PAT-1021 Deepest Root (25 分) 并查集判断成环和联通+求树的深度
A graph which is connected and acyclic can be considered a tree. The height of the tree depends on the selected root. Now you are supposed to find the root that results in a highest tree. Such a root is called the deepest root.
Input Specification:
Each input file contains one test case. For each case, the first line contains a positive integer N (≤104) which is the number of nodes, and hence the nodes are numbered from 1 to N. Then N−1 lines follow, each describes an edge by given the two adjacent nodes' numbers.
Output Specification:
For each test case, print each of the deepest roots in a line. If such a root is not unique, print them in increasing order of their numbers. In case that the given graph is not a tree, print Error: K components
where K
is the number of connected components in the graph.
Sample Input 1:
5
1 2
1 3
1 4
2 5
Sample Output 1:
3
4
5
Sample Input 2:
5
1 3
1 4
2 5
3 4
Sample Output 2:
Error: 2 components
交了一发暴力,居然过了,关键就是这个求树的深度,这题的主要坑点在于,如果不是一颗树要输出那个信息,如果成环了但是只有一个连通块,要输出
Error: 1 components
所以注意判断逻辑
int dfs(int x)
{
//de(x);
vis[x]=1;
int ma=0;
for(int i=0;i<(int)G[x].size();i++){
int v=G[x][i];
if(vis[v])continue;
ma=max(ma,dfs(G[x][i]));
}
return ma+1;
}
#include <iostream>
#include<bits/stdc++.h>
#define each(a,b,c) for(int a=b;a<=c;a++)
#define de(x) cout<<#x<<" "<<(x)<<endl
using namespace std;
const int maxn=1e4+5;
int father[maxn]; // 储存i的father父节点
void makeSet(int n) {
for (int i = 1; i <=n; i++)
father[i] = i;
}
int findRoot(int x) { // 迭代找根节点
int root = x; // 根节点
while (root != father[root]) { // 寻找根节点
root = father[root];
}
while (x != root) {
int tmp = father[x];
father[x] = root; // 根节点赋值
x = tmp;
}
return root;
}
void Union(int x, int y) { // 将x所在的集合和y所在的集合整合起来形成一个集合。
int a, b;
a = findRoot(x);
b = findRoot(y);
father[a] = b; // y连在x的根节点上 或father[b] = a为x连在y的根节点上;
}
vector<int>G[maxn];
/*
5
1 2
1 3
1 4
2 5
*/
int maxx;
int depth[maxn];
int vis[maxn];
int dfs(int x)
{
//de(x);
vis[x]=1;
int ma=0;
for(int i=0;i<(int)G[x].size();i++){
int v=G[x][i];
if(vis[v])continue;
ma=max(ma,dfs(G[x][i]));
}
return ma+1;
}
int main()
{
int n;
cin>>n;
makeSet(n);
int m=n-1;
int a,b;
int tree_flag=true;
while(m--)
{
scanf("%d%d",&a,&b);
if(findRoot(a)!=findRoot(b)){
Union(a,b);
G[a].push_back(b);
G[b].push_back(a);
}
else tree_flag=false;
}
//int components=0;
set<int>s;
for(int i=1;i<=n;i++)
{
//de(i);
//de(findRoot(i));
s.insert(findRoot(i));
}
//de(s.size());
if(tree_flag==false||s.size()!=1)
{
printf("Error: %d components\n",(int)s.size());
return 0;
}
maxx=0;
each(i,1,n)
{
memset(vis,0,sizeof(vis));
//de(i);
depth[i]=dfs(i);
}
each(i,1,n)
{
maxx=max(maxx,depth[i]);
}
each(i,1,n)
{
if(depth[i]==maxx)
{
cout<<i<<endl;
}
}
return 0;
}
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