What is the optimal time complexity of solving Largest Rectangle In Histogram?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Largest Rectangle In Histogram?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Largest Rectangle In Histogram?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Largest Rectangle In Histogram?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Largest Rectangle In Histogram

Learn how to solve the 'Largest Rectangle In Histogram' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Given an array of integers heights representing the histogram's bar height where the width of each bar is 1, return the area of the largest rectangle in the histogram.

Write a function largestRectangleArea(heights: List[int]) -> int.

Constraints

•1 <= len(heights) <= 10^5
•0 <= heights[i] <= 10^4

Examples

Example 1

Input

heights = [2, 1, 5, 6, 2, 3]

Output

Explanation

The largest rectangle has area 10, formed by bars at index 2 and 3 (heights 5 and 6), with width 2 and height 5.

Example 2

Input

heights = [2, 4]

Output

Explanation

The largest rectangle is the bar at index 1 with height 4 and width 1, giving area 4.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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