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# System prepended metadata

title: 10 / 12

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# 10 / 12 

{%hackmd theme-dark %}
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.

```
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.
```
##
dp[m][n] -> best of m, n

> "10" dp[m][n] = max (dp[m][n], dp[m-1][n-1] + 1)
>                                     ^0   ^1

1. "10" ->  1/0 1/1 -> max (dp[m][n], dp[m-1][n-1] + 1)
5 3 -> 4 2
3. "0001" -> 3/0 1/1 -> max (dp[m][n], dp[m-3][n-1] + 1)



step1 m = 1, n = 1
> ["0", "1"] -> 2

step2 m = 3, n = 2
based on step2 


{"10", "0001", "1", "0"}, so the answer is 4.
5 0s and 3 1s
```cpp=


```