# Lowest Common Ancestor of a Binary Search Tree 🐳

2 min readApr 4, 2022

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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 = 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.

**Example 3:**

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

**Output:** 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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