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Maximal Square

Problem Statement​

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.

Leetcode Link

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'.

Code​

Python Code

class Solution:
    def maximalSquare(self, matrix: List[List[str]]) -> int:
        if matrix is None or len(matrix) < 1:
            return 0

        rows = len(matrix)
        cols = len(matrix[0])

        dp = [[0]*(cols+1) for _ in range(rows+1)]
        max_side = 0

        for r in range(rows):
            for c in range(cols):
                if matrix[r][c] == '1':
                    dp[r+1][c+1] = min(dp[r][c], dp[r+1][c], dp[r][c+1]) + 1 # Be careful of the indexing since dp grid has additional row and column
                    max_side = max(max_side, dp[r+1][c+1])

        return max_side * max_side