Added LCA using Binary Lifting.

Author: avishkarhande

Graph/binarylifting.cpp

@@ -0,0 +1,77 @@
+//author : Avishkar A. Hande
+#include<bits/stdc++.h>
+#define ll long long
+using namespace std;
+
+const int maxS = 1e5+10;
+vector<ll> adj[maxS];
+
+ll LOG;
+int timer;
+vector<int> tin, tout;
+vector<vector<int>> up;
+
+/*
+    Binary Lifting is mostly used to find Lowest Common Ancestor
+    as it reduces the time complexity to log(n);
+*/
+
+void dfs(int v, int p)
+{
+    tin[v] = ++timer;
+    up[v][0] = p;
+    for (int i = 1; i <= LOG; ++i)
+        up[v][i] = up[up[v][i-1]][i-1];
+
+    for (int u : adj[v]) {
+        if (u != p)
+            dfs(u, v);
+    }
+
+    tout[v] = ++timer;
+}
+
+bool is_ancestor(int u, int v)
+{
+    return tin[u] <= tin[v] && tout[u] >= tout[v];
+}
+
+int lca(int u, int v)
+{
+    if (is_ancestor(u, v))
+        return u;
+    if (is_ancestor(v, u))
+        return v;
+    for (int i = LOG; i >= 0; --i) {
+        if (!is_ancestor(up[u][i], v))
+            u = up[u][i];
+    }
+    return up[u][0];
+}
+
+void preprocess(int root, int n) {
+    tin.resize(n);
+    tout.resize(n);
+    timer = 0;
+    LOG = ceil(log2(n)) + 1;
+    up.assign(n+1, vector<int>(LOG + 1));
+    dfs(root, root);
+}
+
+int main()
+{
+	ll node, queries;
+	cin >> node >> queries;
+	for(int i = 0; i < node-1; i++){
+		ll u, v;
+		cin >> u >> v;
+		adj[u].push_back(v);
+		adj[v].push_back(u);
+	}
+    preprocess(1, node);
+    while(queries--){
+        ll a, b;
+        cin >> a >> b;
+        cout << lca(a, b) << endl;
+    }
+}