# How to find lowest common ancestor of a binary tree ?

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

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).”

Given the following binary tree: root = [3,5,1,6,2,0,8,null,null,7,4]

**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.

Below is a simple code in javascript with clean comments which are self explanatory.

/** * Definition for a binary tree node. * function TreeNode(val) { * this.val = val; * this.left = this.right = null; * } */ /** * @param {TreeNode} root * @param {TreeNode} p * @param {TreeNode} q * @return {TreeNode} */ var lowestCommonAncestor = function(root, p, q) { if (!root || root === p || root === q) return root // if match is found or entire tree is traversed, return root var left = lowestCommonAncestor(root.left, p, q); // recursive tree traversal visit left node var right = lowestCommonAncestor(root.right, p, q); // recursive tree traversal visit right node if (!left) return right; // if not NULL return left node as p and q are in left subtree if (!right) return left; // if not NULL return right node as p and q are in left subtree return root; // return root node };