"""
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.

A set x is a subset of a set y if all elements of x are also elements of y.



Example 1:

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.
Other valid but smaller subsets include {"0001", "1"} and {"10", "1", "0"}.
{"111001"} is an invalid subset because it contains 4 1's, greater than the maximum of 3.
Example 2:

Input: strs = ["10","0","1"], m = 1, n = 1
Output: 2
Explanation: The largest subset is {"0", "1"}, so the answer is 2.


Constraints:

1 <= strs.length <= 600
1 <= strs[i].length <= 100
strs[i] consists only of digits '0' and '1'.
1 <= m, n <= 100
"""
from typing import List


class Solution:
    def findMaxForm(self, strs: List[str], m: int, n: int) -> int:
        sz = len(strs)
        dp = [[[0] * (n + 1) for _ in range(m + 1)] for _ in range(sz + 1)]

        def count_ones_and_zeros(num):
            res = [0, 0]
            for c in num:
                if c == '0':
                    res[0] += 1
                elif c == '1':
                    res[1] += 1
            return res

        for i, num in enumerate(strs):
            cnt = count_ones_and_zeros(num)
            for j in range(m + 1):
                for k in range(n + 1):
                    dp[i + 1][j][k] = dp[i][j][k]
                    if j >= cnt[0] and k >= cnt[1]:
                        dp[i + 1][j][k] = max(dp[i + 1][j][k], dp[i][j - cnt[0]][k - cnt[1]] + 1)
        return dp[sz][m][n]
