找树的重心和树的直径

重心题

重心就是把这个点删掉后剩下的子树大小最小，siz数组表示以x为根的子树总的大小，maxsiz数组表示以x为根的每个子树的最大的大小，sum表示整个树的大小，那么sum-siz就是除了x为根所有子树外的那颗子树的大小。

代码：

#include<bits/stdc++.h>
using namespace std;
using ll = long long;
#define fi first
#define se second
const ll mod=1e9+7;
const int N=2e5+10;
#define int ll
const double eps=1e-6;

ll qpow(ll a,ll b){
	ll res=1;
	while(b){
		if(b&1) res=(res*a)%mod;
		a=(a*a)%mod;
		b>>=1;
	}
	return res;
}

int n,sum;
vector<int> v[N];
int siz[N],root,maxsiz[N];

void dfs(int x,int f){
	siz[x]=1;
	for(auto y:v[x]){
		if(y==f) continue;
		dfs(y,x);
		siz[x]+=siz[y];
		maxsiz[x]=max(maxsiz[x],siz[y]);
	}
	maxsiz[x]=max(maxsiz[x],sum-siz[x]);
	if(maxsiz[x]<maxsiz[root])
		root=x;
}
void solve(){
	cin>>n;
	for(int i=1;i<n;i++){
		int x,y;cin>>x>>y;
		v[x].push_back(y);
		v[y].push_back(x);
	}
	sum=maxsiz[root=0]=n;
	dfs(1,0);
	cout<<root<<' '<<maxsiz[root];
}

signed main(){
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    int t=1;
    //cin>>t;
	while (t--){
		solve();
	}
	return 0;
}

直径题

两次dfs里的dis最大值就是直径的两端

代码：

#include<bits/stdc++.h>
using namespace std;
using ll = long long;
#define fi first
#define se second
const ll mod=1e9+7;
const int N=2e5+10;
#define int ll
const double eps=1e-6;

ll qpow(ll a,ll b){
	ll res=1;
	while(b){
		if(b&1) res=(res*a)%mod;
		a=(a*a)%mod;
		b>>=1;
	}
	return res;
}

int n,a[N];
int dis[N],root1,root2;
vector<int>v[N];

void dfs1(int x,int f){
	dis[x]=dis[f]+a[x];
	if(dis[x]>dis[root1]){
		root1=x;
	}
	for(auto y:v[x]){
		if(y==f) continue;
		dfs1(y,x);
	}
}
void dfs2(int x,int f){
	dis[x]=dis[f]+a[x];
	if(dis[x]>dis[root2]){
		root2=x;
	}
	for(auto y:v[x]){
		if(y==f) continue;
		dfs2(y,x);
	}
}
void solve(){
	while(cin>>n){
		for(int i=1;i<=n;i++){
			cin>>a[i];
		}
		for(int i=1;i<n;i++){
			int x,y;cin>>x>>y;
			v[x].push_back(y);
			v[y].push_back(x);
		}
		dis[root1=n+1]=dis[root2=n+2]=-0x3f3f3f3f;
		dfs1(1,0);
		dfs2(root1,0);
		cout<<dis[root2];
	}
	
}

signed main(){
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    int t=1;
    //cin>>t;
	while (t--){
		solve();
	}
	return 0;
}