Task — Arithmetic progression

You are given an array of numbers. Write a script to return true if the given array can be re-arranged to form an arithmetic progression, otherwise return false. A sequence of numbers is called an arithmetic progression if the difference between any two consecutive elements is the same.

Examples

Example 1
Input: @num = (1, 3, 5, 7, 9)
Output: true
Already AP with common difference 2.

Example 2
Input: @num = (9, 1, 7, 5, 3)
Output: true
The given array re-arranged like (1, 3, 5, 7,
   9) with common difference 2.

Example 3
Input: @num = (1, 2, 4, 8, 16)
Output: false
This is geometric progression and not arithmetic 
   progression.

Example 4
Input: @num = (5, -1, 3, 1, -3)
Output: true
The given array re-arranged like (-3, -1, 1, 3,
   5) with common difference 2.

Example 5
Input: @num = (1.5, 3, 0, 4.5, 6)
Output: true
The given array re-arranged like (0, 1.5, 3, 4.5,
   6) with common difference 1.5.

Analysis

As with task 1, I have taken the view that an arithmetic progression requires at least 3 elements.

That said, I do the obvious and sort the array, and then check that the increments between successive elements are the same.

This will always result in a positive increment, even for input such as (-1, -2, -3, -4) which will get sorted to (-4, -3, -2, -1) with an increment of 1.

Try it 

#!/usr/bin/perl

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

use v5.26;    # The Weekly Challenge - 2025-12-08
use utf8;     # Week 351 - task 2 - Arithmetic progression
use warnings; # Peter Campbell Smith
binmode STDOUT, ':utf8';
use Encode;

arithmetic_progression(9, 1, 7, 5, 3);
arithmetic_progression(-1, -2, -3, -4);
arithmetic_progression(-4, -3, -2, -1);
arithmetic_progression(1e6, 3e6, 5e6, 7e6, 9e6);
arithmetic_progression(111);
arithmetic_progression(111, 222);
arithmetic_progression(111, 222, 333);
arithmetic_progression(11/7, 14/7, 17/7, 29/7);

sub arithmetic_progression {
    
    my (@sorted, $increment, $j);
    
    # initialise
    say qq[\nInput:  (] . join(', ', @_) . ')';
    
    # need at lleast 3 elements
    if (@_ < 3) {
        say qq[Output: indeterminate - array too short];
        return;
    }
        
    # check for arithmetic progression
    @sorted = sort {$a <=> $b} @_;
    $increment = $sorted[1] - $sorted[0];
    
    for $j (1 .. @sorted - 2) {
        next if $sorted[$j + 1] = $sorted[$j] + $increment;
        say qq[Output: false as $sorted[$j + 1] - $sorted[$j] != $increment];
        return;
    }
    say qq[Output: true with increment of $increment];

}

Output

Input:  (9, 1, 7, 5, 3)
Output: true with increment of 2

Input:  (-1, -2, -3, -4)
Output: true with increment of 1

Input:  (-4, -3, -2, -1)
Output: true with increment of 1

Input:  (1000000, 3000000, 5000000, 7000000, 9000000)
Output: true with increment of 2000000

Input:  (111)
Output: indeterminate - array too short

Input:  (111, 222)
Output: indeterminate - array too short

Input:  (111, 222, 333)
Output: true with increment of 111

Input:  (1.57142857142857, 2, 2.42857142857143,
   4.14285714285714)
Output: true with increment of 0.428571428571429