236. Lowest Common Ancestor of a Binary Tree #

Problem #

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.

Note:

• All of the nodes’ values will be unique.
• p and q are different and both values will exist in the binary tree.

Problem Summary #

Given a binary tree, find the lowest common ancestor of two specified nodes in the tree.

The definition of the lowest common ancestor on Baidu Baike is: “For two nodes p and q in a rooted tree T, the lowest common ancestor is represented as a node x, such that x is an ancestor of p and q and the depth of x is as large as possible (a node can also be its own ancestor).”

Solution Approach #

• This is a classic problem: finding the LCA (lowest common ancestor) of two nodes in any binary tree, testing recursion

Code #

package leetcode

/**
 * Definition for TreeNode.
 * type TreeNode struct {
 *     Val int
 *     Left *ListNode
 *     Right *ListNode
 * }
 */
func lowestCommonAncestor236(root, p, q *TreeNode) *TreeNode {
	if root == nil || root == q || root == p {
		return root
	}
	left := lowestCommonAncestor236(root.Left, p, q)
	right := lowestCommonAncestor236(root.Right, p, q)
	if left != nil {
		if right != nil {
			return root
		}
		return left
	}
	return right
}