# ETOOBUSY đźš€ minimal blogging for the impatient

# PWC080 - Count Candies

**TL;DR**

On with Perl Weekly Challenge TASK #2 in issue #080.

# The challenge

You are given rankings of @N candidates. Write a script to find out the total candies needed for all candidates. You are asked to follow the rules below:

- You must given at least one candy to each candidate.
- Candidate with higher ranking get more candies than their immediate neighbors on either side.

# The questions

First and foremostâ€¦ itâ€™s nowhere to be found that we should find the
*minimum* number of candies that still satisfy the constraints.
This makes the problem prone to something like *just sum up the ranks*
or, in case, use that sum plus the number of candidates (which
corresponds to adding one candy to everyone).

Which also brings us toâ€¦ are ranks positive? Non-negative? Any possible real value? Finding the minimum value and offseting by it, as well as taking integers might help. But I digress.

As often happens, a question or two about corner cases and invalid input would be well placed, like:

- what happens if an input rank is not a number?
- what happens if the input list is empty? (I guess the result can be 0â€¦ or any number above it!)

# The solution

Assuming we want to calculate the *minimum number of candies that still
satisfy the requirements*, the best I could think of was to just
starting distributing candies in *waves* and stop when all constraints
are satisfied.

We *know* that we will stop at some time because adjacent candidates
with the same ranking do not interact with each other - in other terms,
itâ€™s perfectly OK to have two equally ranked candidates hold a different
number of candies.

Enough with talking, letâ€™s take a look at the solution:

```
1 sub candies_for_candidates (@N) {
2 return unless @N;
3
4 my @candies = (1) x @N; # everybody gets a candy!
5 push @N, max($N[0], $N[-1]) + 1; # add "edge" value to simplify loops
6
7 while ('necessary') {
8 my $something_changed = 0;
9 for my $i (0 .. $#candies) {
10 for my $delta (-1, 1) {
11 next if $N[$i] <= $N[$i + $delta];
12 next if $candies[$i] > $candies[$i + $delta];
13 $candies[$i] = $candies[$i + $delta] + 1;
14 $something_changed = 1;
15 }
16 }
17 last unless $something_changed;
18 }
19 return sum @candies;
20 }
```

The `@candies`

return value is initialized with one candy per candidate
in line 4.

Then we add a *fake candidate* at the end of the list (but not at the
end of the candy list) which is surely *better* thank both the first and
the last candidates. This will not change the candies assigned to these
two candidates, but makes it easy to loop over the inputs because this
*fake candidate* will be the follower of the last candidate, as well as
the predecessor of the first one (thatâ€™s thanks to how Perl handles
negative indexes while accessing arrays). So we will not have to do
anyting special for these two candidates, which simplifies our loops
later.

Line 7 is my take on an *indefinitely long* loop; string `necessary`

is
*true* (because itâ€™s not a value that Perl thinks is *false*), so
the `while`

condition is always true. As a matter of fact, exiting from
the loop *can* happen in line 17, where we exit from this outer loop
only when we didnâ€™t add any new candy to the lot. Variable
`$something_changed`

(defined in line 10) allows us figure out if this
happened or not.

The medium loop in line 9 sweeps through the list of indexes in the
candies and the *actual* input candidates (i.e. disregarding the *fake*
one). At each of the index, we compare the element with its neighbors
(using `$delta`

to look on the left and the right, defined in line 10).

If the element under analisys is lower than the neighborâ€¦ move on, and this happens in line 11.

Otherwise: if the current candidate *already* holds more candiesâ€¦ move
on, it does not get more!

Otherwiseâ€¦ well, we have to give more candies. For good measure, letâ€™s just add one to the neighborâ€™s count, and weâ€™re done.

After the last wave, we exit from the outer loop in line 17 and return the sum of candies.

Sweet!

# Full code for playing

Here you go, with all `use`

s and some tests to play with:

```
#!/usr/bin/env perl
use 5.024;
use warnings;
use English qw< -no_match_vars >;
use experimental qw< postderef signatures >;
no warnings qw< experimental::postderef experimental::signatures >;
use List::Util qw< max sum >;
sub candies_for_candidates (@N) {
return unless @N;
my @candies = (1) x @N; # everybody gets a candy!
push @N, max($N[0], $N[-1]) + 1; # add "edge" value to simplify loops
while ('necessary') {
my $something_changed = 0;
for my $i (0 .. $#candies) {
for my $delta (-1, 1) {
next if $N[$i] <= $N[$i + $delta];
next if $candies[$i] > $candies[$i + $delta];
$candies[$i] = $candies[$i + $delta] + 1;
$something_changed = 1;
}
}
last unless $something_changed;
}
return sum @candies;
}
for my $test (
[ 1, 2, 2 ],
[ 1, 3, 4, 1 ],
[ 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7 ],
) {
say candies_for_candidates($test->@*);
}
```

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