From c45683bb8cb4d4df1d4ddcd19c487cd63c1a6411 Mon Sep 17 00:00:00 2001
From: rohan <rgkbitw@gmail.com>
Date: Fri, 4 Oct 2019 19:05:23 +0530
Subject: [PATCH]  Added LCA binary Lifting O(nlogn)

---
 Graph/lca.cpp | 90 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 90 insertions(+)
 create mode 100644 Graph/lca.cpp

diff --git a/Graph/lca.cpp b/Graph/lca.cpp
new file mode 100644
index 000000000..b0ff12750
--- /dev/null
+++ b/Graph/lca.cpp
@@ -0,0 +1,90 @@
+#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.
+}