Largest Rectangle in Histogram

Author: anantkaushik

84-largest-rectangle-in-histogram.py

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+"""
+Problem Link: https://leetcode.com/problems/largest-rectangle-in-histogram/
+
+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 <= 105
+0 <= heights[i] <= 104
+"""
+# Time Complexity: O(N)
+
+class Solution:
+ def largestRectangleArea(self, heights: List[int]) -> int:
+ lb = [] # left boundary
+ stack = []
+ 
+ for index in range(len(heights)):
+ while stack and heights[stack[-1]] >= heights[index]:
+ stack.pop()
+ 
+ lb.append(stack[-1] if stack else -1)
+ stack.append(index)
+ 
+ rb = [0] * len(heights) # right boundary
+ stack = []
+ 
+ for index in range(len(heights)-1, -1, -1):
+ while stack and heights[stack[-1]] >= heights[index]:
+ stack.pop()
+ 
+ rb[index] = stack[-1] if stack else len(heights)
+ stack.append(index)
+ 
+ max_area = 0
+ for index in range(len(heights)):
+ width = rb[index] - lb[index] - 1
+ max_area = max(max_area, width * heights[index])
+ 
+ return max_area