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.

Input and output examples

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.

Example 2:

Input: heights = [2,4] Output: 4

Constraints:

1 <= heights.length <= 105 0 <= heights[i] <= 104

Solution

class Solution(object): def largestRectangleArea(self, heights): """ :type heights: List[int] :rtype: int """ if not heights: return 0 stack = [] max_area = 0 for i in range(len(heights)): if not stack or heights[i] >= heights[stack[-1]]: stack.append(i) else: while stack and heights[i] < heights[stack[-1]]: h = heights[stack.pop()] w = i if not stack else i - stack[-1] - 1 max_area = max(max_area, h * w) stack.append(i) while stack: h = heights[stack.pop()] w = len(heights) if not stack else len(heights) - stack[-1] - 1 max_area = max(max_area, h * w) return max_area

Test the the solution:

s = Solution() print(s.largestRectangleArea([2,1,5,6,2,3])) print(s.largestRectangleArea([2,4])) print(s.largestRectangleArea([2,4,5,6,7,8,9])) print(s.largestRectangleArea([9,8,7,6,5,4,3,2,1])) print(s.largestRectangleArea([1,2,3,4,5,6,7,8,9]))

More interview questions can be found here: Algorithm

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