To find the lowest common ancestor of a binary tree in java requires that we run through a binary search tree and how it operates.

What
then is a binary search tree? A Binary tree is a data structure in
which each node can have at most two children. That is, each node in the
binary tree will have data, left child and right child. The first node
of the tree is called the **Root**.

Below is the image of the Binary search tree, the first circle with 15 is called the root node and it has two children, left and right nodes with the values,10 and 20 respectively. Node 10 has two children too with 5 and 13 as values. The left child of node 10 does not have any child but, the right node with value 13 has two children nodes 12 and 14 respectively.

Fig 1.0: Finding the lowest common ancestor.

There are some important things to note when determining is if a tree is a binary tree or not, which are :

All data in the nodes of the left sub-tree are lesser than the right.

In the Children nodes, all data on the left are lesser than the right.

All data in the nodes of the left sub-tree is lesser than the root

All data in the nodes of the right sub-tree is greater than the root.

So, with all these bullet points you can determine if a tree is a binary tree or not.

Now, before looking into codes what do we mean by the lowest common ancestor? Let’s see.

The lowest common ancestor is defined between two nodes n1 and n2 as the lowest node in T that has both n1 and n2 as descendants(where we allow a node to be a descendant of itself).

Or we can say **The lowest common
Ancestor (LCA) of two nodes and in a rooted tree is the lowest (deepest)
node that is an ancestor of both **and remember that an ancestor of a
node in a rooted tree is any node that lies on the path from the root to
(including).

Note the following:

· All of the node’s values will be unique.

· node1 and node2 are different and both values will exist in the binary tree.

· You can use extra memory, helper functions, and can modify the node structure but, you can’t add a parent pointer.

__Java Program to find the Lowest Common Ancestor of a Binary Tree__

We would be looking at how to find the lowest common ancestor of a binary search tree in java. I'm sure the picture above communicates something about the problem we are about to solve. Let's check some codes!

- public class LowestCommonAncestor {
- static class Node {
- int data;
- Node left, right;
- public Node(int data) {
- this.data = data;
- left = right = null;
- }
- }
- public static int LCA(Node root, int n1, int n2) {
- if (root == null) {
- return -1;
- }
- Node current= root;
- int lca = -1;
- while (current != null) {
- if (current.data < n1 && current.data < n2) {
- // LCA is present in the right sub tree
- current = current.right;
- } else if (current.data > n1 &¤t.data > n2) {
- // LCA is present in left sub tree
- current = current.left;
- } else {
- lca = current.data;
- break;
- }
- }
- return lca;
- }
- public static void main(String[] args) {
- LowestCommonAncestor.Node root = new LowestCommonAncestor.Node(20);
- root.left = new LowestCommonAncestor.Node(11);
- root.right = new LowestCommonAncestor.Node(24);
- root.right.left = new LowestCommonAncestor.Node(21);
- root.right.right = new LowestCommonAncestor.Node(35);
- root.right.right.left = new LowestCommonAncestor.Node(32);
- root.right.right.right = new LowestCommonAncestor.Node(40);
- System.out.println(LCA(root, 24, 40));
- System.out.println(LCA(root, 11, 21));
- System.out.println(LCA(root, 32, 40));
- }
- }

**OUTPUT:**

24 20 35

Line 1 was the class declaration with an embedded Node class with instance variables: data of type int, right, and left of type node respectively. Constructor was declared in line 5 that takes in parameter “data” of type int and was assigned to the instance variable in line 6. In line 7, right was assigned to left, and null was assigned to the right.

In other words, it means left is null. The method LCA was declared in line 10 with three parameters which are the root of type node, int n1, and n2 respectively. If the root is null then it should return -1 in line 12.

Line 14 stored the root parameter into the variable "current" of the type node. Variable "lca" of type int was set to -1 too.

So, from line 17, inasmuch as the root is not null it would proceed to check if the data in the current node is less than n1 and n2 and if so current.right is assigned to current(which means "lca" is present in the right sub-tree) else, if the data in the current node is greater than n1 and n2, current.left is assigned to current(which means "lca" is present in the left sub-tree).

But if the two conditions are not met. Variable "lca" should still hold current.data. Line 25 breaks the loop and "lca" was returned in line 28

The
main method starts from line 30 and line 31 created the instance of the
“LowestCommonAncestor” class, with the value of 20 as the root.

Line
32 to line 37 were adding data to the nodes as specified from the root
whether left or right. Line 38,39 and 40 called the method “LCA”
respectively and was printed out.

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