Is Verify Preorder Sequence in Binary Search Tree easy or hard?

Verify Preorder Sequence in Binary Search Tree is generally considered a medium difficulty problem. The challenge lies in recognizing the preorder traversal pattern of a BST and translating that constraint into a linear stack-based validation algorithm.

Verify Preorder Sequence in Binary Search Tree Python/Java solution

Python and Java implementations typically use a stack to store ancestor values and a variable to track the minimum allowed value. Iterate through the preorder array, pop smaller elements when transitioning to a right subtree, update the lower bound, and push the current value. If any value becomes smaller than the lower bound, return false.

How to solve Verify Preorder Sequence in Binary Search Tree in O(n)?

Traverse the preorder array once while maintaining a stack and a variable that represents the lowest valid value. If the current number is smaller than the allowed lower bound, the sequence is invalid. While the stack contains smaller values, pop them and update the lower bound because the traversal has entered a right subtree. Push the current value onto the stack. This single pass verifies the BST preorder property in linear time.

What is the best approach for Verify Preorder Sequence in Binary Search Tree?

The most efficient approach uses a monotonic stack with a lower bound check. As you scan the preorder array, the stack keeps track of ancestors whose right subtree has not been processed. Whenever a value is larger than the stack top, nodes are popped and the lower bound is updated. This ensures all nodes in the right subtree remain greater than their parent. The algorithm runs in O(n) time.

Is Verify Preorder Sequence in Binary Search Tree asked at Google/Amazon/Meta?

Verify Preorder Sequence in Binary Search Tree appears in interviews at companies that emphasize tree traversal reasoning and stack-based algorithms. Variants of this problem have been reported at companies such as Google, Meta, and Amazon because it tests understanding of BST properties and preorder traversal behavior.

What data structure is used in Verify Preorder Sequence in Binary Search Tree?

The optimal solution relies on a stack to simulate traversal through ancestors while validating BST constraints. The stack helps track nodes whose right subtree has not yet been visited. A lower bound variable ensures that once the traversal enters a right subtree, all future nodes remain greater than the parent value.

What is the time complexity of Verify Preorder Sequence in Binary Search Tree?

The optimal monotonic stack solution runs in O(n) time because each element is pushed and popped from the stack at most once. Space complexity is O(n) in the worst case when the preorder sequence represents a completely decreasing tree. Recursive solutions also run in O(n) time but use recursion stack space proportional to the tree height.

255. Verify Preorder Sequence in Binary Search Tree - Practice Online

Given an array of unique integers preorder, return true if it is the correct preorder traversal sequence of a binary search tree.

Example 1:

Input: preorder = [5,2,1,3,6]
Output: true

Example 2:

Input: preorder = [5,2,6,1,3]
Output: false

Constraints:

1 <= preorder.length <= 10⁴
1 <= preorder[i] <= 10⁴
All the elements of preorder are unique.

Follow up: Could you do it using only constant space complexity?