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Medium

Lowest Common Ancestor of a Binary Search Tree

Given a binary search tree (BST), find the lowest common ancestor (LCA) node 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)."

Examples

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

Constraints

  • The number of nodes in the tree is in the range [2, 10^5].
  • -10^9 <= Node.val <= 10^9
  • All Node.val are unique.
  • p != q
  • p and q will exist in the BST.

Approach

Leverage the BST property. If both `p` and `q` are greater than the root, the LCA must be in the right subtree. If both are less, the LCA must be in the left subtree. Otherwise (they split, or one is equal to the root), the root is the LCA.

Complexity Analysis

Time Complexity
O(h)
Space Complexity
O(h)

Where h is the height of the tree. The space complexity is due to the recursion stack.

Solution.java
class Solution {    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {        if (p.val > root.val && q.val > root.val) {            return lowestCommonAncestor(root.right, p, q);        } else if (p.val < root.val && q.val < root.val) {            return lowestCommonAncestor(root.left, p, q);        } else {            return root;        }    }}