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one to nine puzzle

Solve the one to nine puzzle with a utility function that handles the depth first search. First saw the puzzle here: http://msdn.microsoft.com/en-us/vcsharp/ee957404

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/// Helper to manage depth first search of a problem.
/// next_f generates new states, and done_f test for the 
/// end of the search.
let solve next_f done_f initial =
    let rec go state =
        seq {
            if done_f state then
               yield state
            else
               for state' in next_f state do
                   yield! go state'
            }
    go initial


let one_to_nine () =
    let next_f (number, digits, idx) =
        let idx' = idx + 1
        seq {
            for d in digits do
               let number' = number * 10 + d
               if number' % idx' = 0 then
                   yield number', Set.remove d digits, idx'
            }

    let done_f (_, _, idx) = idx = 9

    solve next_f done_f (0, Set.ofList [1..9], 0)
    |> Seq.map (fun (num, _, _) -> num)
    |> Seq.head

printfn "solution: %A" (one_to_nine())
val solve : next_f:('a -> #seq<'a>) -> done_f:('a -> bool) -> initial:'a -> seq<'a>

Full name: Script.solve


 Helper to manage depth first search of a problem.
 next_f generates new states, and done_f test for the
 end of the search.
val next_f : ('a -> #seq<'a>)
val done_f : ('a -> bool)
val initial : 'a
val go : ('a -> seq<'a>)
val state : 'a
Multiple items
val seq : sequence:seq<'T> -> seq<'T>

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

--------------------
type seq<'T> = System.Collections.Generic.IEnumerable<'T>

Full name: Microsoft.FSharp.Collections.seq<_>
val state' : 'a
val one_to_nine : unit -> int

Full name: Script.one_to_nine
val next_f : (int * Set<int> * int -> seq<int * Set<int> * int>)
val number : int
val digits : Set<int>
val idx : int
val idx' : int
val d : int
val number' : int
Multiple items
module Set

from Microsoft.FSharp.Collections

--------------------
type Set<'T (requires comparison)> =
  interface IComparable
  interface IEnumerable
  interface IEnumerable<'T>
  interface ICollection<'T>
  new : elements:seq<'T> -> Set<'T>
  member Add : value:'T -> Set<'T>
  member Contains : value:'T -> bool
  override Equals : obj -> bool
  member IsProperSubsetOf : otherSet:Set<'T> -> bool
  member IsProperSupersetOf : otherSet:Set<'T> -> bool
  ...

Full name: Microsoft.FSharp.Collections.Set<_>

--------------------
new : elements:seq<'T> -> Set<'T>
val remove : value:'T -> set:Set<'T> -> Set<'T> (requires comparison)

Full name: Microsoft.FSharp.Collections.Set.remove
val done_f : ('a * 'b * int -> bool)
val ofList : elements:'T list -> Set<'T> (requires comparison)

Full name: Microsoft.FSharp.Collections.Set.ofList
module Seq

from Microsoft.FSharp.Collections
val map : mapping:('T -> 'U) -> source:seq<'T> -> seq<'U>

Full name: Microsoft.FSharp.Collections.Seq.map
val num : int
val head : source:seq<'T> -> 'T

Full name: Microsoft.FSharp.Collections.Seq.head
val printfn : format:Printf.TextWriterFormat<'T> -> 'T

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

Link:http://fssnip.net/6m
Posted:9 years ago
Author:dave jones
Tags: puzzle