Lowest Common Ancestor
(Graph/lca.hpp)

• View this file on GitHub
• Last update: 2022-10-16 23:53:47+09:00
• Include: #include "Graph/lca.hpp"

Required by

• Auxiliary Tree(Virtual Tree) (Graph/auxiliarytree.hpp)

Verified with

• Verify/LC_lca_2.test.cpp
• Verify/YUKI_901.test.cpp

Code

#pragma once

struct LCA{
    LCA(int _n=0):n(_n),g(_n),depth(_n+1,inf),start(_n){}
    void add_edge(int u,int v){
        g[u].push_back(v);
        g[v].push_back(u);
    }
    void run(int root=0){
        depth[root]=0;
        dfs(root,-1);
        N=1;
        while(N<int(euler.size()))N<<=1;
        tree.resize(N*2,n);
        rep(i,0,euler.size())tree[N+i]=euler[i];
        for(int i=N-1;i>0;i--)tree[i]=op(tree[i*2],tree[i*2+1]);
    }
    int lca(int u,int v){
        int a=start[u],b=start[v];
        if(a>b)swap(a,b);
        b++;
        int res=n;
        for(int T=b-a;T>=1;T=b-a){
            int x=a|((1U<<31)>>__builtin_clz(T));
            int y=x&-x,k=__builtin_ctz(x);
            res=op(res,tree[(N|a)>>k]);
            a+=y;
        }
        return res;
    }
private:
    int n,N;
    vector<vector<int>> g;
    vector<int> depth,start,euler,tree;
    void dfs(int v,int p){
        start[v]=euler.size();
        euler.push_back(v);
        for(auto& to:g[v])if(to!=p){
            depth[to]=depth[v]+1;
            dfs(to,v);
            euler.push_back(v);
        }
    }
    int op(int u,int v){
        if(depth[u]<depth[v])return u;
        else return v;
    }
};

/**
 * @brief Lowest Common Ancestor
 */

#line 2 "Graph/lca.hpp"

struct LCA{
    LCA(int _n=0):n(_n),g(_n),depth(_n+1,inf),start(_n){}
    void add_edge(int u,int v){
        g[u].push_back(v);
        g[v].push_back(u);
    }
    void run(int root=0){
        depth[root]=0;
        dfs(root,-1);
        N=1;
        while(N<int(euler.size()))N<<=1;
        tree.resize(N*2,n);
        rep(i,0,euler.size())tree[N+i]=euler[i];
        for(int i=N-1;i>0;i--)tree[i]=op(tree[i*2],tree[i*2+1]);
    }
    int lca(int u,int v){
        int a=start[u],b=start[v];
        if(a>b)swap(a,b);
        b++;
        int res=n;
        for(int T=b-a;T>=1;T=b-a){
            int x=a|((1U<<31)>>__builtin_clz(T));
            int y=x&-x,k=__builtin_ctz(x);
            res=op(res,tree[(N|a)>>k]);
            a+=y;
        }
        return res;
    }
private:
    int n,N;
    vector<vector<int>> g;
    vector<int> depth,start,euler,tree;
    void dfs(int v,int p){
        start[v]=euler.size();
        euler.push_back(v);
        for(auto& to:g[v])if(to!=p){
            depth[to]=depth[v]+1;
            dfs(to,v);
            euler.push_back(v);
        }
    }
    int op(int u,int v){
        if(depth[u]<depth[v])return u;
        else return v;
    }
};

/**
 * @brief Lowest Common Ancestor
 */

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