10 May 2024 | Challenge 268 |

# Sorting This and That

## Task 1: Magic Number

**Submitted by: Mohammad Sajid Anwar**

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 elements of one of the array gives the second array. Elements order is not important.

### 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
```

### Solution

Adding a constant to all elements of an array does not change the elements’ ranking, i.e. their position in the sorted array. Thus we may sort both given arrays and look at the differences between the number pairs at the same position in each array. If a magic number exists, all the differences must be the same. This can be checked by comparing the minimum and the maximum difference.

There is no specification about the cases, where no magic number exists.
Choosing `undef`

as the result here.

Using `PDL`

, the task can be solved with two statements:

```
use strict;
use warnings;
use PDL;
use experimental 'signatures';
sub magic_number ($x, $y) {
my ($min, $max) = minmax pdl($y)->qsort - pdl($x)->qsort;
$min == $max ? $min : undef;
}
```

See the full solution to task 1.

## Task 2: Number Game

**Submitted by: Mohammad Sajid Anwar**

You are given an array of integers, `@ints`

, with even number of elements.

Write a script to create a new array made up of elements of the given array. Pick the two smallest integers and add it to new array in decreasing order i.e. high to low. Keep doing until the given array is empty.

### Example 1

```
Input: @ints = (2, 5, 3, 4)
Output: (3, 2, 5, 4)
Round 1: we picked (2, 3) and push it to the new array (3, 2)
Round 2: we picked the remaining (4, 5) and push it to the new array (5, 4)
```

### Example 2

```
Input: @ints = (9, 4, 1, 3, 6, 4, 6, 1)
Output: (1, 1, 4, 3, 6, 4, 9, 6)
```

### Example 3

```
Input: @ints = (1, 2, 2, 3)
Output: (2, 1, 3, 2)
```

### Solution

The task may be generalized to:

You are given a positive integer

`$n`

and an array of integers,`@ints`

, with a number of elements that is a multiple of`$n`

.Write a script to create a new array made up of elements of the given array. Pick the

`$n`

smallest integers and add it to new array in decreasing order i.e. high to low. Keep doing until the given array is empty.

The generalized task can be solved without extra effort by:

```
use strict;
use warnings;
use PDL;
use PDL::NiceSlice;
sub number_game {
my $n = shift;
long(@_)->qsort->splitdim(0, $n)->(-1:0)->flat;
}
```

See the full solution to task 2.