2397: Maximum Rows Covered by Columns

You are given an m x n binary matrix matrix and an integer numSelect.

Your goal is to select exactly numSelect distinct columns from matrix such that you cover as many rows as possible.

A row is considered covered if all the 1's in that row are also part of a column that you have selected. If a row does not have any 1s, it is also considered covered.

More formally, let us consider selected = {c1, c2, ...., cnumSelect} as the set of columns selected by you. A row i is covered by selected if:

Return the maximum number of rows that can be covered by a set of numSelect columns.

Example 1:

Output: 3

Explanation:

One possible way to cover 3 rows is shown in the diagram above.
We choose s = {0, 2}.
- Row 0 is covered because it has no occurrences of 1.
- Row 1 is covered because the columns with value 1, i.e. 0 and 2 are present in s.
- Row 2 is not covered because matrix[2][1] == 1 but 1 is not present in s.
- Row 3 is covered because matrix[2][2] == 1 and 2 is present in s.
Thus, we can cover three rows.
Note that s = {1, 2} will also cover 3 rows, but it can be shown that no more than three rows can be covered.

Example 2:

Output: 2

Explanation:

Selecting the only column will result in both rows being covered since the entire matrix is selected.

Constraints: