apl: n-queens via permute + diagonal filter, q(8)=92 (+10 tests, 306/306)

lib/apl/runtime.sx

@@ -865,6 +865,48 @@
         (ones (apl-add (apl-mul cs (apl-scalar 0)) (apl-scalar 1))))
       (apl-mandelbrot-step cs zero zero ones max-iter))))
 
+(define
+  apl-insert-everywhere
+  (fn
+    (x lst)
+    (map
+      (fn (i) (append (take lst i) (cons x (drop lst i))))
+      (range 0 (+ (len lst) 1)))))
+
+(define
+  apl-permutations
+  (fn
+    (n)
+    (if
+      (<= n 1)
+      (list (list 1))
+      (let
+        ((sub (apl-permutations (- n 1))))
+        (reduce
+          (fn (acc p) (append acc (apl-insert-everywhere n p)))
+          (list)
+          sub)))))
+
+(define
+  apl-queens-no-conflict?
+  (fn
+    (perm i j n)
+    (cond
+      ((>= i n) true)
+      ((>= j n) (apl-queens-no-conflict? perm (+ i 1) (+ i 2) n))
+      ((= (abs (- i j)) (abs (- (nth perm i) (nth perm j)))) false)
+      (else (apl-queens-no-conflict? perm i (+ j 1) n)))))
+
+(define
+  apl-queens-valid?
+  (fn (perm) (apl-queens-no-conflict? perm 0 1 (len perm))))
+
+(define
+  apl-queens
+  (fn
+    (n)
+    (apl-scalar (len (filter apl-queens-valid? (apl-permutations n))))))
+
 (define
   apl-reduce
   (fn