474. Ones and Zeroes

Medium

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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

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))