Pastebin: O(n) -> amortized O(1)

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+---
+
+title: SICP persistent amortized O(1) queue
+
+date: 2021-09-03
+
+layout: post
+
+lang: en
+
+ref: sicp-persistent-amortized-o1-queue
+
+---
+
+```scheme
+(define (queue)
+  (cons '()
+	'()))
+
+(define (enqueue x q)
+  (cons (car q)
+	(cons x (cdr q))))
+
+(define (flush q)
+  (cons (reverse (cdr q))
+	'()))
+
+(define (dequeue q)
+  (if (null? (car q))
+    (dequeue (flush q))
+    (cons (caar q)
+	  (cons (cdar q)
+		(cdr q)))))
+
+(define (empty? q)
+  (and (null? (car q))
+       (null? (cdr q))))
+
+(define (peek q)
+  (car (dequeue q)))
+
+(define (print-queue q)
+  (define (rec l leading-space?)
+    (when (not (null? l))
+      (when leading-space?
+	(display " "))
+      (display (car l))
+      (rec (cdr l) #t)))
+
+  (display "#q(")
+  (rec (car q) false)
+  (rec (reverse (cdr q)) (not (null? (car q))))
+  (display ")")
+  (newline))
+```
+
+Sample interactive session:
+```scheme
+scheme@(guile-user)> (define true #t)
+scheme@(guile-user)> (define false #f)
+scheme@(guile-user)> (define q (queue))
+scheme@(guile-user)> (print-queue q)
+#q()
+scheme@(guile-user)> (print-queue (enqueue 'a q))
+#q(a)
+scheme@(guile-user)> (print-queue q)
+#q()
+scheme@(guile-user)> (set! q (enqueue 'a q))
+scheme@(guile-user)> (print-queue q)
+#q(a)
+scheme@(guile-user)> (set! q (enqueue 'e (enqueue 'd (enqueue 'c (enqueue 'b q)))))
+scheme@(guile-user)> (print-queue q)
+#q(e d c b a)
+scheme@(guile-user)> (peek q)
+$28 = a
+scheme@(guile-user)> (define ret (dequeue q))
+scheme@(guile-user)> (define value (car ret))
+scheme@(guile-user)> (set! q (cdr ret))
+scheme@(guile-user)> value
+$29 = a
+scheme@(guile-user)> (print-queue q)
+#q(b c d e)
+scheme@(guile-user)> (print-queue (cdr (dequeue (cdr (dequeue (enqueue 'g (enqueue 'f q)))))))
+#q(d e f g)
+```