From 1fe04a96cf1999054411ba183259a220f923ba97 Mon Sep 17 00:00:00 2001
From: Mayank Musaddi <32260560+mayankmusaddi@users.noreply.github.com>
Date: Mon, 8 Oct 2018 02:56:27 +0530
Subject: [PATCH] Create lca.cpp

---
 lca.cpp | 101 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 101 insertions(+)
 create mode 100644 lca.cpp

diff --git a/lca.cpp b/lca.cpp
new file mode 100644
index 0000000..6ef5be6
--- /dev/null
+++ b/lca.cpp
@@ -0,0 +1,101 @@
+#include<bits/stdc++.h>
+using namespace std;
+typedef long long int ll;
+const ll lt=100005;
+vector<int> adj[lt];
+vector<int> arr;
+vector<int> st(lt,0);
+vector<int> en(lt,0);
+vector<int> ht(lt,0);
+vector<int> par(lt,0);
+int p[lt][25];
+
+int tp=0;
+bool visited[lt];
+
+void dfs(int u,int l)
+{
+	ht[u]=l;
+	arr.push_back(u);
+	visited[u]=1;
+	st[u]=tp++;
+	for(int i=0;i<adj[u].size();i++)
+	{
+		int v=adj[u][i];
+		if(!visited[v])
+		{
+			par[v]=u;
+			p[v][0]=u;
+			dfs(v,l+1);
+		}
+	}
+	en[u]=tp+1;
+}
+
+int find_lca(int a,int b)
+{
+	if(ht[a]==ht[b])
+	{
+		if(a==b)
+			return a;
+		else
+			return find_lca(par[a],par[b]);
+	}
+	else if(ht[a]>ht[b])
+	{
+		a=par[a];
+		return find_lca(a,b);
+	}
+	else
+		return find_lca(b,a);
+}
+
+int find_lca2(int a,int b)
+{
+	if(ht[a]==ht[b])
+	{
+		if(a==b)
+			return a;
+		else
+			return find_lca2(p[a][0],p[b][0]);
+	}
+	else if(ht[a]>ht[b])
+	{
+		int diff=ht[a]-ht[b];
+
+		for(int i=0;i<21 && diff>0;i++)
+		{
+			if((diff>>i) & 1)
+				a=p[a][i];
+		}
+
+		return find_lca2(a,b);
+	}
+	else
+		return find_lca2(b,a);
+}
+
+int main()
+{
+	int n;
+	cin >> n;
+	for(int i=0;i<n-1;i++)
+	{
+		int u,v;
+		cin >> u >> v;
+		adj[u].push_back(v);
+		adj[v].push_back(u);
+	}
+	dfs(1,0);
+
+	p[1][0]=1;
+
+	for(int j=1;j<=21;j++)
+		for(int i=1;i<=n;i++)
+			p[i][j]=p[p[i][j-1]][j-1];
+
+	int a,b;
+	cin >> a >> b;
+	cout << find_lca(a,b) << endl;
+	cout << find_lca2(a,b) << endl;
+}