### Perl Weekly Challenge: Week 188

#### Challenge 1:

**Divisible Pairs**

You are given list of integers

`@list`

of size`$n`

and divisor`$k`

.Write a script to find out count of pairs in the given list that satisfies the following rules.

```
The pair (i, j) is eligible if and only if
a) 0 <= i < j < len(list)
b) list[i] + list[j] is divisible by k
```

##### Example 1

```
Input: @list = (4, 5, 1, 6), $k = 2
Output: 2
```

##### Example 2

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

##### Example 3

```
Input: @list = (1, 3, 4, 5), $k = 3
Output: 2
```

##### Example 4

```
Input: @list = (5, 1, 2, 3), $k = 4
Output: 2
```

##### Example 5

```
Input: @list = (7, 2, 4, 5), $k = 4
Output: 1
```

In Raku this problem can be solved as a one-liner but I've chosen to spread it out a bit for clarity.

I found the way condition a in the spec is described to be a little unclear; what it
actually means is that the values of `i`

and `j`

range between 0 and the size of the list.

```
(0 ..^ @list.elems)
```

For that range, we get a list of all the pairs of values with `.combinations()`

...

```
.combinations(2)
```

...We `.grep()`

through that list to find all the pairs where their `.sum()`

is evenly
divisible by `$k`

...

```
.grep({ @$_.sum %% $k})
```

...Then we count how many pairs we found... .elems

...and print that out.

```
.say;
```

The Perl solution is not quite so concise. For one thing, I had to supply my own `combinations()`

function which
luckily I had from previous challenges. I also missed having the integer modulus operator `%%`

and the `.sum()`

method.

```
say scalar grep { ($list[$_->[0]] + $list[$_->[1]]) % $k == 0; }
combinations([0 .. scalar @list - 1], 2);
```

#### Challenge 2:

**Total Zero**

You are given two positive integers

`$x`

and`$y`

.Write a script to find out the number of operations needed to make both

`ZERO`

. Each operation is made up either of the followings:

```
$x = $x - $y if $x >= $y
or
$y = $y - $x if $y >= $x (using the original value of $x)
```

##### Example 1

```
Input: $x = 5, $y = 4
Output: 5
```

##### Example 2

```
Input: $x = 4, $y = 6
Output: 3
```

##### Example 3

```
Input: $x = 2, $y = 5
Output: 4
```

##### Example 4

```
Input: $x = 3, $y = 1
Output: 3
```

##### Example 5

```
Input: $x = 7, $y = 4
Output: 5
```

Normally function parameters in Raku are immutable. To be able to change them,
you have to add the `is copy`

trait.

```
sub MAIN(
Int $x is copy, #= a positive integer
Int $y is copy #= a positive integer
) {
```

I defined a counter for the number of operations.

```
my $operations = 0;
```

Then I kept on applying the operations given in the spec until both `$x`

and `$y`

were 0.

```
repeat {
```

In order to perform operation 2 correctly, I had to cache the value of `$x`

before operation 1
was applied.

```
my $prevX = $x;
if $x >= $y {
$x -= $y;
}
if $y >= $prevX {
$y -= $prevX;
}
```

The spec is misleading IMHO. Originally, I incremented `$operations`

within each `if`

block.
But for the example inputs, this gave me a result 1 greater than the expected output. What we
really want is not the total number of operations as I assumed, but the number of times we go
through the loop.

```
$operations++;
} until $x == 0 && $y == 0;
```

Finally, we can print the result.

```
say $operations;
}
```

This is the Perl version. No concerns about immutablity and we use `do ... while`

instead of
`repeat ... until`

in the loop.

```
my ($x, $y) = @ARGV;
my $operations = 0;
do {
my $prevX = $x;
if ($x >= $y) {
$x -= $y;
}
if ($y >= $prevX) {
$y -= $prevX;
}
$operations++;
} while ($x != 0 && $y != 0);
say $operations;
```