Added LCA with binary lifting in trees

Author: prince776

Algorithms/Trees/LCA_binary_lifting.cpp

@@ -0,0 +1,92 @@
+// Finding LCA in a tree using binary lifting
+// Pre processing TC: O(nlogn)
+// TC for finding LCA per query: O(logn)
+
+#include <bits/stdc++.h>
+using namespace std;
+
+constexpr int N = 5; // No. of vertices
+constexpr int L = 4; // ceil(logN / log2) + 1
+
+// Vertices from 1 to N.
+vector<int> adj[N + 1];
+int up[N + 1][L];
+int level[N + 1];
+
+void dfs(int u, int prev = 0)
+{
+	up[u][0] = prev;
+	for (auto &v : adj[u])
+	{
+		if (v == prev) continue;
+
+		level[v] = level[u] + 1;
+		dfs(v, u);
+	}
+}
+
+void binaryLift()
+{
+	dfs(1);
+	for (int i = 1; i < L; i++)
+		for (int j = 1; j <= N; j++)
+			up[j][i] = up[up[j][i - 1]][i - 1];			
+}
+
+int LCA(int a, int b)
+{
+	if (level[a] > level[b])
+		swap(a, b);
+
+	int diff = level[b] - level[a];
+	for (int i = 0; i < L; i++)
+	{
+		if ((diff & (1 << i)))
+			b = up[b][i];
+	}
+
+	if (a == b) return a;
+
+	for (int i = L - 1; i >= 0; i--)
+	{
+		if (up[a][i] != up[b][i])
+		{
+			a = up[a][i];
+			b = up[b][i];
+		}
+	}
+	return up[a][0];
+}
+
+void addEdge(int u, int v)
+{
+	adj[u].push_back(v);
+	adj[v].push_back(u);
+}
+
+int dist(int a, int b)
+{
+	return level[a] + level[b] - 2 * level[LCA(a, b)];
+}
+
+int main()
+{
+	addEdge(1, 2);
+	addEdge(1, 3);
+	addEdge(2, 4);
+	addEdge(2, 5);
+	
+	binaryLift();
+
+	cout << "LCA:\n";
+	cout << LCA(4, 3) << "\n";
+	cout << LCA(4, 5) << "\n";
+	cout << LCA(4, 2) << "\n";
+	
+	cout << "Distances:\n";
+	cout << dist(4, 3) << "\n";
+	cout << dist(4, 5) << "\n";
+	cout << dist(4, 2) << "\n";
+	
+	return 0;
+}