# 474. Ones and Zeroes

#### Medium

***

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`

```python
class Solution:
    def findMaxForm(self, strs: List[str], m: int, n: int) -> int:
        self.counts = [[s.count("0"), s.count("1")] for s in strs]
        return self.dp(m,n,0)
        
    @lru_cache(None)
    def dp(self, m, n, k):
        if m < 0 or n < 0:
            return -float("inf")
        if k == len(self.counts):
            return 0
        x, y = self.counts[k]
        return max(1+self.dp(m-x, n-y, k+1), self.dp(m,n,k+1))
        
```