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Ones and Zeroes

Difficulty: Medium

Problem Description

You are given an array of binary strings strs and two integers m and n. Return the size of the largest subset of strs such that there are at most m 0's and n 1's in the subset.

Key Insights

  • The problem can be approached using dynamic programming to maximize the subset size under given constraints.
  • Each string contributes a certain number of 0's and 1's, which must be accounted for when forming the subset.
  • The solution involves maintaining a 2D DP array where each cell represents the maximum size of the subset that can be formed with a specific number of 0's and 1's.

Space and Time Complexity

Time Complexity: O(L * m * n), where L is the number of strings in strs.
Space Complexity: O(m * n), for the DP table.

Solution

The problem can be solved using a dynamic programming approach. We maintain a DP table, dp, where dp[i][j] represents the maximum size of the subset that can be formed with at most i 0's and j 1's. For each string, we count the number of 0's and 1's it contains, and then update the DP table in reverse to avoid overwriting the results of the current iteration.

Code Solutions

def findMaxForm(strs, m, n):
    # Create a DP table with dimensions (m+1) x (n+1)
    dp = [[0] * (n + 1) for _ in range(m + 1)]
    
    # Iterate over each string in the input list
    for s in strs:
        # Count the number of 0's and 1's in the current string
        zeros = s.count('0')
        ones = s.count('1')
        
        # Update the DP table in reverse order
        for i in range(m, zeros - 1, -1):
            for j in range(n, ones - 1, -1):
                dp[i][j] = max(dp[i][j], dp[i - zeros][j - ones] + 1)
    
    return dp[m][n]
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