LeetCode-221. 最大正方形

在一个由 ‘0’ 和 ‘1’ 组成的二维矩阵内，找到只包含 ‘1’ 的最大正方形，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：4

示例 2：

输入：matrix = [["0","1"],["1","0"]]
输出：1

示例 3：

输入：matrix = [["0"]]
输出：0

来源：力扣（LeetCode）
链接：https://leetcode.cn/problems/maximal-square
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代码1：

class Solution:
    def maximalSquare(self, matrix: List[List[str]]) -> int:
        m, n = len(matrix), len(matrix[0])
        dp = [[0]*(n+1) for _ in range(m+1)]
        maxside = 0
        for i in range(m):
            for j in range(n):
                if matrix[i][j] == '1':
                    dp[i][j] = min(dp[i-1][j], dp[i][j-1], dp[i-1][j-1]) + 1
                    maxside = max(dp[i][j], maxside)
        return maxside**2

代码2：优化空间

class Solution:
    def maximalSquare(self, matrix: List[List[str]]) -> int:
        m, n = len(matrix), len(matrix[0])
        dp = [0]*(n+1)
        maxside = 0
        for i in range(m):
            northwest = 0
            for j in range(n):
                nextnorthwest = dp[j+1]
                if matrix[i][j] == '1':
                    dp[j+1] = min(dp[j], dp[j+1], northwest) + 1
                    maxside = max(dp[j+1], maxside)
                else:
                    dp[j+1] = 0
                northwest = nextnorthwest
        return maxside**2