两遍 $bfs$ 求树的直径，第三遍求以直径中点为根各个点的深度。

#include<bits/stdc++.h>
using namespace std;
const int N = 2e5 + 10;
int n,k;
struct node{
	int to,next;
}tr[2 * N];
int h[N], idx = 0;
void add(int from,int to){
	tr[++idx].to = to;
	tr[idx].next = h[from];
	h[from] = idx;
}
int d[N],dd,fa[N],id;
bool vis[N];
queue<int> q;
int maxdeep[N],deep[N];
void bfs(int x){
	while(!q.empty()) q.pop();
	memset(d,0,sizeof(d));
	memset(fa,0,sizeof(fa));
	memset(vis,0,sizeof(vis));
	q.push(x);vis[x] = true;
	while(!q.empty()){
		int u = q.front();
		q.pop();
		for(int i = h[u] ; i ; i = tr[i].next){
			int y = tr[i].to;
			if(!vis[y]){
				d[y] = d[u] + 1;
				vis[y] = true;
				fa[y] = u;
				q.push(y);
			}
		}
	}
	for(int i = 1 ; i <= n ; i ++) if(dd < d[i]) id = i,dd = d[i];
}
void dfs(int x,int last){
	maxdeep[x] = d[x];
	for(int i = h[x] ; i ; i = tr[i].next){
		int y = tr[i].to;
		if(y != last){
			dfs(y,x);
			maxdeep[x] = max(maxdeep[x],maxdeep[y]);
		}
	}
}
bool cmp(int aa,int bb) {return aa > bb;}
int main(){
	cin >> n >> k;
	for(int i = 1 ; i < n ; i ++){
		int u,v;
		cin >> u >> v;
		add(u,v);add(v,u);
	}
	bfs(1); 
	bfs(id); 
	for(int i = 1 ; i <= (dd + 1) / 2 ; i ++) id = fa[id];
	bfs(id);
//	memset(d,0,sizeof(d));
	dfs(id,-1);
	for(int i = 1 ; i <= n ; i ++) deep[i] = maxdeep[i] - d[i];
	sort(deep + 1,deep + 1 + n,cmp);
	cout << deep[k + 1] + 1;
	return 0;
}