POJ1679The Unique MST(次小生成树)
Time Limit: 1000MS | Memory Limit: 10000K | |
Total Submissions: 25203 | Accepted: 8995 |
Description
Definition 1 (Spanning Tree): Consider a connected, undirected graph G = (V, E). A spanning tree of G is a subgraph of G, say T = (V', E'), with the following properties:
1. V' = V.
2. T is connected and acyclic.
Definition 2 (Minimum Spanning Tree): Consider an edge-weighted, connected, undirected graph G = (V, E). The minimum spanning tree T = (V, E') of G is the spanning tree that has the smallest total cost. The total cost of T means the sum of the weights on all the edges in E'.
Input
Output
Sample Input
2
3 3
1 2 1
2 3 2
3 1 3
4 4
1 2 2
2 3 2
3 4 2
4 1 2
Sample Output
3
Not Unique! 题意:问一棵最小生成树是否唯一
找次小生成树,如果相等不唯一,否则唯一 次小生成树:就是最小生成树换一条边而成的生成树;用maxd【x】【y】存储最小生成树两个节点(x,y)路径中最大的那条边的权值,也就是最小生成树中x-z-...-y中那个最大的那一个权值,然后就可以换边了,到底换哪一个边就从不在生成树中的边一个一个枚举咯,假设x-y,如果要用x-y替换x-z...-y肯定得替换x-z...-y中权值最大的那条边才能让最后得到结果只比x-z...-y小一点,也就是仅次于
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
using namespace std;
const int MAX = ;
const int INF = ;
int n,m,ans,cnt;
int edge[MAX][MAX],vis[MAX],used[MAX][MAX],dist[MAX];
int pre[MAX],maxd[MAX][MAX];
void prime()
{
memset(vis,,sizeof(vis));
memset(used,false,sizeof(used));
memset(maxd,,sizeof(maxd));
for(int i = ; i <= n; i++)
{
dist[i] = edge[][i];
pre[i] = ;
}
dist[] = ;
vis[] = ;
pre[] = -;
for(int i = ; i < n; i++)
{
int minn = INF,pos = -;
for(int j = ; j <= n; j++)
{
if(vis[j] == && dist[j] < minn)
{
minn = dist[j];
pos = j;
}
}
if(minn == INF)
{
ans = INF;
return;
}
ans += minn;
vis[pos] = ;
used[pos][pre[pos]] = used[ pre[pos] ][pos] = true;
for(int j = ; j <= n; j++)
{
if(vis[j])
maxd[j][pos] = maxd[pos][j] = max(dist[pos], maxd[j][pre[pos]]);
if(vis[j] == && dist[j] > edge[pos][j])
{
dist[j] = edge[pos][j];
pre[j] = pos;
}
}
}
}
void smst()
{
cnt = INF;
for(int i = ; i <= n; i++)
{
for(int j = i + ; j <= n; j++)
{
if(used[i][j] == false && edge[i][j] != INF)
{
cnt = min(cnt, ans - maxd[i][j] + edge[i][j]);
}
}
}
}
int main()
{
int t;
scanf("%d", &t);
while(t--)
{
for(int i = ; i <= MAX; i++)
for(int j = ; j <= MAX; j++) //初始化的时候把MAX,写成了n, orz....
{
if(i != j)
edge[i][j] = INF;
else
edge[i][i] = ;
}
scanf("%d%d", &n,&m);
for(int i = ; i < m; i++)
{
int x,y,w;
scanf("%d%d%d", &x, &y, &w);
edge[x][y] = edge[y][x] = w;
}
ans = ;
prime();
smst();
if(ans == INF)
{
printf("Not Unique!\n");
continue;
}
if(cnt == ans)
{
printf("Not Unique!\n");
}
else
{
printf("%d\n",ans);
}
}
return ;
}
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