[LeetCode] Largest Rectangle in Histogram

84. Largest Rectangle in Histogram

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.


For example,

Given heights = [2,1,5,6,2,3],

return 10.

Solution

class Solution(object):
    def largestRectangleArea(self, heights):
        stack = [-1]
        heights.append(0)
        res = 0
        for i in xrange(len(heights)):
            while heights[i] < heights[stack[-1]]:
                h = heights[stack.pop()]
                w = i - stack[-1] - 1
                res = max(res, h*w)
            stack.append(i)
        return res

解析：

stack中存储已遍历方块中与未遍历方块连通的最大高度（由小于左边方块高度的方块的高度决定）