The Unique MST----poj1679次小生成树

题目链接：http://poj.org/problem?id=1679

判断最小生成数是否唯一：如果唯一这权值和次小生成树不同，否则相同；

 

#include<stdio.h>

#include<string.h>

#include<map>

#include<iostream>

#include<algorithm>

#include<math.h>

#define N 110

#define INF 0xfffffff



using namespace std;



int Max[N][N], used[N][N], vis[N], maps[N][N], dist[N], fa[N], n;



void Init()

{

    memset(vis, 0, sizeof(vis));

    memset(used, 0, sizeof(used));

    memset(Max, 0, sizeof(Max));

    memset(fa, 0, sizeof(fa));

    for(int i=0; i<=n; i++)

    {

        dist[i] = INF;

        for(int j=0; j<=n; j++)

            if(i == j)

                maps[i][j] = 0;

            else

                maps[i][j] = INF;

    }

}



int Prim(int start)

{

    int ans=0;

    for(int i=1; i<=n; i++)

    {

        dist[i] = maps[start][i];

        fa[i] = start;

    }

    vis[start] = 1;

    for(int i=1; i<=n; i++)

    {

        int Min = INF, index = -1;

        for(int j=1; j<=n; j++)

        {

            if(vis[j]==0 && Min > dist[j])

            {

                Min = dist[j];

                index = j;

            }

        }

        if(index == -1)break;

        vis[index] = 1;

        ans += Min;

        used[fa[index]][index] = used[index][fa[index]] = 1;

        for(int j=1; j<=n; j++)

        {

            if(vis[j] == 1 && index != j)

            {

                Max[index][j] = Max[j][index] = max(Max[fa[index]][j], dist[index]);

            }

            else if(vis[j] == 0 && dist[j] > maps[index][j])

            {

                dist[j] = maps[index][j];

                fa[j] = index;

            }

        }

    }

    return ans;

}



int SMST(int ans)

{

    int Min = INF;

    for(int i=1; i<=n;i++)

    {

        for(int j=i+1; j<=n; j++)

        {

            if(used[i][j]==0 && maps[i][j] != INF)

                Min=min(Min, ans-Max[i][j]+maps[i][j]);

        }

    }

    return Min;

}



int main()

{

    int T, m, a, b, c;

    scanf("%d", &T);

    while(T--)

    {

        scanf("%d%d", &n, &m);

        Init();

        for(int i=0; i<m; i++)

        {

            scanf("%d%d%d", &a, &b, &c);

            maps[a][b] = maps[b][a] = c;

        }

        int num1 = Prim(1);

        int num2 = SMST(num1);

        if(num1 != num2)

            printf("%d\n", num1);

        else

            printf("Not Unique!\n");

    }

    return 0;

}

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