Ones and Zeroes — LeetCode 474 Python Solution

The problem

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.

Example

Input

strs = ["10","0001","111001","1","0"], m = 5, n = 3

Output

4

Explanation

The largest subset with at most 5 0's and 3 1's is {"10", "0001", "1", "0"}, so the answer is 4.

Python solution

class Solution:
    def findMaxForm(self, strs: List[str], m: int, n: int) -> int:
        sz = len(strs)
        f = [[[0] * (n + 1) for _ in range(m + 1)] for _ in range(sz + 1)]
        for i, s in enumerate(strs, 1):
            a, b = s.count("0"), s.count("1")
            for j in range(m + 1):
                for k in range(n + 1):
                    f[i][j][k] = f[i - 1][j][k]
                    if j >= a and k >= b:
                        f[i][j][k] = max(f[i][j][k], f[i - 1][j - a][k - b] + 1)
        return f[sz][m][n]

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 474. Ones and Zeroes is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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