Dsa Dp Max Square

In this tutorial, you'll learn about How to Fix Maximal Square Errors. We cover key concepts, practical examples, and best practices.

Fix maximal square errors when integer vs character matrix handling and DP recurrence pattern.

Quick Fix

Wrong

def max_sq(m):
    rows,cols=len(m),len(m[0])
    dp=[[int(c) for c in r] for r in m]
    mx=max(max(r) for r in dp)
    for i in range(1,rows):
        for j in range(1,cols):
            if dp[i][j]:
                dp[i][j]=min(dp[i-1][j],dp[i][j-1],dp[i-1][j-1])+1
                mx=max(mx,dp[i][j])
    return mx*mx

Correct but must convert char '1' to int 1 first.

Right

def maximalSquare(self, m):
    if not m: return 0
    rows,cols=len(m),len(m[0])
    dp=[[int(m[i][j]) for j in range(cols)] for i in range(rows)]
    mx=max(max(r) for r in dp)
    for i in range(1,rows):
        for j in range(1,cols):
            if dp[i][j]:
                dp[i][j]=min(dp[i-1][j],dp[i][j-1],dp[i-1][j-1])+1
                mx=max(mx,dp[i][j])
    return mx*mx

[['1','0','1','0','0'],['1','0','1','1','1'],['1','1','1','1','1'],['1','0','0','1','0']] -> 4 (2x2 square). O(rows*cols).

Prevention

DP: dp[i][j] = side length of largest square ending at (i,j). If cell=1: min(left,up,diagonal)+1.

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