Task — Divisible Pairs

You are given list of integers @list of size $n and a divisor $k.

Write a script to find out count of pairs in the given list that satisfies the following rules. The pair (i, j) is eligible if and only if

1. 0 <= i < j < len(list)
2. list[i] + list[j] is divisible by k

Examples

Example 1
Input: @list = (4, 5, 1, 6), $k = 2
Output: 2

Example 2
Input: @list = (1, 2, 3, 4), $k = 2
Output: 2

Example 3
Input: @list = (1, 3, 4, 5), $k = 3
Output: 2

Example 4
Input: @list = (5, 1, 2, 3), $k = 4
Output: 2

Example 5
Input: @list = (7, 2, 4, 5), $k = 4
Output: 1

Analysis

The way I did this is to generate all the pairs and check their divisibility by the given divisor. All the examples given include only unique positive integers. The task is not significantly different if zero and negative integers are included, but if the same integer appears more than once (eg list = 1, 2, 3, 3, divisor = 4) do we count distinct pairings (1 and the first 3, 1 and the second 3) or merely distinct pairs (just 1 and 3)? I guessed yes.

Try it 

Script

#!/usr/bin/perl

# Peter Campbell Smith - 2022-10-26
# PWC 188 task 1

use v5.28;
use utf8;
use warnings;
binmode(STDOUT, ':utf8');

my (@tests, @list, $k, $n, $i, $j, $count, $reason);

# test input (\@list, $k ...)
@tests = ([4, 5, 1, 6], 2, [1, 2, 3, 4], 2, [1, 3, 4, 5], 3, [5, 1, 2, 3], 4, [7, 2, 4, 5], 4,
    [3, 6, 9, 12, 15], 11, [7, 9, 8, 3, 4, 0, 1, 11, 6, 12, 10, 6, 2], 3);

# loop over tests
while ($tests[0]) {
    
    # initialise
    @list = @{shift @tests};
    $k = shift @tests;
    $n = scalar @list;
    $count = 0;
    $reason = '';
    
    #loop over i and j such as to apply test a
    for $i (0 .. $n - 2) {
        for $j ($i + 1 .. $n - 1) {
            
            # apply test b
            next unless (($list[$i] + $list[$j]) % $k) == 0;
            
            # found an answer
            $count ++;
            $reason .= qq[($list[$i] + $list[$j]), ];
        }
    }
    # output
    say qq[\nInput: \@list = ] . join(', ', @list) . qq[, \$k = $k\nOutput: $count\nReason: ] . substr($reason, 0, -2); 
}

Output

Input: @list = 4, 5, 1, 6, $k = 2
Output: 2
Reason: (4 + 6), (5 + 1)

Input: @list = 1, 2, 3, 4, $k = 2
Output: 2
Reason: (1 + 3), (2 + 4)

Input: @list = 1, 3, 4, 5, $k = 3
Output: 2
Reason: (1 + 5), (4 + 5)

Input: @list = 5, 1, 2, 3, $k = 4
Output: 2
Reason: (5 + 3), (1 + 3)

Input: @list = 7, 2, 4, 5, $k = 4
Output: 1
Reason: (7 + 5)

Input: @list = 3, 6, 9, 12, 15, $k = 11
Output: 0
Reason: 

Input: @list = 7, 9, 8, 3, 4, 0, 1, 11, 6, 12, 10, 6, 2, $k = 3
Output: 27
Reason: (7 + 8), (7 + 11), (7 + 2), (9 + 3), (9 + 0), (9 + 6), (9 + 12), (9 + 6), (8 + 4), (8 + 1), (8 + 10), (3 + 0), (3 + 6), (3 + 12), (3 + 6), (4 + 11), (4 + 2), (0 + 6), (0 + 12), (0 + 6), (1 + 11), (1 + 2), (11 + 10), (6 + 12), (6 + 6), (12 + 6), (10 + 2)