poj 1679 The Unique MST （最小生成树是否唯一 ）

题目链接：poj 1679 The Unique MST

 

解题报告：最小生成树是否唯一判断方法

（1）图中每条边，扫描其他边，如果存在权值相同的边，则对其边标记

（2）用kruskal或prim算法求最小生成树的权值

（3）得到最小生成树，如果该最小生成树不包含标记的边，则最小生成树唯一，如果包含了标记的边，则依次去掉标记的边，再求最小生成树，如果求得的最小生成树与原最小生成树的权值相同，则最小生成树不唯一

 

code:

#include<cstdio>
#include<cstring>
#include<algorithm>
#define maxn 105
#define INF 0x7fffffff

using namespace std;

struct node
{
	int u, v, w;
	int equal;
	int used;
	int del;
}edge[maxn*maxn];

int parent[maxn];
int n, m;
bool first;

bool cmp( const node &a, const node &b)
{
	return a.w < b.w;
}

void UFset( )
{
	for(int i = 0; i <= n; i++)
		parent[i] = -1;
}

int Find( int x )
{
	int s ;
	for( s = x; parent[s] >= 0; s = parent[s] );
	while(s != x )
	{
		int temp = parent[x];
		parent[x] = s;
		x = temp;
	}
	return s;
}

void Union( int R1, int R2 )
{
	int r1 = Find(R1);
	int r2 = Find(R2);
	int temp = parent[r1] + parent[r2];
	if(parent[r1] > parent[r2])
	{
		parent[r1] = r2;
		parent[r2] = temp;
	}
	else 
	{
		parent[r2] = r1;
		parent[r1] = temp;
	}
}

int kruskal( )
{
	UFset( );
	int i, j;
	int u, v;
	int sumweight = 0, num = 0;
	for( i = 0; i <m; i++ )
	{
		if(edge[i].del == 1 ) continue;
		
		u = edge[i].u; v = edge[i].v;
		if( Find(u) != Find(v) )
		{
			sumweight += edge[i].w;
			num++;
			Union( u, v );
			if( first ) edge[i].used = 1;
		}
		if( num >= n-1 ) break;
	}
	return sumweight;
}

int main( )
{
	int T, u, v, w, j, i;
	scanf("%d",&T);
	while( T-- )
	{
		memset(edge, 0, sizeof(edge) );
		scanf("%d%d", &n, &m);
		for( i = 0; i < m; i++ )
		{
			scanf("%d%d%d", &u, &v, &w);
			edge[i].u = u;
			edge[i].v = v;
			edge[i].w = w; 
		}
		for(i = 0; i < m; i++ )
		{
			for( j = 0; j < m; j++ )
			{
				if( i == j ) continue;
				if( edge[i].w == edge[j].w )
					edge[j].equal = 1;
			}
		}
		sort(edge, edge + m, cmp);
		first = true;
		int ans1 = kruskal( );
		int ans2;
		first = false;
		for( i = 0; i < m; i++ )
		{
			if(edge[i].used && edge[i].equal )
			{
				edge[i].del = 1;
				ans2 = kruskal( );
				if(ans1 == ans2 )
				{
					printf("Not Unique!\n");
					break;
				}
				edge[i].del = 0;
			}
		}
		if( i >= m )
			printf("%d\n", ans1);
	}
	return 0;
}