P3379 【模板】最近公共祖先（LCA）(树链剖分)版

#include <bits/stdc++.h>
#define read read()
#define up(i,l,r) for(register int i = (l);i <= (r);i++)
#define down(i,l,r) for(register int i = (l);i >= (r);i--)
#define traversal_vedge(i) for(register int i = head[u]; i ;i = e[i].nxt)
#define ll long long
using namespace std;
int read
{
    int x = 0, f = 1; char ch = getchar();
    while(ch < 48 || ch > 57) {if(ch == '-')f = -1; ch = getchar();}
    while(ch >=48 && ch <=57) {x = 10 * x + ch - 48;ch = getchar();}
    return x * f; 
}

int n,m,s;
const int N = 500005;
int dep[N],fa[N],size[N],top[N];

struct edge{
    int v,nxt;
}e[N<<1];int cnt,head[N];
void add(int u,int v){
    e[++cnt] = (edge){v,head[u]};
    head[u] = cnt;
}

void readdata()
{
    n = read; m = read; s = read;
    up(i,1,n-1)
    {
        int u = read,v = read;
        add(u,v);
        add(v,u);
    }
}
//-----------------------------------------------------------------------
void dfs(int u)
{
    dep[u] = dep[fa[u]] + 1;
    size[u] = 1;
    top[u] = u;
    //debug 未写 top[u] = u; 
    int heavyson_id = 0,heavyson_size = 0;
    traversal_vedge(i)
    {
        int v = e[i].v;
        if(v == fa[u]) continue;
        fa[v] = u; //top[v] = u;
         
        //debug 不写top[v] = u;
        dfs(v);
        size[u] += size[v];
        //heavyson = max(heavyson,size[v]);
        if(size[v] > heavyson_size) heavyson_id = v,heavyson_size = size[v]; 
    }
    if(heavyson_id) top[heavyson_id] = u;//debug heavyson_id -> u;
    //有重儿子才更新top[] 
    //dfs后,top[]只相当于重链上的fa[] 
    
    //调用find(u)过后,从u到链首的所有top[]才指向链首; 
}

int find(int u)
{
    if(u == top[u]) return u;
    top[u] = find(top[u]);//debug top[u] -> u
    return top[u];
    //逆向搜索,并修改值; 
}

int lca(int x,int y)
{
    if(find(x) != find(y)) //如果不在一条链上
    //**一条链:重链为一条链,轻链单独一条边为一条链;
    {
        if(dep[top[x]] > dep[top[y]]) return lca(fa[top[x]] , y);//debug fa[top[x]] -> fa[dep[top[x]]];
        else return lca(x , fa[top[y]]);
    }
    return dep[x] > dep[y] ? y : x;
}

void work()
{
    dfs(s);
    while(m--)
    {
        int a = read,b = read;
        printf("%d\n",lca(a,b)); 
    }
}

int main()
{
    freopen("input.txt","r",stdin);
    readdata();
    work();
    return 0;
} 

总结:

树链剖分版的LCA的dfs1稍有不同，不需要用数组记录每个点的重儿子；

树链剖分维护7个数组，树链剖分——LCA维护4个数组（fa[],dep[],size[],top[]）son[]简化成heavyson_id