Lowest Common Ancestor of a Binary Search Tree 🐳

Question

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).”

Example 1:

`Input: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 8Output: 6Explanation: 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 = 4Output: 2Explanation: The LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition.`

Example 3:

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

Constraints:

• The number of nodes in the tree is in the range `[2, 105]`.
• `-109 <= Node.val <= 109`
• All `Node.val` are unique.
• `p != q`
• `p` and `q` will exist in the BST.

Solution

Time complexity O(3n) -> O(n)

Space complexity O(3n) -> O(n)

Time Complexity O(n)

Space Complexity O(n)

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