Leetcode: Maximal Square

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本文介绍了一种解决二维二进制矩阵中寻找包含所有元素为1的最大正方形问题的方法。通过高度数组记录每列连续1的数量，并利用最大矩形面积算法求解最大正方形面积。

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Question

Given a 2D binary matrix filled with 0’s and 1’s, find the largest square containing all 1’s and return its area.

For example, given the following matrix:

1 0 1 0 0
1 0 1 1 1
1 1 1 1 1
1 0 0 1 0
Return 4.
Credits:
Special thanks to @Freezen for adding this problem and creating all test cases.

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Solution 1

Get idea from here.

class Solution(object):
    def maximalSquare(self, matrix):
        """
        :type matrix: List[List[str]]
        :rtype: int
        """

        maxv = 0

        if matrix==[] or len(matrix)==0 or len(matrix[0])==0:
            return maxv

        m, n = len(matrix), len(matrix[0])
        height = [0]*n
        for mind in range(m):
            for nind in range(n):
                height[nind] += int(matrix[mind][nind])
            maxv = max( maxv, self.largestRectangle(height) ) 

        return maxv

    def largestRectangle(self,height):

        maxv = 0

        if height==[] or len(height)==0:
            return maxv

        stack = []
        for ind in range(len(height)):
            while stack!=[] and height[ind]<=height[stack[-1]]:
                index = stack.pop()
                curarea = ind*height[index] if stack==[] else (ind-stack[-1]-1)*height[index]
                maxv = max(maxv, curarea)

            stack.append(ind)

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

        return maxv

Solution 2

python