## 474. Ones and Zeroes

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`

## Rust Solution

``````struct Solution;

use std::collections::HashMap;

impl Solution {
fn find_max_form(strs: Vec<String>, m: i32, n: i32) -> i32 {
let mut count: Vec<(i32, i32)> = strs
.iter()
.map(|s| {
(
s.chars().filter(|&c| c == '0').count() as i32,
s.chars().filter(|&c| c == '1').count() as i32,
)
})
.collect();
count.sort_unstable();
let mut memo: HashMap<(usize, i32, i32), usize> = HashMap::new();
Self::dp(0, m, n, &mut memo, &count, strs.len()) as i32
}

fn dp(
start: usize,
zero: i32,
one: i32,
memo: &mut HashMap<(usize, i32, i32), usize>,
count: &[(i32, i32)],
n: usize,
) -> usize {
if start == n {
return 0;
}
if let Some(&res) = memo.get(&(start, zero, one)) {
return res;
}
let skip = Self::dp(start + 1, zero, one, memo, count, n);
let res = if zero >= count[start].0 && one >= count[start].1 {
let keep = 1 + Self::dp(
start + 1,
zero - count[start].0,
one - count[start].1,
memo,
count,
n,
);
skip.max(keep)
} else {
skip
};
memo.insert((start, zero, one), res);
res
}
}

#[test]
fn test() {
let strs = vec_string!["10", "0001", "111001", "1", "0"];
let m = 5;
let n = 3;
let res = 4;
assert_eq!(Solution::find_max_form(strs, m, n), res);
let strs = vec_string!["10", "0", "1"];
let m = 1;
let n = 1;
let res = 2;
assert_eq!(Solution::find_max_form(strs, m, n), res);
}
``````

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