Special and unique numbers

Weekly challenge 252 — 15 January 2024

Week 252: 15 Jan 2024

Task 1

You are given an array of integers, @ints. Write a script to find the sum of the squares of all special elements of the given array.

An element $int[i] of @ints is called special if i divides n, i.e. n % i == 0 where n is the length of the given array. Also the array is 1-indexed for the task.

Example 1Input: @ints = (1, 2, 3, 4) Output: 21 There are exactly 3 special elements in the given array: $ints[1] since 1 divides 4, $ints[2] since 2 divides 4, and $ints[4] since 4 divides 4. Hence, the sum of the squares of all special elements of given array: 1 * 1 + 2 * 2 + 4 * 4 = 21.Example 2Input: @ints = (2, 7, 1, 19, 18, 3) Output: 63 There are exactly 4 special elements in the given array: $ints[1] since 1 divides 6, $ints[2] since 2 divides 6, $ints[3] since 3 divides 6, and $ints[6] since 6 divides 6. Hence, the sum of the squares of all special elements of given array: 2 * 2 + 7 * 7 + 1 * 1 + 3 * 3 = 63

This is just a case of passing once along the array, accumulating the square of the values on the elements whose indices (1-based) are factors of the array length.

Note that the first and last elements are always special so we never have the case of there being no special numbers.

#!/usr/bin/perl use v5.26; # The Weekly Challenge - 2024-01-15 use utf8; # Week 252 task 1 - Special numbers use strict; # Peter Campbell Smith use warnings; # Blog: http://ccgi.campbellsmiths.force9.co.uk/challenge binmode STDOUT, ':utf8'; my ($j, @ints); special_numbers(1, 2, 3, 4); special_numbers(2, 7, 1, 19, 18, 3); special_numbers(7, 7, 7, 7, 11); for $j (0 .. 31) { push @ints, int(rand(20) + 1); } special_numbers(@ints); sub special_numbers { my (@ints, $j, $squares, @specials, $last); # initialise @ints = @_; $last = @ints - 1; # check each member for $j (0 .. $last) { if (($last + 1) / ($j + 1) == int(($last + 1) / ($j + 1))) { $squares += $ints[$j] ** 2; push @specials, $j + 1; } } # show results say qq[\nInput: \@ints = (] . join(', ', @ints) . ')'; say qq[Output: $squares ∵ \@specials: ] . join(', ', @specials); }

Input: @ints = (1, 2, 3, 4) Output: 21 ∵ @specials: 1, 2, 4 Input: @ints = (2, 7, 1, 19, 18, 3) Output: 63 ∵ @specials: 1, 2, 3, 6 Input: @ints = (7, 7, 7, 7, 11) Output: 170 ∵ @specials: 1, 5 Input: @ints = (12, 18, 4, 5, 4, 20, 16, 3, 16, 20, 1, 9, 4, 15, 19, 16, 10, 18, 17, 2, 12, 16, 15, 19, 8, 19, 12, 9, 11, 18, 11, 13) Output: 927 ∵ @specials: 1, 2, 4, 8, 16, 32

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