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Add new practice exercise palindrome-products (exercism#758)
* Add new practice exercise `palindrome-products` * remove unused imported type * add instruction appendix
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‎config.json‎

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"records"
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],
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"difficulty": 4
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},
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{
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"slug": "palindrome-products",
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"name": "Palindrome Products",
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"uuid": "3ef15a49-8f28-4a27-aa83-695db65177f9",
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"practices": [
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"tail-call-recursion"
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],
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"prerequisites": [
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"recursion",
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"tail-call-recursion",
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"lists",
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"records",
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"result",
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"pattern-matching",
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"custom-types",
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"comparison",
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"maybe",
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"set",
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"array",
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"strings"
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],
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"difficulty": 8
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}
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],
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"foregone": [

‎exercises/practice/palindrome-products/.docs/instructions.append.md‎

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# Instructions Append
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```exercism/note
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Naive solutions may take a long time to pass the tests involving four digit factors, likely longer than the time limit allocated to the online test runner.
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You may need to work on the exercise locally to profile your solution.
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There are efficient solutions to this exercise, but they are challenging.
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```

‎exercises/practice/palindrome-products/.docs/instructions.md‎

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# Instructions
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Detect palindrome products in a given range.
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A palindromic number is a number that remains the same when its digits are reversed.
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For example, `121` is a palindromic number but `112` is not.
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Given a range of numbers, find the largest and smallest palindromes which
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are products of two numbers within that range.
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Your solution should return the largest and smallest palindromes, along with the factors of each within the range.
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If the largest or smallest palindrome has more than one pair of factors within the range, then return all the pairs.
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## Example 1
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Given the range `[1, 9]` (both inclusive)...
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And given the list of all possible products within this range:
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`[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 15, 21, 24, 27, 20, 28, 32, 36, 25, 30, 35, 40, 45, 42, 48, 54, 49, 56, 63, 64, 72, 81]`
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The palindrome products are all single digit numbers (in this case):
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`[1, 2, 3, 4, 5, 6, 7, 8, 9]`
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The smallest palindrome product is `1`.
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Its factors are `(1, 1)`.
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The largest palindrome product is `9`.
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Its factors are `(1, 9)` and `(3, 3)`.
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## Example 2
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Given the range `[10, 99]` (both inclusive)...
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The smallest palindrome product is `121`.
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Its factors are `(11, 11)`.
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The largest palindrome product is `9009`.
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Its factors are `(91, 99)`.

‎exercises/practice/palindrome-products/.meta/config.json‎

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{
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"authors": [
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"jiegillet"
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],
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"files": {
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"solution": [
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"src/PalindromeProducts.elm"
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],
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"test": [
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"tests/Tests.elm"
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],
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"example": [
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".meta/src/PalindromeProducts.example.elm"
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]
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},
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"blurb": "Detect palindrome products in a given range.",
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"source": "Problem 4 at Project Euler",
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"source_url": "https://projecteuler.net/problem=4"
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}

‎exercises/practice/palindrome-products/.meta/src/PalindromeProducts.example.elm‎

