Ciel the Commander(树的重心，分治)

Posted 2021-09-09 thusloop

传送门

每次找树的重心，涂色为当前最大可涂的字母

#include<bits/stdc++.h>
#define int long long
#define ios ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
using namespace std;
const int inf=2e18+100;
const int maxn=2e5+100;
vector<int>g[maxn];
int sum;
bool vis[maxn];
int son[maxn];
int res,root;
bool fg=1;
char col[maxn];
void getroot(int x,int fa)
{
	son[x]=1;
	int mx=0;
	for(auto it:g[x])
	{
		if(it==fa||vis[it])continue;
		getroot(it,x);
		son[x]+=son[it];
		mx=max(mx,son[it]);
	}
	mx=max(mx,sum-son[x]);
	if(mx<res)
	{
		res=mx;
		root=x;
	}
}
void dfs(int x,int dep)
{
	if(dep>=26)
	{
		fg=0;
		return ;		
	}
	col[x]='A'+dep;
	vis[x]=1;
	for(auto it:g[x])
	{
		if(fg==0)return;
		if(vis[it])continue;
		res=inf;root=0;sum=son[it];
		getroot(it,-1);
		dfs(root,dep+1);
		if(fg==0)return;
	}
}
signed main()
{
	IOS
	int n;
	cin>>n;
	sum=n;
	for(int i=1;i<n;i++)
	{
		int u,v;
		cin>>u>>v;
		g[u].push_back(v);
		g[v].push_back(u);
	}
	res=inf;
	getroot(1,-1);
	dfs(root,0);
	if(fg==0)
	{
		cout<<"Impossible"<<"\\n";
	}
	else 
	{
		for(int i=1;i<=n;i++)
		{
			cout<<col[i]<<" ";
		}
		cout<<"\\n";
	}
}