# ETOOBUSY đźš€ minimal blogging for the impatient

# Aquarium - constraints

**TL;DR**

Itâ€™s time to start coding for aquarium, letâ€™s begin from the

constraintsthat allow us to tell a good - if partial - solution from an evidently wrong one.

The code for this stage can be found in stage 3.

# Letâ€™s start from the rules

The rules for aquarium are simple, from the site:

- The puzzle is played on a rectangular grid divided into blocks called â€śaquariumsâ€ť
- You have to â€śfillâ€ť the aquariums with water up to a certain level or leave it empty.
- The water level in each aquarium is one and the same across its full width
- The numbers outside the grid show the number of filled cells horizontally and vertically.

The constraints are stated in the third and fourth bullet, letâ€™s address them individually. The following sections assume that youâ€™re comfortable with the data structure to represent the whole puzzle, you can take a refresher in the first post Aquarium - parse puzzle input.

# Water has one level only in one aquarium

This constraint can be translated into the following checks:

- vertically in one column, if two adjacent cells belong to the same
aquarium, the upper one MUST have a value that is less than, or equal to,
the lower one. This stems from the fact that
*empty*(-1) is lighter than or equal to*unknown*(0), which is lighter than or equal to*water*(1); - horizontally, whatever level we find for the leftmost cell of an aquarium, all other cells in the same aquarium MUST hold the same value.

This is the code for this constraint:

```
1 sub assert_water_level ($puzzle) {
2 my ($n, $field, $status) = $puzzle->@{qw< n field status >};
3 for my $i (0 .. $n - 1) { # iterate rows from top to bottom
4 my %expected;
5 for my $j (0 .. $n - 1) {
6 my $id = $field->[$i][$j];
7 my $st = $status->[$i][$j];
8
9 die "wrong vertical leveling for aquarium $id\n"
10 if ($i > 0)
11 && ($id == $field->[$i - 1][$j])
12 && ($st < $status->[$i - 1][$j]);
13
14 $expected{$id} //= $st;
15 die "wrong horizontal leveling for aquarium $id\n"
16 if $expected{$id} != $st;
17
18 } ## end for my $j (0 .. $n - 1)
19 } ## end for my $i (0 .. $n - 1)
10 return $puzzle;
21 } ## end sub assert_water_level ($puzzle)
```

It is basically a straight translation into code of the bullets above.

The vertical check is performed in lines 9 to 12; it can only be performed from the second row on, which is the reason of the test in line 10.

Hash `%expected`

tracks the expected value for each aquarium at the *same
level* (second bullet), initializing it with the first value found for each
aquarium (line 14 `$expected{$id //= $st`

) and complaining if values differ
(lines 15 and 16). This test is only for the single horizontal level, hence
`%expected`

is declared *inside* the outer loop so that it is reset for each
new row.

# Row-level and Column-level constraints

Boundary conditions are easy to check: it suffices to count how many water-
filled cells are there, and check that itâ€™s the right number. Put it like
this, anyway, the check would be somehowâ€¦ *strict* because it can only be
fulfilled by a complete solution. We will check that there is not *too much
water* instead, as well as not *too much emptiness*:

```
1 sub assert_boundary_conditions ($puzzle) {
2 my ($n, $status, $items_by_row, $items_by_col) =
3 $puzzle->@{qw< n status items_by_row items_by_col >};
4
5 # the field is square and this is an advantage, $i and $j can be
6 # thought as either row-column or column-row
7 for my $i (0 .. $n - 1) {
8 my $i1 = $i + 1; # useful for the exception
9 my ($water_row, $empty_row, $water_col, $empty_col) = (0) x 4;
10 for my $j (0 .. $n - 1) {
11 $water_row++ if $status->[$i][$j] > 0;
12 $empty_row++ if $status->[$i][$j] < 0;
13 $water_col++ if $status->[$j][$i] > 0;
14 $empty_col++ if $status->[$j][$i] < 0;
15 }
16
17 die "too many filled cells in row $i1\n"
18 if $water_row > $items_by_row->[$i];
19
20 die "too many empty cells in row $i1\n"
21 if $empty_row > $n - $items_by_row->[$i];
22
23 die "too many filled cells in col $i1\n"
24 if $water_col > $items_by_col->[$i];
25
26 die "too many empty cells in col $i1\n"
27 if $empty_col > $n - $items_by_col->[$i];
28
29 }
30 return $puzzle;
31 }
```

In other terms, we allow for some cells to still be *unknown*, so our checks
translate into ensuring that the count of *empty* or *filled* cells is
within the expected bounds.

Iteration over variable `$i`

(*outer iteration*) does the trick for both
rows and columns at the same time - the trick is to keep track of four
different variables to count the amount of water and confirmed empty spaces
for row `$i`

*and* column `$i`

. The actual counting is done in lines 10 to
15, where variable `$j`

iterates *the other* dimension.

Tests in lines 17 to 27 are straightforward: if the specific quantity is out of bounds, an exception is raised.

# Constraints in action!

The following asciinema recording shows examples of all the different ways to fail the constraints:

Until next timeâ€¦ happy coding!

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