Is Maximum Binary Tree easy or hard?

Maximum Binary Tree is rated Medium difficulty on LeetCode. The recursive solution is straightforward once the definition is understood, but identifying and implementing the optimal monotonic stack solution requires stronger algorithmic insight.

Maximum Binary Tree Python/Java solution

Python and Java implementations typically follow either recursive divide and conquer or the monotonic stack approach. The recursive version is shorter and closely mirrors the problem definition, while the stack-based version achieves optimal O(n) time and is preferred for large inputs.

How to solve Maximum Binary Tree in O(n)?

Use a monotonic decreasing stack. Iterate through the array, popping smaller elements and assigning them as the left child of the current node. If a larger element remains on the stack, it becomes the parent and the current node becomes its right child. Each element is pushed and popped once, resulting in linear O(n) time.

What is the best approach for Maximum Binary Tree?

The optimal approach uses a monotonic decreasing stack. It processes the array once and links nodes while maintaining decreasing order, ensuring each element is pushed and popped at most once. This builds the same tree as the recursive definition but runs in O(n) time with O(n) space.

Is Maximum Binary Tree asked at Google/Amazon/Meta?

Maximum Binary Tree is a classic stack and tree construction problem commonly seen in coding interviews at companies like Amazon and Google. It tests understanding of divide and conquer, monotonic stacks, and binary tree construction from arrays.

What data structure is used in Maximum Binary Tree?

The key data structures are binary trees and stacks. The recursive solution relies on divide and conquer to build the tree, while the optimized solution uses a monotonic stack to determine parent-child relationships efficiently.

What is the time complexity of Maximum Binary Tree?

The divide and conquer approach has O(n^2) worst-case time because each recursive call scans the remaining subarray to find the maximum. The optimized monotonic stack solution reduces this to O(n) time since each element is processed once. Space complexity for both approaches is O(n).

Description Solution Video 11:54

654. Maximum Binary Tree

Medium86.3% acceptance3 companies

You are given an integer array nums with no duplicates. A maximum binary tree can be built recursively from nums using the following algorithm:

Create a root node whose value is the maximum value in nums.
Recursively build the left subtree on the subarray prefix to the left of the maximum value.
Recursively build the right subtree on the subarray suffix to the right of the maximum value.

Return the maximum binary tree built from nums.

Example 1:

Input: nums = [3,2,1,6,0,5]
Output: [6,3,5,null,2,0,null,null,1]
Explanation: The recursive calls are as follow:
- The largest value in [3,2,1,6,0,5] is 6. Left prefix is [3,2,1] and right suffix is [0,5].
    - The largest value in [3,2,1] is 3. Left prefix is [] and right suffix is [2,1].
        - Empty array, so no child.
        - The largest value in [2,1] is 2. Left prefix is [] and right suffix is [1].
            - Empty array, so no child.
            - Only one element, so child is a node with value 1.
    - The largest value in [0,5] is 5. Left prefix is [0] and right suffix is [].
        - Only one element, so child is a node with value 0.
        - Empty array, so no child.

Example 2:

Input: nums = [3,2,1]
Output: [3,null,2,null,1]

Constraints:

1 <= nums.length <= 1000
0 <= nums[i] <= 1000
All integers in nums are unique.

Asked at 3 companies

Microsoft

Google Meta

Topics

11:54

Still stuck?Read 3 approaches, or watch a walkthrough.

Open solution

654. Maximum Binary Tree

Asked at 3 companies

Topics

Similar problems