Leetcode 221. Maximal Square

Problem

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.

Algorithm

Dynamic Programming (DP). Tracks the largest square ending at (i,j). The key recurrence relation is derived from:

dp[i][j] = min(dp[i-1][j], dp[i][j-1], dp[i-1][j-1]) + 1

Code

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)]
        
        ans = 0
        for i in range(1, m + 1):
            for j in range(1, n + 1):
                if matrix[i-1][j-1] == '1':
                    dp[i][j] = min(dp[i-1][j], dp[i][j-1], dp[i-1][j-1]) + 1
                    if ans < dp[i][j]:
                        ans = dp[i][j]
        
        return ans * ans