Maximize the number of binary strings chosen under zero and one budgets

You are given a list of binary strings and two budgets: at most `max_zeros` characters `'0'` and at most `max_ones` characters `'1'` in total. Choose a subset of the strings such that, counted over all chosen strings together, there are at most `max_zeros` zeros and at most `max_ones` ones. Return the largest possible number of strings in such a subset. ### Function Signature ```python def largest_subset(strs: list[str], max_zeros: int, max_ones: int) -> int: ``` ### Rules - Each element of `strs` can be chosen at most once. Equal strings at different positions are different elements, and both can be chosen. - The empty subset is always allowed, so the answer is at least `0`. - Return only the size of a largest valid subset, not the subset itself. ### Constraints - `1 <= len(strs) <= 600` - `1 <= len(strs[i]) <= 100`, and each `strs[i]` consists only of `'0'` and `'1'` - `0 <= max_zeros <= 100` - `0 <= max_ones <= 100` ### Examples **Example 1** ```text Input: strs = ["01", "0", "110", "1", "0011"], max_zeros = 3, max_ones = 2 Output: 3 ``` Choosing `"0"`, `"01"` and `"1"` uses 2 zeros and 2 ones. The five strings contain 6 ones in total, and leaving out any single string still leaves at least 4 ones, so no 4 strings fit. **Example 2** ```text Input: strs = ["1", "1", "0"], max_zeros = 0, max_ones = 1 Output: 1 ``` Only one `"1"` fits in the ones budget, and `"0"` needs a zero that the budget does not allow. **Example 3** ```text Input: strs = ["111", "000"], max_zeros = 2, max_ones = 2 Output: 0 ``` Each string on its own exceeds one of the budgets, so only the empty subset is valid.