Largest Rectangle in Histogram

Problem Description
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.

For example,
Given height = [2,1,5,6,2,3],
return 10.
Solutions
I. Using stack:
The idea is using stack to store non-decreasing elements.

class Solution:
    # @param {integer[]} height
    # @return {integer}
    def largestRectangleArea(self, height):
        height.append(0)
        stack, area = [], 0
        for i in range(len(height)):
            while stack and height[stack[-1]] > height[i]:
                h = height[stack.pop()]
                w = i if not stack else i-stack[-1]-1
                area = max(area, h*w)
            stack.append(i)
        return area

Further Discussion
This is a pretty interesting problem. It has many applications, one of which you can see in this post.
We also can expand the problem to some other problems. Can you solve the following problems? Please post a comment to discuss ^_^.
A. Find the largest rectangle in this special "Historgram"
We expand the histogram to both directions - positive and negative, as in the picture below.

B. Find the largest box in 3-d Histogram
The original problem is a 2D histogram. Suppose we have 3D histogram, can we find the box with maximum volume?