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module PalindromeProducts exposing (largest, smallest)
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import Array exposing (Array)
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import Set
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type alias PalindromeProduct =
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{ value : Int
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, factors : List ( Int, Int )
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}
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smallest : Int -> Int -> Result String (Maybe PalindromeProduct)
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smallest min max =
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if min > max then
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Err "min must be <= max"
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else
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let
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initQueue =
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new (\( i, j ) -> i * j) (<=)
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|> insert ( min, min )
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traverse queue visited =
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case pop queue of
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Nothing ->
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Ok Nothing
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Just ( ( i, j ), product, poppedQueue ) ->
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if isPalindrome product then
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popUntilDifferent { value = product, factors = [ ( i, j ) ] } poppedQueue
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else if j > max then
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traverse poppedQueue visited
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else
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let
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newVisited =
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visited |> Set.insert ( i, j + 1 ) |> Set.insert ( i + 1, j + 1 )
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newQueue =
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[ ( i, j + 1 ), ( i + 1, j + 1 ) ] |> List.filter (\pair -> not (Set.member pair visited)) |> List.foldl insert poppedQueue
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in
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traverse newQueue newVisited
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in
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traverse initQueue Set.empty
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largest : Int -> Int -> Result String (Maybe PalindromeProduct)
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largest min max =
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if min > max then
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Err "min must be <= max"
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else
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let
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initQueue =
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new (\( i, j ) -> i * j) (>)
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|> insert ( max, max )
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traverse queue visited =
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case pop queue of
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Nothing ->
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Ok Nothing
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Just ( ( i, j ), product, poppedQueue ) ->
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if isPalindrome product then
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popUntilDifferent { value = product, factors = [ ( i, j ) ] } poppedQueue
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else if i < min then
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traverse poppedQueue visited
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else
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let
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neighbors =
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[ ( i - 1, j ), ( i - 1, j - 1 ) ]
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newVisited =
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List.foldl Set.insert visited neighbors
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newQueue =
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neighbors
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|> List.filter (\pair -> not (Set.member pair visited))
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|> List.foldl insert poppedQueue
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in
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traverse newQueue newVisited
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in
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traverse initQueue Set.empty
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isPalindrome : Int -> Bool
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isPalindrome n =
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let
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string =
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String.fromInt n
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in
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string == String.reverse string
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popUntilDifferent : PalindromeProduct -> PriorityQueue ( Int, Int ) -> Result String (Maybe PalindromeProduct)
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popUntilDifferent product queue =
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case pop queue of
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Nothing ->
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Ok (Just { product | factors = List.sort product.factors })
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Just ( pair, value, newQueue ) ->
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if value == product.value then
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popUntilDifferent { product | factors = pair :: product.factors } newQueue
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else
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Ok (Just { product | factors = List.sort product.factors })
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-- Priority Queue
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type alias PriorityQueue a =
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{ leq : Int -> Int -> Bool
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, toPriority : a -> Int
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, heap : Heap a
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}
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type alias Heap a =
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Array ( a, Int )
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new : (a -> Int) -> (Int -> Int -> Bool) -> PriorityQueue a
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new toPriority leq =
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PriorityQueue leq toPriority Array.empty
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insert : a -> PriorityQueue a -> PriorityQueue a
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insert a ({ leq, toPriority, heap } as queue) =
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{ queue | heap = insertHeap leq a (toPriority a) heap }
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insertHeap : (Int -> Int -> Bool) -> a -> Int -> Heap a -> Heap a
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insertHeap leq a p heap =
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bubbleUp leq (Array.length heap) (Array.push ( a, p ) heap)
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bubbleUp : (Int -> Int -> Bool) -> Int -> Heap a -> Heap a
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bubbleUp leq index heap =
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let
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parentIndex =
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(index - 1) // 2
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in
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case ( Array.get index heap, Array.get parentIndex heap ) of
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( Just ( newA, newP ), Just ( parentA, parentP ) ) ->
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if index > 0 && leq newP parentP then
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bubbleUp leq
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parentIndex
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(heap
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|> Array.set index ( parentA, parentP )
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|> Array.set parentIndex ( newA, newP )
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)
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else
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heap
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_ ->
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heap
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pop : PriorityQueue a -> Maybe ( a, Int, PriorityQueue a )
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pop ({ leq, heap } as queue) =
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case Array.get 0 heap of
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Nothing ->
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Nothing
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Just ( aTop, pTop ) ->
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let
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newHeap =
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case Array.get (Array.length heap - 1) heap of
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Nothing ->
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heap
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Just ( a, p ) ->
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heap
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|> Array.set 0 ( a, p )
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|> Array.slice 0 (Array.length heap - 1)
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|> bubbleDown leq 0
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in
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Just ( aTop, pTop, { queue | heap = newHeap } )
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bubbleDown : (Int -> Int -> Bool) -> Int -> Heap a -> Heap a
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bubbleDown leq index heap =
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let
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leftIndex =
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index * 2 + 1
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rightIndex =
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index * 2 + 2
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in
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case ( Array.get index heap, Array.get leftIndex heap, Array.get rightIndex heap ) of
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( Just ( a, p ), Just ( leftA, leftP ), Nothing ) ->
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if leq p leftP then
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heap
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else
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heap |> Array.set index ( leftA, leftP ) |> Array.set leftIndex ( a, p )
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( Just ( a, p ), Just ( leftA, leftP ), Just ( rightA, rightP ) ) ->
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if leq p leftP && leq p rightP then
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heap
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else if leq leftP rightP then
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bubbleDown leq leftIndex (heap |> Array.set index ( leftA, leftP ) |> Array.set leftIndex ( a, p ))
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else
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bubbleDown leq rightIndex (heap |> Array.set index ( rightA, rightP ) |> Array.set rightIndex ( a, p ))
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_ ->
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heap

