Magic numbers

You are given two arrays of integers of same size, @x and @y. Write a script to find the magic number that when added to each element of the first array gives the second array. The elements' order is not important.

Examples

Example 1
Input: @x = (3, 7, 5)
       @y = (9, 5, 7)
Output: 2

The magic number is 2.
@x = (3, 7, 5)
   +  2  2  2
@y = (5, 9, 7)

Example 2
Input: @x = (1, 2, 1)
       @y = (5, 4, 4)
Output: 3

The magic number is 3.
@x = (1, 2, 1)
   +  3  3  3
@y = (5, 4, 4)

Example 3
Input: @x = (2)
       @y = (5)
Output: 3

Analysis

I have given in to the temptation of a one-line answer, which may require a few lines of explanation.

Firstly, I have taken the task literally to the extent that I am not testing the assertion that all the elements of @y are indeed those of @x incremented by a constant amount. In a production environment I would of course check that.

So if we sort @x and @y the answer is simply $y[0] - $x[0].

My code works because:

• the second argument to the sub is $_[1], which is a reference to @y,
• so @{$_[1]} is @y,
• and sort {$a <=> $b} @{$_[1]} returns an array which is @y sorted,
• and [sort {$a <=> $b} @{$_[1]}] is an anonymous reference to that sorted @y,
• and [sort {$a <=> $b} @{$_[1]}]->[0] returns the first and smallest element of sorted @y,
• and the smallest value in @x is derived in the same way,
• so the answer is the difference between these two.

You might argue that that isn't very readable, and I would agree with you. In production code I would almost certainly have expanded it to a few lines to make it easier to read, but in The Weekly Challenge brevity is often seen as praiseworthy!

Peter finally gave in and created one-liner in Perl. It is so much fun to see how powerful it is.

Try it 

#!/usr/bin/perl

# Blog: http://ccgi.campbellsmiths.force9.co.uk/challenge

use v5.26;    # The Weekly Challenge - 2024-05-06
use utf8;     # Week 268 - task 1 - Magic number
use warnings; # Peter Campbell Smith
binmode STDOUT, ':utf8';

magic_number([3, 7, 5], [9, 5, 7]);
magic_number([1, 2, 1], [5, 4, 4]);
magic_number([2], [5]);
magic_number([9, 10, 11, 12], [2, 1, 0, -1]);

sub magic_number {
    
    # show input
    say qq[\nInput: ] . sprintf('@x = (%s), @y = (%s)',
        join(', ', @{$_[0]}), join(', ', @{$_[1]}));
        
    # show output   
    say qq[Output: ] . 
        ([sort {$a <=> $b} @{$_[1]}]->[0] - 
         [sort {$a <=> $b} @{$_[0]}]->[0]);
}

6 lines of code

Output from script

Input: @x = (3, 7, 5), @y = (9, 5, 7)
Output: 2

Input: @x = (1, 2, 1), @y = (5, 4, 4)
Output: 3

Input: @x = (2), @y = (5)
Output: 3

Input: @x = (9, 10, 11, 12), @y = (2, 1, 0, -1)
Output: -10