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221. Maximal Square

Array Dynamic Programming Matrix

Problem - Maximal Square

Medium

Given an m x n binary matrix filled with 0's and 1's, find the largest square containing only 1's and return its area.

 

Example 1:

Input: matrix = [["1","0","1","0","0"],["1","0","1","1","1"],["1","1","1","1","1"],["1","0","0","1","0"]]
Output: 4

Example 2:

Input: matrix = [["0","1"],["1","0"]]
Output: 1

Example 3:

Input: matrix = [["0"]]
Output: 0

 

Constraints:

  • m == matrix.length
  • n == matrix[i].length
  • 1 <= m, n <= 300
  • matrix[i][j] is '0' or '1'.

Solutions

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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)]
        max_sq = 0

        for i in range(m):
            for j in range(n):
                if matrix[i][j] == "1":
                    dp[i + 1][j + 1] = min(dp[i + 1][j], dp[i][j + 1], dp[i][j]) + 1
                    max_sq = max(max_sq, dp[i + 1][j + 1])

        return max_sq**2

Submission Stats:

  • Runtime: 127 ms (69.00%)
  • Memory: 33.2 MB (39.96%)