> ## Documentation Index
> Fetch the complete documentation index at: https://leetcode-py.wisl.dev/llms.txt
> Use this file to discover all available pages before exploring further.

> ## Agent Instructions
> leetcode-py is a Python LeetCode practice environment generator with one CLI: lcpy. It is not a service or platform.
> Each problem is a directory under leetcode/ with README.md, solution.py, test_solution.py, helpers.py, and playground.ipynb. lcpy gen creates them from JSON templates bundled with the package.
> Examples are backed by tests; copy them verbatim.

# Ones and Zeroes Python Solution with Tests

> Tested Python solution for LeetCode 474 with 15 pytest cases. Generate a practice environment with lcpy.

LeetCode 474, [Medium](/catalog/medium). Topics: [Array](/catalog/topics/array), [String](/catalog/topics/string), [Dynamic Programming](/catalog/topics/dynamic-programming). [View on LeetCode](https://leetcode.com/problems/ones-and-zeroes/description/).

Generate this problem as a practice environment: tested reference solution, 15 [parametrized pytest cases](/practice/testing), and a playground notebook:

```bash theme={"theme":{"light":"github-light","dark":"github-dark"}}
lcpy gen -n 474   # by problem number
lcpy gen -s ones_and_zeroes   # by problem name
```

## 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*.

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

### Examples

```
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.
```

```
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`

## Solution

Reference implementation from [solution.py on GitHub](https://github.com/wislertt/leetcode-py/blob/main/leetcode/ones_and_zeroes/solution.py), full suite in [test\_solution.py](https://github.com/wislertt/leetcode-py/blob/main/leetcode/ones_and_zeroes/test_solution.py):

```python theme={"theme":{"light":"github-light","dark":"github-dark"}}
class Solution:
    # Time: O(l * m * n + total chars)
    # Space: O(m * n)
    def find_max_form(self, strs: list[str], m: int, n: int) -> int:
        dp = [[0] * (n + 1) for _ in range(m + 1)]
        for s in strs:
            zeros = s.count("0")
            ones = len(s) - zeros
            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]
```

## Complexity

| Time | Space |
| - | - |
| O(l \* m \* n + total chars) | O(m \* n) |

## Tags

[NeetCode All](/catalog/neetcode).


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