老卫带你学---leetcode刷题(221. 最大正方形)

221. 最大正方形

问题：

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
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5

示例 2：


输入：matrix = [["0","1"],["1","0"]]
输出：1
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5

示例 3：

输入：matrix = [["0"]]
输出：0
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4

提示：

m == matrix.length
n == matrix[i].length
1 <= m, n <= 300
matrix[i][j] 为 '0' 或 '1'
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解决：

dp

dp数组维护的正方形的变长

dp[i+1][j+1]=min(min(dp[i+1][j],dp[i][j+1]),dp[i][j])
那最大正方形的面积就是 最大的边长*最大的边长

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