Verify Preorder Sequence in Binary Search Tree

Verify Preorder Sequence in Binary Search Tree - Problem

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

In a binary search tree, for any node:

All values in the left subtree are less than the node's value
All values in the right subtree are greater than the node's value

In a preorder traversal, we visit nodes in the order: root → left subtree → right subtree

Input & Output

Example 1 — Valid BST Preorder

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

› Output: true

💡 Note: This represents a valid BST: root=5, left subtree has 2,1,3 (all < 5), right subtree has 6 (> 5). The preorder traversal follows root→left→right pattern.

Example 2 — Invalid BST Preorder

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

› Output: false

💡 Note: After visiting 6 (right subtree of 5), we cannot visit 1 which is less than 5. This violates BST property as we're in the right subtree where all values should be > 5.

Example 3 — Single Node

$ Input: preorder = [1]

› Output: true

💡 Note: A single node is always a valid BST, so any single element array is a valid preorder sequence.

Constraints

1 ≤ preorder.length ≤ 10⁴
1 ≤ preorder[i] ≤ 10⁸
All integers in preorder are unique

Visualization

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Understanding the Visualization

Input

Preorder array [5,2,1,3,6]

Process

Use stack to track path and validate BST property

Output

Return true if valid BST preorder sequence

Key Takeaway

🎯 Key Insight: Use a monotonic stack to efficiently validate BST constraints during preorder traversal

Asked in

G Google 25 a Amazon 20 f Facebook 15 M Microsoft 12

The key insight is to use a monotonic stack to simulate the path from root to current node. The optimal approach maintains a minimum bound and validates each element against BST constraints. Time: O(n), Space: O(n)

Common Approaches

Approach	Time	Space	Notes
✓ Recursive Tree Construction	O(n)	O(n)	Try to construct the actual BST from the preorder sequence
Monotonic Stack	O(n)	O(n)	Use a stack to track the path and validate BST property efficiently

Recursive Tree Construction — Algorithm Steps

Step 1: Start with full range [-∞, +∞] for root
Step 2: For each node, recursively build left subtree with upper bound as current value
Step 3: Build right subtree with lower bound as current value
Step 4: Return true if all elements are consumed

Visualization

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Step-by-Step Walkthrough

Start with Root

First element becomes root with bounds [-∞, +∞]

Build Left Subtree

Recursively process elements with upper bound as root value

Build Right Subtree

Process remaining elements with lower bound as root value

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <limits.h>
#include <stdbool.h>

int index_global;

bool buildTree(int* preorder, int size, int minVal, int maxVal) {
    if (index_global >= size) {
        return true;
    }
    
    int val = preorder[index_global];
    if (val < minVal || val > maxVal) {
        return true;
    }
    
    index_global++;
    bool leftValid = buildTree(preorder, size, minVal, val);
    bool rightValid = buildTree(preorder, size, val, maxVal);
    return leftValid && rightValid;
}

bool solution(int* preorder, int size) {
    index_global = 0;
    buildTree(preorder, size, INT_MIN, INT_MAX);
    return index_global == size;
}

int main() {
    char line[10000];
    fgets(line, sizeof(line), stdin);
    line[strcspn(line, "\n")] = 0;
    
    int preorder[1000];
    int size = 0;
    
    char* token = strtok(line + 1, ",]");
    while (token != NULL) {
        preorder[size++] = atoi(token);
        token = strtok(NULL, ",]");
    }
    
    bool result = solution(preorder, size);
    printf(result ? "true\n" : "false\n");
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Visit each element once with proper bounds checking

✓ Linear Growth

Space Complexity

O(n)

Recursion stack can go up to n levels in worst case

⚡ Linearithmic Space

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Medium Frequency

~15 min Avg. Time

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Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Recursive Tree Construction — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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