TheAlgorithms-C-Plus-Plus/Graph/lca.cpp

#include<bits/stdc++.h>
using namespace std;
// Find the lowest common ancestor using binary lifting in O(nlogn)
// Zero based indexing
// Resource : https://cp-algorithms.com/graph/lca_binary_lifting.html
const int N = 1005;
const int LG = log2(N)+1;
struct lca{
	int n;
	vector<int> adj[N]; // Graph
	int up[LG][N]; 			// build this table
	int level[N]; 			// get the levels of all of them

	lca(int n_) : n(n_){
		memset(up,-1,sizeof(up));
		memset(level,0,sizeof(level));
		for(int i=0; i<n-1; ++i){
			int a,b;
      cin>>a>>b; a--; b--;
      adj[a].push_back(b);
      adj[b].push_back(a);
		}
		level[0] = 0;
		dfs(0,-1);
		build();
	}
	void  verify(){
		for(int i=0; i<n; ++i){
			cout<<i<<" : level: "<<level[i]<<endl;
		}
		cout<<endl;
		for(int i=0; i<LG; ++i){
			cout<<"Power:"<<i<<": ";
			for(int j=0; j<n; ++j){
				cout<<up[i][j]<<" ";
			}
			cout<<endl;
		}
	}

	void build(){
		for(int i=1; i<LG; ++i){
			for(int j=0; j<n; ++j){
				if( up[i-1][j] != -1 ){
					up[i][j] = up[i-1][up[i-1][j]];
				}
			}
		}
	}

	void dfs(int node, int par){
		up[0][node] = par;
		for( auto i : adj[node] ){
			if( i != par ){
				level[i] = level[node] + 1;
				dfs(i,node);
			}
		}
	}
	int query(int u, int v){
		u--; v--;
		if( level[v] > level[u] ){ swap(u,v); }
		// u is at the bottom.
		int dist = level[u] - level[v];
		// Go up this much distance
		for(int i=LG-1; i>=0; --i){
			if( dist & ( 1 << i) ){
				u = up[i][u];
			}
		}
		if( u == v ){ return u; }
		assert(level[u] == level[v]);
		for(int i=LG-1; i>=0; --i){
			if( up[i][u] != up[i][v] ){
				u = up[i][u];
				v = up[i][v];
			}
		}
		assert(up[0][u] == up[0][v]);
		return up[0][u];
	}
};

int main(){
	int n; // number of nodes in the tree.
	lca l(n); // will take the input in the format given
	// n-1 edges of the form
	// a b
	// Use verify function to see.
}