Lowest Common Ancestor

Given the root and two nodes in a Binary Tree. Find the lowest common ancestor(LCA) of the two nodes.

The lowest common ancestor is the node with largest depth which is the ancestor of both nodes.

Assume two nodes are exist in tree.

Example:

For the following binary tree:

  4
 / \
3   7
   / \
  5   6

LCA(3, 5) = 4

LCA(5, 6) = 7

LCA(6, 7) = 7

Solution:

Divide and conquer. Find the two nodes in left subtree and right subtree separately, if we can't find neither A or B in one subtree, return null.

Then, if both left and right subtree return non-null values, current node is the LCA. If both of them return null values, current node is not the LCA and return null.

Code:

public class Solution {

    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode A, TreeNode B) {
        if (root == null || root == A || root == B) {
            return root;
        }
        TreeNode left = lowestCommonAncestor(root.left, A, B);
        TreeNode right = lowestCommonAncestor(root.right, A, B);
        if (left != null && right != null) {
            return root;
        }
        if (left != null) {
            return left;
        }
        if (right != null) {
            return right;
        }
        return null;
    }
}