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#lang scribble/lp2

@ ( require scribble/manual aoc-racket/helper )

```
```

@aoc-title [ 17 ]

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```

@defmodule [ aoc-racket/day17 ]

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@link [ " http://adventofcode.com/day/17 " ] { The puzzle } . Our @link-rp [ " day17-input.txt " ] { input } is a list of containers that hold the designated number of liters.

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```

```
```

@chunk [ <day17>

` `<day17-setup>

` `<day17-q1>

` `<day17-q2>

` `<day17-test> ]

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```

@section { How many combinations of containers fit exactly 150 liters? }

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```

This is a lot like the second part of @secref { Day_15 } , where we had to find cookie recipes that totaled 500 calories. This time , rather than recipes , we need to generate combinations of the containers that add up to exactly 150 liters ( though we don ' t have to use all the containers , and multiple containers of the same size are deemed to create unique arrangements ) .

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We do this by creating the @italic { power set } of the containers — that is , a list of all possible subsets — and counting how many meet our criterion. As with the recipe problem , our @racket [ powerset ] function is a simple recursive operation.

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```

@chunk [ <day17-setup>

` `( require racket rackunit )

` `( provide ( all-defined-out ) )

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```

` `( define ( powerset xs )

` `( if ( empty? xs )

` `( list empty )

` `( append-map

` `( λ ( s ) ( list ( cons ( car xs ) s ) s ) )

` `( powerset ( cdr xs ) ) ) ) )

` `]

```
```

@chunk [ <day17-q1>

` `( define ( q1 input-str )

` `( define containers

` `( map string->number ( string-split input-str ) ) )

` `( length ( filter ( λ ( s ) ( = 150 ( apply + s ) ) )

` `( powerset containers ) ) ) ) ]

```
```

```
```

```
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@section { How many combinations have the minimum number of containers? }

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Same as above , except we find the minimum length among the winners , and then count how many other winners have that length.

```
```

@chunk [ <day17-q2>

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```

` `( define ( q2 input-str )

` `( define containers

` `( map string->number ( string-split input-str ) ) )

` `( let* ( [ winners ( filter ( λ ( s ) ( = 150 ( apply + s ) ) )

` `( powerset containers ) ) ]

` `[ shortest ( apply min ( map length winners ) ) ] )

` `( length ( filter ( λ ( w ) ( = shortest ( length w ) ) ) winners ) ) ) )

```
```

` `]

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```

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```

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@section { Testing Day 17 }

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@chunk [ <day17-test>

` `( module+ test

` `( define input-str ( file->string " day17-input.txt " ) )

` `( check-equal? ( q1 input-str ) 1638 )

` `( check-equal? ( q2 input-str ) 17 ) ) ]

```
```

```
```