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Search in a Binary Search Tree

Easy Trees & BST BST Basics Original on LeetCode

Search in a Binary Search Tree is a easy trees & bst problem solved with the bst basics pattern. The best approach, iterative, runs in O(h) time and O(1) space. Below are 2 approaches in Java, from recursive up.

Problem

Given the root of a binary search tree and a value, return the subtree rooted at the node with that value, or null if it does not exist.

Examples

Example 1

Input
root = [4, 2, 7, 1, 3], val = 2
Output
[2, 1, 3]
Why
Return the subtree rooted at the node with value 2.

Example 2

Input
root = [4, 2, 7, 1, 3], val = 5
Output
[]

Constraints

  • The tree has 1 to 5000 nodes; it is a valid BST.

Animated walkthrough

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Concepts first, then the problem and every approach, step by step.

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Solutions

Try it yourself first. Then compare: each approach lists its idea, the steps, its time and space, and the Java code.

ApproachTimeSpace
RecursiveO(h)O(h)
IterativeO(h)O(1)

1Recursive

TimeO(h)
SpaceO(h)

If val is smaller, search left; if larger, search right; if equal, return the node.

  1. if root == null || root.val == val return root.
  2. return val < root.val ? search(left) : search(right).
Java
class Solution {
    public TreeNode searchBST(TreeNode root, int val) {
        if (root == null || root.val == val) return root;
        return val < root.val ? searchBST(root.left, val) : searchBST(root.right, val);
    }
}

2Iterative

TimeO(h)h is O(log n) for a balanced tree, O(n) for a skewed one.
SpaceO(1)

Same decisions in a loop, with no call stack.

  1. while root != null && root.val != val: move left or right.
Java
class Solution {
    public TreeNode searchBST(TreeNode root, int val) {
        while (root != null && root.val != val) root = val < root.val ? root.left : root.right;
        return root;
    }
}

Edge cases to test

  • Value not present
  • Value at the root

Hints

Hint 1

At each node, the BST property tells you which one subtree could contain val.

FAQ

What is the best time complexity for Search in a Binary Search Tree?

Iterative runs in O(h) time and O(1) extra space. h is O(log n) for a balanced tree, O(n) for a skewed one.

Which pattern does Search in a Binary Search Tree use?

It is a trees & bst problem that uses the bst basics pattern. Other problems with the same pattern: Minimum element in BST, Insert into a Binary Search Tree.

Is there a brute force solution for Search in a Binary Search Tree?

Yes. Recursive takes O(h) time and O(h) space. If val is smaller, search left; if larger, search right; if equal, return the node.

Which edge cases should I test for Search in a Binary Search Tree?

Value not present; Value at the root.