‎exercises/practice/palindrome-products/.meta/tests.toml‎

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# This is an auto-generated file.
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#
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# Regenerating this file via `configlet sync` will:
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# - Recreate every `description` key/value pair
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# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications
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# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion)
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# - Preserve any other key/value pair
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#
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# As user-added comments (using the # character) will be removed when this file
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# is regenerated, comments can be added via a `comment` key.
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[5cff78fe-cf02-459d-85c2-ce584679f887]
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description = "find the smallest palindrome from single digit factors"
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[0853f82c-5fc4-44ae-be38-fadb2cced92d]
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description = "find the largest palindrome from single digit factors"
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[66c3b496-bdec-4103-9129-3fcb5a9063e1]
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description = "find the smallest palindrome from double digit factors"
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[a10682ae-530a-4e56-b89d-69664feafe53]
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description = "find the largest palindrome from double digit factors"
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[cecb5a35-46d1-4666-9719-fa2c3af7499d]
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description = "find the smallest palindrome from triple digit factors"
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[edab43e1-c35f-4ea3-8c55-2f31dddd92e5]
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description = "find the largest palindrome from triple digit factors"
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[4f802b5a-9d74-4026-a70f-b53ff9234e4e]
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description = "find the smallest palindrome from four digit factors"
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[787525e0-a5f9-40f3-8cb2-23b52cf5d0be]
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description = "find the largest palindrome from four digit factors"
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[58fb1d63-fddb-4409-ab84-a7a8e58d9ea0]
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description = "empty result for smallest if no palindrome in the range"
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[9de9e9da-f1d9-49a5-8bfc-3d322efbdd02]
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description = "empty result for largest if no palindrome in the range"
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[12e73aac-d7ee-4877-b8aa-2aa3dcdb9f8a]
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description = "error result for smallest if min is more than max"
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[eeeb5bff-3f47-4b1e-892f-05829277bd74]
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description = "error result for largest if min is more than max"
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[16481711-26c4-42e0-9180-e2e4e8b29c23]
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description = "smallest product does not use the smallest factor"

‎exercises/practice/palindrome-products/elm.json‎

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{
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"type": "application",
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"source-directories": [
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"src"
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],
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"elm-version": "0.19.1",
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"dependencies": {
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"direct": {
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"elm/core": "1.0.5",
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"elm/json": "1.1.3",
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"elm/parser": "1.1.0",
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"elm/random": "1.0.0",
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"elm/regex": "1.0.0",
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"elm/time": "1.0.0",
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"elm/html": "1.0.0"
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},
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"indirect": {}
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},
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"test-dependencies": {
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"direct": {
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"elm-explorations/test": "2.1.0",
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"rtfeldman/elm-iso8601-date-strings": "1.1.4"
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},
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"indirect": {
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"elm/bytes": "1.0.8",
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"elm/virtual-dom": "1.0.3"
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}
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}
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}

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