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Largest palindrome made from the product of two n-digit numbers

A generalised version of the solution to the fourth Project Euler problem - Largest palindrome product, using sequences. The key to understanding this code is how "Seq.map (fun x -> (Seq.map (fun y -> x * y) baseSeq)) baseSeq" generates a sequence of sequences that contains the products of all possible combinations of two n-digit numbers. "Seq.map (fun x -> (Seq.map (fun y -> x * y) {1..3})) {1..3}" will generate: seq [seq [1; 2; 3]; seq [2; 4; 6]; seq [3; 6; 9]]

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let numDigits = 3
if (numDigits < 1) then failwith "Number of digits must be at least 1" 

let lowestNumDigitNumber = pown 10 (numDigits - 1)  
let highestNumDigitNumber = (pown 10 numDigits) - 1
let baseSeq = {lowestNumDigitNumber..highestNumDigitNumber}  

let reverse (t : string) =
    new string(t.ToCharArray() |> Array.rev)
    
let isPalindrome t = reverse (string t) = string t

Seq.map (fun x -> (Seq.map (fun y -> x * y) baseSeq)) baseSeq
|> Seq.concat
|> Seq.filter isPalindrome
|> Seq.max
|> printfn "Largest palindrome made from the product of two %d-digit numbers: %A" numDigits

val numDigits : int

Full name: Script.numDigits

val failwith : message:string -> 'T

Full name: Microsoft.FSharp.Core.Operators.failwith

val lowestNumDigitNumber : int

Full name: Script.lowestNumDigitNumber

val pown : x:'T -> n:int -> 'T (requires member get_One and member ( * ) and member ( / ))

Full name: Microsoft.FSharp.Core.Operators.pown

val highestNumDigitNumber : int

Full name: Script.highestNumDigitNumber

val baseSeq : seq<int>

Full name: Script.baseSeq

val reverse : t:string -> string

Full name: Script.reverse

val t : string

Multiple items
val string : value:'T -> string

Full name: Microsoft.FSharp.Core.Operators.string

--------------------
type string = System.String

Full name: Microsoft.FSharp.Core.string

System.String.ToCharArray() : char []
System.String.ToCharArray(startIndex: int, length: int) : char []

module Array

from Microsoft.FSharp.Collections

val rev : array:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.rev

val isPalindrome : t:int -> bool

Full name: Script.isPalindrome

val t : int

module Seq

from Microsoft.FSharp.Collections

val map : mapping:('T -> 'U) -> source:seq<'T> -> seq<'U>

Full name: Microsoft.FSharp.Collections.Seq.map

val x : int

val y : int

val concat : sources:seq<#seq<'T>> -> seq<'T>

Full name: Microsoft.FSharp.Collections.Seq.concat

val filter : predicate:('T -> bool) -> source:seq<'T> -> seq<'T>

Full name: Microsoft.FSharp.Collections.Seq.filter

val max : source:seq<'T> -> 'T (requires comparison)

Full name: Microsoft.FSharp.Collections.Seq.max

val printfn : format:Printf.TextWriterFormat<'T> -> 'T

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.printfn

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More information

Link:	http://fssnip.net/hE
Posted:	11 years ago
Author:	Bjørn Bæverfjord
Tags:	puzzles , seq , pipeline , project euler