235. Lowest Common Ancestor of a Binary Search Tree #

Problem #

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

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 binary search tree: root = [6,2,8,0,4,7,9,null,null,3,5]

Example 1:

Input: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 8
Output: 6
Explanation: The LCA of nodes 2 and 8 is 6.

Example 2:

Input: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 4
Output: 2
Explanation: The LCA of nodes 2 and 4 is 2, 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 BST.

Problem Statement #

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

The definition of 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 #

• To find the lowest common ancestor of two nodes in a binary search tree, because of the special properties of a binary search tree, finding the lowest common ancestor of any two nodes is very simple.

Code #

package leetcode

/**
 * Definition for TreeNode.
 * type TreeNode struct {
 *     Val int
 *     Left *ListNode
 *     Right *ListNode
 * }
 */
func lowestCommonAncestor(root, p, q *TreeNode) *TreeNode {
	if p == nil || q == nil || root == nil {
		return nil
	}
	if p.Val < root.Val && q.Val < root.Val {
		return lowestCommonAncestor(root.Left, p, q)
	}
	if p.Val > root.Val && q.Val > root.Val {
		return lowestCommonAncestor(root.Right, p, q)
	}
	return root
}