84. Largest Rectangle in Histogram

Question

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.

Example 1

Input: heights = [2,1,5,6,2,3]
Output: 10
Explanation: The above is a histogram where width of each bar is 1.
The largest rectangle is shown in the red area, which has an area = 10 units.

Solution 1: Brute-Force (TLE)

Time Complexity: O(N^3)
Space Complexity: O(1)

Solution 2: Pruning Brute-Force

Time Complexity: O(N^2)
Space Complexity: O(1)

Solution 3: Stack

class Solution:
    def largestRectangleArea(self, heights: List[int]) -> int:
        ans = 0
        heights.append(0) # dummy tail 0
        stack = []        # Store the index of local maximum
        for idx in range(len(heights)):
            while stack and heights[stack[-1]] >= heights[idx]:
                idxOfLocalMax = stack.pop()
                width = (idx - stack[-1] - 1) if stack else idx
                ans = max(ans, heights[idxOfLocalMax] * width) 
            stack.append(idx)
        return ans

Time Complexity: O(N^2)
Space Complexity: O(N)

Reference

https://www.cnblogs.com/grandyang/p/4322653.html
https://medium.com/hoskiss-stand/largest-rectangle-b3a7473320c1