Pretty printing pascal's triangle, sort of

cc-graph.scm

@@ -0,0 +1,69 @@
+(define (count-change amount)
+  (cc amount 5))
+
+(define (cc amount kinds-of-coins)
+  (cond ((= amount 0) 1)
+        ((or (< amount 0) (= kinds-of-coins 0)) 0)
+        (else (+ (cc amount
+                     (- kinds-of-coins 1))
+                 (cc (- amount
+                        (first-denomination kinds-of-coins))
+                     kinds-of-coins)))))
+
+(define (first-denomination kinds-of-coins)
+  (cond ((= kinds-of-coins 1) 1)
+        ((= kinds-of-coins 2) 5)
+        ((= kinds-of-coins 3) 10)
+        ((= kinds-of-coins 4) 25)
+        ((= kinds-of-coins 5) 50)))
+
+(define (cc-graph amount kinds-of-coins)
+
+  (define (display-node label amount kinds-of-coins)
+    (display "  ")
+    (display label)
+    (display " [label=\"")
+    (display `(cc ,amount ,kinds-of-coins))
+    (display "\"];")
+    (newline))
+
+  (define (display-edge a b)
+    (display "  ")
+    (display a)
+    (display " -> ")
+    (display b)
+    (display ";")
+    (newline))
+
+  (define (base-case amount kinds-of-coins)
+    (or (< amount 0)
+        (= kinds-of-coins 0)
+        (= amount 0)))
+
+  (define (left label)
+    (string-append label "l"))
+
+  (define (right label)
+    (string-append label "r"))
+
+  ; label is the unique label of the function invocation, e.g.  "sllrl" is
+  ; reached by traveling (from the root) left then left then right then left.
+  (define (recurse label amount kinds-of-coins)
+    (cond ((base-case amount kinds-of-coins)
+           (display-node label amount kinds-of-coins))
+          (else
+           (display-node label amount kinds-of-coins)
+           (display-edge label (left label))
+           (display-edge label (right label))
+           (recurse (left label) amount (- kinds-of-coins 1))
+           (recurse (right label)
+                    (- amount (first-denomination kinds-of-coins))
+                    kinds-of-coins))))
+
+  (display "digraph {")
+  (newline)
+  (recurse "s" amount kinds-of-coins)
+  (newline)
+  (display "}"))
+
+(cc-graph 100 5)

ex1.10.scm

@@ -42,3 +42,4 @@
 (define (h n) (A 2 n))
 
 ; 2^2^2^2...^2, with (- n 1) 2's in total
+; 2^n^n

ex1.12.scm

@@ -2,11 +2,64 @@
 
 ; assumes row and col are integers >= 0, and that col <= row
 (define (pascal row col)
-  (cond ((= col 0) 1)
+  (cond ((> col row) (display "bad input"))
+        ((= col 0) 1)
         ((= col row) 1)
         (else (+ (pascal (- row 1) (- col 1))
                  (pascal (- row 1) col)))))
 
+(define (pascal-triangle row)
+  (define (pt-helper row from-col)
+    (cond ((= from-col row) '(1))
+          (else
+           (cons (pascal row from-col)
+                 (pt-helper
+                  row
+                  (+ 1 from-col))))))
+  (pt-helper row 0))
+
+(define (pascal-triangle-until row)
+  (define (ptu-helper row)
+    (cond ((< row 0) '())
+          (else
+           (cons
+            (pascal-triangle row)
+            (ptu-helper (- row 1))))))
+  (reverse (ptu-helper row)))
+
+(define (display-pt pt-list)
+  (cond ((null? pt-list) (newline))
+        (else
+         (display (indent (length pt-list)))
+         (pp-list (car pt-list))
+         (display-pt (cdr pt-list)))))
+
+(define (pp-list lst)
+  (cond ((null? lst) (newline))
+        (else
+         (display
+          (string-append
+           (indent
+            (floor
+             (/ (- 3
+                   (string-length
+                    (string (car lst))))
+                2)))
+           (string (car lst))
+           (indent
+            (floor
+             (/ (- 4
+                   (string-length
+                    (string (car lst))))
+                2)))))
+         (pp-list (cdr lst)))))
+
+(define (indent n)
+  (cond ((= n 0) "")
+        (else
+         (string-append " " (indent (- n 1))))))
+
+(display-pt (pascal-triangle-until 8))
 
 1 ]=> (pascal 0 0)
 

ex1.14.scm

@@ -1,4 +1,4 @@
- (count-change amount)
+(define (count-change amount)
   (cc amount 5))
 
 (define (cc amount kinds-of-coins)