From d93492b2d8522a1489e2dda07f2e70aef3643e67 Mon Sep 17 00:00:00 2001
From: Dhruv Panwar <60705641+dhruvinfo28@users.noreply.github.com>
Date: Thu, 7 Oct 2021 23:55:00 +0530
Subject: [PATCH] Add Lowest Common Ancestor of two vertices in a tree (#2380)

---
 DataStructures/Trees/LCA.java | 107 ++++++++++++++++++++++++++++++++++
 1 file changed, 107 insertions(+)
 create mode 100644 DataStructures/Trees/LCA.java

diff --git a/DataStructures/Trees/LCA.java b/DataStructures/Trees/LCA.java
new file mode 100644
index 00000000..0f3d63de
--- /dev/null
+++ b/DataStructures/Trees/LCA.java
@@ -0,0 +1,107 @@
+package Trees;
+
+import java.util.ArrayList;
+import java.util.Scanner;
+
+public class LCA {
+    private static Scanner scanner = new Scanner(System.in);
+    public static void main(String[] args){
+
+        //The adjacency list representation of a tree:
+        ArrayList<ArrayList<Integer>> adj = new ArrayList<>();
+
+        //v is the number of vertices and e is the number of edges
+        int v = scanner.nextInt(), e = v-1;
+
+        for(int i=0;i<v;i++){
+            adj.add(new ArrayList<Integer>());
+        }
+
+        //Storing the given tree as an adjacency list
+        int to, from;
+        for(int i=0;i<e;i++){
+
+            to = scanner.nextInt();
+            from = scanner.nextInt();
+
+            adj.get(to).add(from);
+            adj.get(from).add(to);
+        }
+
+        //parent[v1] gives parent of a vertex v1
+        int[] parent = new int[v];
+
+        //depth[v1] gives depth of vertex v1 with respect to the root
+        int[] depth = new int[v];
+
+        //Assuming the tree to be rooted at 0, hence calculating parent and depth of every vertex
+        dfs(adj,0,-1,parent,depth);
+
+        //Inputting the two vertices whose LCA is to be calculated
+        int v1 = scanner.nextInt(), v2 = scanner.nextInt();
+
+        //Outputting the LCA
+        System.out.println(getLCA(v1,v2,depth,parent));
+
+    }
+
+    /**
+     * Depth first search to calculate parent and depth of every vertex
+     * @param adj The adjacency list representation of the tree
+     * @param s The source vertex
+     * @param p Parent of source
+     * @param parent An array to store parents of all vertices
+     * @param depth An array to store depth of all vertices
+     */
+    private static void dfs(ArrayList<ArrayList<Integer>> adj, int s, int p, int[] parent, int[] depth){
+        for(int adjacent: adj.get(s)){
+            if(adjacent!=p){
+                parent[adjacent] = s;
+                depth[adjacent] = 1 + depth[s];
+                dfs(adj,adjacent,s,parent,depth);
+            }
+        }
+    }
+
+    /**
+     * Method to calculate Lowest Common Ancestor
+     * @param v1 The first vertex
+     * @param v2 The second vertex
+     * @param depth An array with depths of all vertices
+     * @param parent An array with parents of all vertices
+     * @return Returns a vertex that is LCA of v1 and v2
+     */
+    private static int getLCA(int v1, int v2, int[] depth, int[] parent){
+        if(depth[v1] < depth[v2]){
+            int temp = v1;
+            v1 = v2;
+            v2 = temp;
+        }
+        while(depth[v1]!=depth[v2]){
+            v1 = parent[v1];
+        }
+        if(v1==v2) return v1;
+        while(v1!=v2){
+            v1 = parent[v1];
+            v2 = parent[v2];
+        }
+        return v1;
+    }
+}
+
+/**
+ * Input:
+ * 10
+ * 0 1
+ * 0 2
+ * 1 5
+ * 5 6
+ * 2 4
+ * 2 3
+ * 3 7
+ * 7 9
+ * 7 8
+ * 9 4
+ * Output:
+ * 2
+ */
\ No newline at end of file