235 Lowest Common Ancestor of a Binary Search Tree¶

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] alt

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.

Solution: Recursion¶

Time complexity: O(n) Space complexity: O(n)

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
        int min = Math.min(p.val, q.val);
        int max = Math.max(p.val, q.val);
        return lca(root, min, max);
    }
    private TreeNode lca(TreeNode root, int min, int max) {
        if (root.val >= min && root.val <= max) {
            return root;
        }
        if (root.val > max) {
            return lca(root.left, min, max);
        }
        if (root.val < min) {
            return lca(root.right, min, max);
        }
        return null;
    }
}

class Solution {
public:
  TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {
    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;
  }
};