题目描述
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.
image
Above is a histogram where width of each bar is 1, given height = [2,1,5,6,2,3]
image
<small style="box-sizing: border-box; font-size: 12px;">The largest rectangle is shown in the shaded area, which has area = 10 unit.</small>
Example:
Input: [2,1,5,6,2,3]
Output: 10思路
用栈来模拟，遍历heights数组，如果大于栈顶元素，就push进去；否则，持续弹栈来计算从栈顶点到降序点的矩阵大小。然后将这一部分全部替换为降序点的值，即做到了整体依然是有序非降的。
整个过程中，即把所有的局部最大矩阵计算过了，又在宽度范围内保留了全部的场景。
代码实现
class Solution:
def largestRectangleArea(self, height):
height.append(0)
stack = [-1]
ans = 0
for i in range(len(height)):
while height[i] < height[stack[-1]]:
h = height[stack.pop()]
w = i - stack[-1] - 1
ans = max(ans, h * w)
stack.append(i)
height.pop()
return ans
