PWC199 - Good Pairs


Here we are with TASK #1 from The Weekly Challenge #199. Enjoy!

The challenge

You are given a list of integers, @list.

Write a script to find the total count of Good Pairs.

A pair (i, j) is called good if list[i] == list[j] and i < j.

Example 1

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

There are 4 good pairs found as below:

Example 2

Input: @list = (1,2,3)
Output: 0

Example 3

Input: @list = (1,1,1,1)
Output: 6

Good pairs are below:

The questions

I wonder if all these definitions of “good” are a leftover from Santa, just to make sure that every kid can get a present.

The solution

This is… just plain counting.

The input can be partitioned into subsets of elements that are equal to each other. As these items have to be considered “ordered” (because of the i < j constraint in the definition), for each of these partitions/subsets we have to calculate the triangular number.

This is the theory.

In practice, we can just sweep the input list one element at a time, and add to the total counter the number of times we saw this element before in the list (each of those members makes a “good pair” with the current element). Then we increase the count for that element.

In more practice, we can track these members using a hash, and take advantage of the post-increment ++ operator to get the we already saw so far count while increasing count for the same time, all in a single instruction.

In Raku terms:

#!/usr/bin/env raku
use v6;
sub MAIN (*@args) { put good-pairs(@args ?? @args !! (1, 2, 3, 1, 1, 3))}
sub good-pairs (*@list) { my %c;{%c{$_}++}).sum }

The %c hash keeps track of the count as explained above. The map returns the list of items to sum, which we then… .sum. Nice and compact.

The Perl counterpart suffers a bit from the lack of a batteries-included sum function. Right, there is one in the CORE module List::Util, but who wants to use it anyway?!?

#!/usr/bin/env perl
use v5.24;
say good_pairs(@ARGV ? @ARGV : (1, 2, 3, 1, 1, 3));
sub good_pairs { my $s = 0; my %c; $s += $c{$_}++ for @_; $s }

I’m taking a bad habit in these examples, i.e. to avoid warnings. Keep in mind, these are toy challenges and these are less-than-5-lines program, so it’s OK. Remove either condition, and it becomes much less OK.

I guess it’s everything for this challenge, stay safe!

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