Given n non-negative integers representing the histogram's bar height where the width of each bar is 1, find the area of largest rectangle in the histogram.


Above is a histogram where width of each bar is 1, given height = [2,1,5,6,2,3].

 


The largest rectangle is shown in the shaded area, which has area = 10 unit.

 

Example:


Input: [2,1,5,6,2,3]
Output: 10

Difficulty: MEDIUM_HARD
Starter code: class Solution:
    def largestRectangleArea(self, heights: List[int]) -> int:
        

Solutions:
class Solution:

	def largestRectangleArea(self, heights):
		if not heights:
			return 0
		stack = [0]
		heights.append(0)
		max_area = 0
		for i in range(len(heights)):
			if heights[i] >= stack[-1]:
				stack.append(heights[i])
			else:
				k = len(stack) - 1
				count = 0
				while heights[i] < stack[k] and k >= 0:
					count += 1
					area = count * stack[k]
					if max_area < area:
						max_area = area
					k -= 1
				stack = stack[:-count] + [heights[i]] * (count + 1)
		return max_area


class Solution:

	def largestRectangleArea(self, heights):
		if not heights:
			return 0
		max_area = 0
		stack = []
		i = 0
		while i < len(heights):
			while i < len(heights) and (len(stack) == 0 or heights[i] > heights[stack[-1]]):
				stack.append(i)
				i += 1
			tmp = stack.pop()
			if stack:
				area = heights[tmp] * (i - stack[-1] - 1)
			else:
				area = heights[tmp] * i
			max_area = max(area, max_area)
		while stack:
			tmp = stack.pop()
			if stack:
				area = heights[tmp] * (i - stack[-1] - 1)
			else:
				area = heights[tmp] * i
			max_area = max(area, max_area)
		return max_area


class Solution:

	def largestRectangleArea(self, heights):
		stack = list()
		helper_stack = list()
		max_area = 0
		for i in heights:
			if not stack:
				stack.append(i)
			elif i >= stack[-1]:
				stack.append(i)
			else:
				width = 0
				helper_stack.append(i)
				while stack and stack[-1] > i:
					width += 1
					height = stack.pop()
					helper_stack.append(i)
					max_area = max(max_area, height * width)
				while helper_stack:
					stack.append(helper_stack.pop())
		width = 0
		while stack:
			width += 1
			height = stack.pop()
			max_area = max(max_area, height * width)
		return max_area


class Solution:

	def largestRectangleArea(self, heights):
		stk = []
		res = 0
		for i in range(len(heights)):
			if len(stk) == 0 or heights[i] >= heights[stk[-1]]:
				stk.append(i)
			else:
				end_p = stk[-1]
				while len(stk) > 0 and heights[stk[-1]] >= heights[i]:
					start_p = stk.pop()
					res = max(res, (end_p - start_p + 1) * heights[start_p])
				res = max(res, heights[i] * (i - start_p + 1))
				heights[start_p] = heights[i]
				stk.append(start_p)
				stk.append(i)
		if len(stk) > 0:
			end_p = stk[-1]
			while len(stk) > 0:
				start_p = stk.pop()
				res = max(res, (end_p - start_p + 1) * heights[start_p])
		return res


class Solution:

	def largestRectangleArea(self, heights):
		(ans, stack) = (0, [])
		for i in range(len(heights)):
			while stack and heights[i] < heights[stack[-1]]:
				h = heights[stack.pop()]
				w = i - 1 - stack[-1] if stack else i
				ans = max(ans, h * w)
			stack.append(i)
		while stack:
			h = heights[stack.pop()]
			w = len(heights) - 1 - stack[-1] if stack else len(heights)
			ans = max(ans, h * w)
		return ans


class Solution:

	def largestRectangleArea(self, heights):
		n = len(heights)
		if n == 0:
			return 0
		left = [i for i in range(n)]
		right = [i + 1 for i in range(n)]
		print(heights)
		for i in range(1, n):
			cur = i - 1
			while cur >= 0 and heights[cur] >= heights[i]:
				left[i] = left[cur]
				cur = left[cur] - 1
		for j in range(n - 1, -1, -1):
			cur = j + 1
			while cur < n and heights[cur] >= heights[j]:
				right[j] = right[cur]
				cur = right[cur]
		print(left)
		print(right)
		max_val = 0
		for i in range(n):
			tmp = heights[i] * (right[i] - left[i])
			if max_val < tmp:
				max_val = tmp
		return max_val


class Solution:

	def largestRectangleArea(self, heights):
		if not heights:
			return 0
		N = len(heights)
		(left, right) = ([1] * N, [1] * N)
		for i in range(1, N):
			j = i - 1
			while j >= 0 and heights[j] >= heights[i]:
				left[i] += left[j]
				j -= left[j]
		for i in range(N - 1, -1, -1):
			j = i + 1
			while j <= N - 1 and heights[j] >= heights[i]:
				right[i] += right[j]
				j += right[j]
		return max(((l + r - 1) * h for (l, r, h) in zip(left, right, heights)))


class Solution:

	def largestRectangleArea(self, heights):
		stack = []
		ans = 0
		heights += [-1]
		for i in range(len(heights)):
			left = i
			while 1:
				if len(stack) == 0:
					stack.append((heights[i], left))
					break
				if stack[-1][0] < heights[i]:
					stack.append((heights[i], left))
					break
				elif stack[-1][0] == heights[i]:
					break
				else:
					ans = (i - stack[-1][1]) * stack[-1][0] if (i - stack[-1][1]) * stack[-1][0] > ans else ans
					left = stack[-1][1]
					del stack[-1]
		return ans