From: Ramakrishnan Muthukrishnan <vu3rdd@gmail.com>
Date: Mon, 7 Jan 2013 17:04:08 +0000 (+0530)
Subject: Solution to 4.44. A bit too verbose. Can be improved by better
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Solution to 4.44. A bit too verbose. Can be improved by better
board representation.
---

diff --git a/src/sicp/ex4_44.rkt b/src/sicp/ex4_44.rkt
new file mode 100644
index 0000000..5672d7e
--- /dev/null
+++ b/src/sicp/ex4_44.rkt
@@ -0,0 +1,81 @@
+#lang racket
+
+(require "amb-eli.rkt")
+(require "distinct.rkt")
+
+(define (queens)
+  (let ([q1r (amb 1 2 3 4 5 6 7 8)]
+        [q1c (amb 1 2 3 4 5 6 7 8)]
+        [q2r (amb 1 2 3 4 5 6 7 8)]
+        [q2c (amb 1 2 3 4 5 6 7 8)])
+    (assert (distinct? (list q1r q2r)))
+    (assert (distinct? (list q1c q2c)))
+    (assert (not (diagonal? (list q1r q1c) (list q2r q2c))))
+    (let ([q3r (amb 1 2 3 4 5 6 7 8)]
+          [q3c (amb 1 2 3 4 5 6 7 8)])
+      (for ([qr (list q1r q2r)])
+        (assert (distinct? (list q3r qr))))
+      (for ([qc (list q1c q2c)])
+        (assert (distinct? (list q3c qc))))
+      (for ([q (list (list q1r q1c) (list q2r q2c))])
+        (assert (not (diagonal? (list q3r q3c) q))))
+      (let ([q4r (amb 1 2 3 4 5 6 7 8)]
+            [q4c (amb 1 2 3 4 5 6 7 8)])
+        (for ([qr (list q1r q2r q3r)])
+          (assert (distinct? (list q4r qr))))
+        (for ([qc (list q1c q2c q3c)])
+          (assert (distinct? (list q4c qc))))
+        (for ([q (list (list q1r q1c) (list q2r q2c) (list q3r q3c))])
+          (assert (not (diagonal? (list q4r q4c) q))))
+        (let ([q5r (amb 1 2 3 4 5 6 7 8)]
+              [q5c (amb 1 2 3 4 5 6 7 8)])
+          (for ([qr (list q1r q2r q3r q4r)])
+            (assert (distinct? (list q5r qr))))
+          (for ([qc (list q1c q2c q3c q4c)])
+            (assert (distinct? (list q5c qc))))
+          (for ([q (list (list q1r q1c) (list q2r q2c) (list q3r q3c) (list q4r q4c))])
+            (assert (not (diagonal? (list q5r q5c) q))))
+          (let ([q6r (amb 1 2 3 4 5 6 7 8)]
+                [q6c (amb 1 2 3 4 5 6 7 8)])
+            (for ([qr (list q1r q2r q3r q4r q5r)])
+              (assert (distinct? (list q6r qr))))
+            (for ([qc (list q1c q2c q3c q4c q5c)])
+              (assert (distinct? (list q6c qc))))
+            (for ([q (list (list q1r q1c) (list q2r q2c) (list q3r q3c) (list q4r q4c) (list q5r q5c))])
+              (assert (not (diagonal? (list q6r q6c) q))))
+            (let ([q7r (amb 1 2 3 4 5 6 7 8)]
+                  [q7c (amb 1 2 3 4 5 6 7 8)])
+              (for ([qr (list q1r q2r q3r q4r q5r q6r)])
+                (assert (distinct? (list q7r qr))))
+              (for ([qc (list q1c q2c q3c q4c q5c q6c)])
+                (assert (distinct? (list q7c qc))))
+              (for ([q (list (list q1r q1c) (list q2r q2c) (list q3r q3c) (list q4r q4c) (list q5r q5c) (list q6r q6c))])
+                (assert (not (diagonal? (list q7r q7c) q))))
+              (let ([q8r (amb 1 2 3 4 5 6 7 8)]
+                    [q8c (amb 1 2 3 4 5 6 7 8)])
+                (for ([qr (list q1r q2r q3r q4r q5r q6r q7r)])
+                  (assert (distinct? (list q8r qr))))
+                (for ([qc (list q1c q2c q3c q4c q5c q6c q7c)])
+                  (assert (distinct? (list q8c qc))))
+                (for ([q (list (list q1r q1c) (list q2r q2c) (list q3r q3c) (list q4r q4c) (list q5r q5c) (list q6r q6c) (list q7r q7c))])
+                  (assert (not (diagonal? (list q8r q8c) q))))
+                (list (list 'q1 q1r q1c)
+                      (list 'q2 q2r q2c)
+                      (list 'q3 q3r q3c)
+                      (list 'q4 q4r q4c)
+                      (list 'q5 q5r q5c)
+                      (list 'q6 q6r q6c)
+                      (list 'q7 q7r q7c)
+                      (list 'q8 q8r q8c))))))))))
+
+(define (diagonal? p1 p2)
+  (let ([x1 (first p1)]
+        [y1 (second p1)]
+        [x2 (first p2)]
+        [y2 (second p2)])
+    (= (abs (- x1 x2))
+       (abs (- y1 y2)))))
+
+(queens)
+
+;; '((q1 1 1) (q2 2 5) (q3 3 8) (q4 4 6) (q5 5 3) (q6 6 7) (q7 7 2) (q8 8 4))
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