Inspired by this question and refined by Luis Mendo.
Challenge
Given a 2D matrix of integers, each row has a maximum value. One or more elements of each row will be equal to the maximum value of their respective row. Your goal is to determine which column(s) contain the most entries which are equal to their respective row's maximum value as well as the number of row-wise maxima found in these columns.
Input
- The input will be a non-empty
MxNmatrix (M> 0 andN> 0) in whatever form is well-suited to your language of choice.
Output
- Your program should return the index of each column containing the maximum number of row-wise maxima (either as separate values or a list). Either 0- or 1-based indexing can be used (specify in your description).
- Your program should also return the number of maxima that were present in these columns (a single number).
- The order/format of the output is flexible but should be explained in the text accompanying your answer.
Additional Information
- All entries in the input matrix will be positive integers.
- If the maximum value of a row is shared by multiple elements in that row, all occurrences of that value count towards their columns' total.
- If multiple columns contain the same number of maxima, you should return a list of all columns which had this number of maxima.
An Example
Consider input
7 93
69 35
77 30
Row 1 has maxium 93, which occurs only once, namely at column 2. Row 2: occurs at column 1. Row 3: also at column 1. So the winner column is 1, with 2 maxima. Thus the output will be [1] [2]. If we change the input to
7 93
69 35
77 77
the output will be [1 2] [2], because both columns have 2 maxima.
Test Cases
input => output ( [1-based index array], [nMaxima] )
----------------------------------------------
7 93
69 35 => [1], [2]
77 30
7 93
69 35 => [1 2], [2]
77 77
1 2 3 4 => [4], [2]
5 6 7 8
16 2 3 13
5 11 10 8 => [1 2 4], [1]
9 7 6 12
1 1 1 1 => [1 2 3 4], [1]
25 6 13 25 => [1 4], [1]
1
2
3 => [1], [4]
4
100 => [1], [1]
Scoring
This is code-golf, the shortest code in bytes wins. Tiebreaker goes to the earlier answer.
Leaderboard
Below is a stack snippet for analyzing all entries.
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