Lowest Common Ancestor of a Binary Tree

Problem Statement

Given a binary tree, find the lowest common ancestor (LCA) of two given nodes in the tree. (link)

According to the definition of LCA on Wikipedia: “The lowest common ancestor is defined between two nodes p and q as the lowest node in T that has both p and q as descendants (where we allow a node to be a descendant of itself).”

Example 1:

Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 1
Output: 3
Explanation: The LCA of nodes 5 and 1 is 3.

Example 2:

Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 4
Output: 5
Explanation: The LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.

Example 3:

Input: root = [1,2], p = 1, q = 2
Output: 1

Constraints:

• p and q will exist in the tree.

Solution

The idea is to return the same node if we find either p or q. If at any node we find both left and right ancestor return nodes, we return the current node because it will be the ancestor of both p and q. If we don't find any node, we return null.

Time - O(n)

Space - O(n) - Height of the tree

class Solution {
    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {

        if(root == null || root == p || root == q){
            return root;
        }
        TreeNode leftLCA = lowestCommonAncestor(root.left, p, q);
        TreeNode rightLCA = lowestCommonAncestor(root.right, p, q);

        if(leftLCA == null){
            return rightLCA;
        }
        else if(rightLCA == null){
            return leftLCA;
        }
        else{
            return root;
        }
    }
}