题目描述

给定一个仅包含 0 和 1 、大小为 rows x cols 的二维二进制矩阵，找出只包含 1 的最大矩形，并返回其面积。

示例 1：

输入：matrix = [["1","0","1","0","0"],["1","0","1","1","1"],["1","1","1","1","1"],["1","0","0","1","0"]]
输出：6
解释：最大矩形如上图所示。

示例 2：

输入：matrix = [["0"]]
输出：0

示例 3：

输入：matrix = [["1"]]
输出：1

思路

逐行累积，每次一行累加完，就去计算柱状图中最大的矩形：leetcode-84. 柱状图中最大的矩形-CSDN博客【先做84题，在做本题】

class Solution(object):
    def max_area(self, heights):
        heights = [0]+heights+[0] # 这里以后改成这么写
        res = 0
        stack = [0]
        for i in range(1, len(heights)):
            if heights[i]>heights[stack[-1]]:
                stack.append(i)
            elif heights[i] == heights[stack[-1]]:
                stack.pop()
                stack.append(i)
            else:
                while stack and heights[i]<heights[stack[-1]]:
                    mid = stack[-1]
                    stack.pop()
                    if stack:
                        right = i
                        left = stack[-1]
                        w = right-left-1
                        h = heights[mid]
                        res = max(res, w*h)
                stack.append(i)
        return res
    def maximalRectangle(self, matrix):
        """
        :type matrix: List[List[str]]
        :rtype: int
        """
        m,n = len(matrix), len(matrix[0])
        heights = [0]*n
        max_area = 0
        # 助行累加
        for i in range(m):
            for j in range(n):
                if matrix[i][j]=='1':
                    heights[j]+=1
                else:
                    heights[j] = 0
            max_area = max(max_area, self.max_area(heights))
        return max_area

if __name__ == '__main__':
    s = Solution()
    # matrix = [["1"]]
    matrix = [["1", "0", "1", "0", "0"],
              ["1", "0", "1", "1", "1"],
              ["1", "1", "1", "1", "1"],
              ["1", "0", "0", "1", "0"]]
    # matrix = [["1","0"],["1","0"]]
    print(s.maximalRectangle(matrix))