=d;
       }
   }

    sort(edges,edges+m,cmp);

   /* for(int i=0;i<m;i++)
    {
        printf("%lf\n",edges[i].value);
    }*/

    for(int i=0;i<m;i++)
    {
        int fx=find_set(edges[i].l);
        int fy=find_set(edges[i].r);
        if(fx!=fy)
        {
            sum+=edges[i].value;
            p[fy]=fx;
        }
    }
    printf("%.2lf\n",sum);
    return 0;
}

//poj 2560 prim
#include <stdio.h>
#include <string.h>
#include <math.h>

#define INF 0x3f3f3f3f

int n;
double maps[300][300];
bool vis[300];
double dis[300];

struct Point {
    double x;
    double y;
}points[300];

double Prim()
{
    memset(vis,false,sizeof(vis));
    for(int i=1;i<=n;i++)
        dis[i] = INF;

    dis[1] = 0;
    double ans =0;
    for(int i=1;i<=n;i++)
    {
        double tmp = INF;
        int k =0;
        for(int j=1;j<=n;j++)
        {
            if(!vis[j]&&dis[j]<tmp)
            {
                tmp = dis[j];
                k= j;
            }
        }

        vis[k]=true;
        ans+=tmp;
        for(int i=1;i<=n;i++)
        {
            if(!vis[i]&&dis[i]>maps[k][i])
                dis[i] = maps[k][i];
        }
    }
    return ans;
}

int main()
{

    scanf("%d",&n);
    for(int i=1;i<=n;i++)
        scanf("%lf%lf",&points[i].x,&points[i].y);

    for(int i=1;i<=n;i++)
    {
        for(int j=1;j<=n;j++)
        {
            double x = points[i].x - points[j].x;
            double y = points[i].y - points[j].y;
            maps[i][j] = sqrt(x*x+y*y);
        }
    }
    printf("%.2lf\n",Prim());

    return 0;
}

//poj1789 kruskal

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int n;
char str[2050][10];
int p[2050];
typedef struct Edge
{
  int l;
  int r;
  int value;
};
bool cmp(Edge e1,Edge e2)
{
    return e1.value<e2.value;
}
int find_set(int x)
{
    if(x!=p[x])
        p[x]=find_set(p[x]);
    return p[x];
}
Edge edges[2050*2050];
int getDif(int x,int y)
{
    int num=0;
    for(int i=0;i<7;i++)
    {
        if(str[x][i]!=str[y][i])
        {
            num++;
        }
    }
    return num;
}
int main()
{

    while(scanf("%d",&n)&&n!=0)
    {
        memset(edges,0,sizeof(edges));
        memset(str,0,sizeof(str));
        int m=0;
        for(int i=1;i<=n;i++)
        {
            scanf("%s",str[i]);
            p[i]=i;
        }

        for(int i=1;i<=n;i++)
        {
            for(int j=i+1;j<=n;j++)
            {
                int num=getDif(i,j);
                edges[m].l=i;
                edges[m].r=j;
                edges[m++].value=num;
            }
        }
        sort(edges,edges+m,cmp);
        int sum=0;
        for(int i=0;i<m;i++)
        {
            int fx=find_set(edges[i].l);
            int fy=find_set(edges[i].r);
            if(fx!=fy)
            {
                sum+=edges[i].value;
                p[fy]=fx;
            }
        }
        printf("The highest possible quality is 1/%d.\n",sum);

    }

return 0;

}

//poj1789 prim
#include <stdio.h>
#include <string.h>

#define INF 0x3f3f3f3f

int maps[2005][2005];
char str[2005][2005];
int dis[2005];
bool vis[2005];
int n;

int Prim()
{
    memset(vis,false,sizeof(vis));
    for(int i=1; i<=n; i++)
        dis[i] = INF;
    int ans=0;
    dis[1] = 0;
    for(int i=1; i<=n; i++)
    {
        int tmp = INF,k=0;
        for(int j=1; j<=n; j++)
        {
            if(!vis[j]&&dis[j]<tmp)
            {
                tmp = dis[j];
                k=j;
            }
        }

        vis[k] = true;
        ans+=tmp;
        for(int i=1; i<=n; i++)
        {
            if(!vis[i]&&dis[i]>maps[k][i])
                dis[i] = maps[k][i];
        }
    }
    return ans;
}

int main()
{
    while(scanf("%d",&n),n)
    {
        for(int i=0;i<n;i++)
            scanf("%s",str[i]);

        for(int i=0;i<n;i++)
        {
            for(int j=0;j<n;j++)
            {
                int dist = 0;
                for(int k=0;k<7;k++)
                {
                    if(str[i][k]!=str[j][k])
                        dist++;
                }
                maps[i+1][j+1] = dist;
            }
        }
        printf("The highest possible quality is 1/%d.\n",Prim());
    }
    return 0;
}