lca总结

P3379 【模板】最近公共祖先（LCA）

#include <bits/stdc++.h>
using namespace std;

int n,m,s;
vector <int> e[500001];
int fa[500001],dep[500001],lca[500001][40];

void dfs(int x,int d)
{
	dep[x] = d,lca[x][0] = fa[x];
	for (int i = 1; i <= 30; i++)
	{
		lca[x][i] = lca[lca[x][i - 1]][i - 1];
	}
	for (int i = 0; i < e[x].size(); i++)
	{
		int v = e[x][i];
		if(v != fa[x])
		{
			fa[v] = x;
			dfs(v,d + 1);
		}
	}
}

int query(int x,int y)
{
	if(dep[x] < dep[y])swap(x,y);//x is deeper
	for (int i = 30; i >= 0; i--)
	{
		if(dep[ lca[x][i] ] >= dep[y] && dep[lca[x][i]] > 0)
		{
			x = lca[x][i];
		}
	}
	if(x == y)return x;
	for (int i = 30; i >= 0; i--)
	{
		if(lca[x][i] == lca[y][i] || lca[x][i] == 0)continue;//overjump
		x = lca[x][i],y = lca[y][i];
	}
	return lca[x][0];
}

int main()
{
	scanf(" %d %d %d",&n,&m,&s);
	int a,b;
	for (int i = 1; i < n; i++)
	{
		scanf(" %d %d",&a,&b);
		e[a].push_back(b),e[b].push_back(a);
	}
	dfs(s,1);
	for (int i = 1; i <= m; i++)
	{
		scanf(" %d %d",&a,&b);
		printf("%d\n",query(a,b));
	}
	return 0;
}

dfs：处理深度，倍增转移祖先
query：keep x’s depth deeper，从最大的$2^i$开始跳，二进制优化，直到跳到同一高度，，再两个一起跳，同上，最后注意，x与y的father才是答案