September 2017 Update

Task/N-queens-problem/F-Sharp/n-queens-problem-1.fs

@@ -0,0 +1,42 @@
+let rec iterate f value = seq {
+    yield value
+    yield! iterate f (f value) }
+
+let up i = i + 1
+let right i = i
+let down i = i - 1
+
+let noCollisionGivenDir solution number dir =
+    Seq.forall2 (<>) solution (Seq.skip 1 (iterate dir number))
+
+let goodAddition solution number =
+    List.forall (noCollisionGivenDir solution number) [ up; right; down ]
+
+let rec extendSolution n ps =
+    [0..n - 1]
+    |> List.filter (goodAddition ps)
+    |> List.map (fun num -> num :: ps)
+
+let allSolutions n =
+    iterate (List.collect (extendSolution n)) [[]]
+
+// Print one solution for the 8x8 case
+let printOneSolution () =
+    allSolutions 8
+    |> Seq.item 8
+    |> Seq.head
+    |> List.iter (fun rowIndex ->
+        printf "|"
+        [0..8] |> List.iter (fun i -> printf (if i = rowIndex then "X|" else " |"))
+        printfn "")
+
+// Print number of solution for the other cases
+let printNumberOfSolutions () =
+    printfn "Size\tNr of solutions"
+    [1..11]
+    |> List.map ((fun i -> Seq.item i (allSolutions i)) >> List.length)
+    |> List.iteri (fun i cnt -> printfn "%d\t%d" (i+1) cnt)
+
+printOneSolution()
+
+printNumberOfSolutions()

Task/N-queens-problem/F-Sharp/n-queens-problem-2.fs

@@ -0,0 +1,21 @@
+| | | |X| | | | | |
+| |X| | | | | | | |
+| | | | | | |X| | |
+| | |X| | | | | | |
+| | | | | |X| | | |
+| | | | | | | |X| |
+| | | | |X| | | | |
+|X| | | | | | | | |
+
+Size    Nr of solutions
+1       1
+2       0
+3       0
+4       2
+5       10
+6       4
+7       40
+8       92
+9       352
+10      724
+11      2680