Largest Rectangle In Histogram
Problem
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.
Example 2:
Input: heights = [2,4]
Output: 4
Constraints:
1 <= heights.length <= 1050 <= heights[i] <= 104
Solution
- Stack
- Time: O(n)
- Space: O(n)
class Solution(object):
def largestRectangleArea(self, heights):
"""
:type heights: List[int]
:rtype: int
"""
maxArea = 0
stack = [] # pairL (index, height)
for i, h in enumerate(heights):
start = i
while stack and stack[-1][1] > h:
index, height = stack.pop()
maxArea = max(maxArea, height * (i - index))
start = index
stack.append((start, h))
for i, h in stack:
maxArea = max(maxArea, h * (len(heights) - i))
return maxArea