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 2 3 4 5

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.

1 2 3

Input: strs = ["10","0","1"], m = 1, n = 1 Output: 2 Explanation: The largest subset is {"0", "1"}, so the answer is 2.

Note:

This is a 01 knapsack problem.

Just like optimizing 2D dp array to 1D. This should be a 3D dp array if we do it in a traditional way, but we can simplify the space! Imagine it was dp[i][j][k] = max(dp[i-1][j][k], dp[i-1][j-zeroes][k-ones] + 1), we can simplify it as dp[j][k] = max(dp[j][k], dp[j-zeroes][k-ones] + 1).

Please remember to iterate j and k in reversed order just like what we did in other DP problems.