题目大意: 问一个图的最小生成树是不是唯一的
QAQ prim计算最小生成树的同时,记录最小生成树里面两点间的权值最大的边
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <queue>
using namespace std;
const int INF = 0x3f3f3f3f;
int T,n,m;
int a[1010][1010],pre[1010],d[1010];
bool vis[1010];
int maxd[1010][1010];
int prim(int s)
{
int sum = 0,tmp;
memset(vis,0,sizeof(vis));
for(int i = 1;i <= n; ++i)
d[i] = a[s][i],pre[i] = s;
vis[s] = 1;
d[s] = 0;
for(int i = 1;i < n; ++i)
{
int mincost = INF;
for(int j = 1;j <= n; ++j)
if(!vis[j] && mincost > d[j])
mincost = d[j],tmp = j;
for(int j = 1;j <= n; ++j)
if(vis[j])
maxd[tmp][j] = maxd[j][tmp] = max(mincost,maxd[pre[tmp]][j]);
vis[tmp] = 1;
sum += mincost;
for(int j = 1;j<= n; ++j)
{
if(!vis[j] && d[j] > a[tmp][j])
d[j] = a[tmp][j],pre[j] = tmp;
}
}
return sum;
}
int main()
{
scanf("%d",&T);
while(T--)
{
scanf("%d%d",&n,&m);
memset(a,0x3f,sizeof(a));
for(int i = 0;i <= n; ++i)
a[i][i] = 0;
for(int i = 0;i < m; ++i)
{
int x,y,z;
scanf("%d%d%d",&x,&y,&z);
a[x][y] = a[y][x] = z;
}
int sum = prim(1);
int lsum = INF;
for(int i = 1;i <= n; ++i)
for(int j = i + 1;j <= n; ++j)
{
if(i != pre[j] && j != pre[i] && a[i][j] != INF)
lsum = min(sum - maxd[i][j] + a[i][j],lsum);
}
if(lsum == sum) printf("Not Unique!\n");
else printf("%d\n",sum);
}
return 0;
}