Largest Rectangle in Histogram

最新推荐文章于 2024-11-16 19:28:39 发布

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本文介绍了一种求解直方图中最大矩形面积的有效算法。通过使用栈来跟踪元素，该算法能在O(n)的时间复杂度内找到给定直方图中最大的矩形区域。文章提供了详细的代码实现及解析。

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Question

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 height = [2,1,5,6,2,3],
return 10.

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My first try

class Solution(object):
    def largestRectangleArea(self, height):
        """
        :type height: List[int]
        :rtype: int
        """

        if height==[]:
            return 0

        stack = []
        cur, maxnum = 0, 0
        for ind, elem in enumerate(height):
            while stack!=[] and elem<=height[stack[-1]]:
                index = stack.pop()
                cur = ind*height[index] if stack==[] else (ind - index)*height[index]
                maxnum = max(cur, maxnum)

            stack.append(ind)

        while stack!=[]:
            index = stack.pop()
            cur = len(height)*height[index] if stack==[] else (len(height)-index)*height[index]
            maxnum = max(cur, maxnum)

        return maxnum

Solution

Analysis

Get idea from here1, here2

Code

class Solution(object):
    def largestRectangleArea(self, height):
        """
        :type height: List[int]
        :rtype: int
        """

        if height==[]:
            return 0

        stack = []      # stack contains elements in increasing order
        cur, maxnum = 0, 0
        for ind, elem in enumerate(height):
            while stack!=[] and elem<=height[stack[-1]]:
                index = stack.pop()

                # if stack==[], it means all elems with index less than ind are higher than elem, so area = ind*height[index] 
                cur = ind*height[index] if stack==[] else (ind - stack[-1] -1)*height[index]  
                maxnum = max(cur, maxnum)

            stack.append(ind)

        while stack!=[]:
            index = stack.pop()
            cur = len(height)*height[index] if stack==[] else (len(height)-stack[-1]-1)*height[index]
            maxnum = max(cur, maxnum)

        return maxnum