最近公共祖先lca

倍增法

#include<bits/stdc++.h>
using namespace std;
const int maxn=1000010;
int n,m,s;
int h[maxn],nxt[maxn],to[maxn],tot;
int Log[maxn];
int dep[maxn];
int dis[maxn];
int fa[maxn][20];
void add(int x,int y)
{
	tot++;
	to[tot]=y;
	nxt[tot]=h[x];
	h[x]=tot;
}
void llog(){for (int i=2;i<=n;i++) Log[i]=Log[i>>1]+1;}
void dfs(int now,int f)
{
	dep[now]=dep[f]+1;
	fa[now][0]=f;
	for (int i=1;i<=19;i++)
	{
		fa[now][i]=fa[fa[now][i-1]][i-1];
	}
	for (int i=h[now];i;i=nxt[i])
	{
		int y=to[i];
		if (y==f) continue;
		dis[y]=dis[now]+1;
		dfs(y,now);
	}
}
int lca(int x,int y)
{
	if (dep[x]>dep[y]) swap(x,y);
	int d=dep[y]-dep[x];
	for (int i=Log[d];i>=0;i--)
	{
		if (d>>i&1) y=fa[y][i]; 
	}
	if (x == y) return x;
	for (int i=Log[dep[x]];i>=0;i--)
	{
		if (fa[x][i]!=fa[y][i])
		{
			x=fa[x][i];
			y=fa[y][i];
		}
	}
	return fa[x][0];
}
int main()
{
	cin >> n >> m >> s;
	llog();
	for (int i=1;i<=n-1;i++)
	{
		int x,y;
		cin >> x >> y;
		add(x,y);
		add(y,x);
	}
	dfs(s,s);
	while (m--)
	{
		int x,y;
		cin >> x >> y;
//		int d=dis[x]+dis[y]-dis[lca(x,y)]*2;
//		cout << d << endl;
		cout << lca(x,y) << endl;
	}
	return 0;
}

重剖法

struct Tree_Line_Pow_Divide_to_Lca
{
	int fa[maxn],son[maxn],top[maxn],dep[maxn],siz[maxn];
	int dfn[maxn],rnk[maxn],cnt;
	void dfs1(int x)
	{
		son[x]=-1;siz[x]=1;
		for (int i=h[x];i;i=nxt[i])
		{
			int y=to[i];
			if (dep[y]) continue;
			dep[y]=dep[x]+1;
			fa[y]=x;
			dfs1(y);
			siz[x]+=siz[y];
			if (son[x] == -1 || siz[y]>siz[son[x]]) son[x]=y;
		}
	}
	void dfs2(int x,int t)
	{
		top[x]=t;
		cnt++;
		dfn[x]=cnt;rnk[cnt]=x;
		if (son[x] == -1) return;
		dfs2(son[x],t);
		for (int i=h[x];i;i=nxt[i])
		{
			int y=to[i];
			if (y == son[x] || y == fa[x]) continue;
			dfs2(y,y);
		}
	}
	int lca(int x,int y)
	{
		while (top[x]!=top[y])
		{
			if (dep[top[x]]<dep[top[y]]) swap(x,y);
			x=fa[top[x]];
		}
		return dep[x]<dep[y]?x:y;
	}
}T;

点击查看代码

#include<bits/stdc++.h>
#define Honkai ios::sync_with_stdio(0);
#define StarRail cin.tie(0);cout.tie(0);
#define endl '\n'
using namespace std;
const int maxn=1e6+10;
int n,m,s;
int h[maxn],to[maxn],nxt[maxn],tot;
int fa[maxn],son[maxn],top[maxn],dep[maxn],siz[maxn];
int dfn[maxn],rnk[maxn],cnt;
void add(int x,int y) {tot++;to[tot]=y;nxt[tot]=h[x];h[x]=tot;}
void dfs1(int x)
{
	son[x]=-1;siz[x]=1;
	for (int i=h[x];i;i=nxt[i])
	{
		int y=to[i];
		if (dep[y]) continue;
		dep[y]=dep[x]+1;
		fa[y]=x;
		dfs1(y);
		siz[x]+=siz[y];
		if (son[x] == -1 || siz[y]>siz[son[x]]) son[x]=y;
	}
}
void dfs2(int x,int t)
{
	top[x]=t;
	cnt++;
	dfn[x]=cnt;rnk[cnt]=x;
	if (son[x] == -1) return;
	dfs2(son[x],t);
	for (int i=h[x];i;i=nxt[i])
	{
		int y=to[i];
		if (y == son[x] || y == fa[x]) continue;
		dfs2(y,y);
	}
}
int lca(int x,int y)
{
	while (top[x]!=top[y])
	{
		if (dep[top[x]]<dep[top[y]]) swap(x,y);
		x=fa[top[x]];
	}
	return dep[x]<dep[y]?x:y;
}
int main()
{
	Honkai StarRail
	cin >> n >> m >> s;
	for (int i=1;i<n;i++)
	{
		int x,y;
		cin >> x >> y;
		add(x,y);add(y,x);
	}
	dep[s]=1;
	dfs1(s);dfs2(s,s);
	while (m--)
	{
		int l,r;
		cin >> l >> r;
		cout << lca(l,r) << endl;
	}
	return 0;
}