Maximal Square

Medium Subject: 2-D Dynamic Programming

Time Complexity

O(M * N)

Space Complexity

O(M * N)

Problem Description

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.

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

Optimal Solution

Python

Approach: 2-D DP

dp[i][j] represents the side length of the largest square whose bottom-right corner is at (i, j). If matrix[i][j] == '1', then dp[i][j] = min(dp[i-1][j], dp[i][j-1], dp[i-1][j-1]) + 1. We track the maximum side length seen so far.

class Solution:
    def maximalSquare(self, matrix: List[List[str]]) -> int:
        if not matrix: return 0
        m, n = len(matrix), len(matrix[0])
        dp = [[0] * (n + 1) for _ in range(m + 1)]
        max_side = 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
                    max_side = max(max_side, dp[i][j])

        return max_side * max_side