Finish 1.2

chapter-1/1.2/1.14.dot

@@ -0,0 +1,61 @@
+digraph G {
+  graph [ranksep=0.25];
+  node [color=gray95, style=filled, fontsize=9, shape=box, margin=.08, width=0, height=0 ];
+  edge [penwidth=.5, arrowsize=0.5];
+
+  "[0] (cc 11 5)" [label = "(cc 11 5)"];
+  "[0] (cc 11 5)" -> "[1] (cc 11 4)"; "[1] (cc 11 4)" [label="(cc 11 4)", ];
+  "[1] (cc 11 4)" -> "[2] (cc 11 3)"; "[2] (cc 11 3)" [label="(cc 11 3)", ];
+  "[2] (cc 11 3)" -> "[3] (cc 11 2)"; "[3] (cc 11 2)" [label="(cc 11 2)", ];
+  "[3] (cc 11 2)" -> "[4] (cc 11 1)"; "[4] (cc 11 1)" [label="(cc 11 1)", ];
+  "[4] (cc 11 1)" -> "[5] (cc 11 0)"; "[5] (cc 11 0)" [label="(cc 11 0)", color=gray85];
+  "[4] (cc 11 1)" -> "[5] (cc 10 1)"; "[5] (cc 10 1)" [label="(cc 10 1)", ];
+  "[5] (cc 10 1)" -> "[6] (cc 10 0)"; "[6] (cc 10 0)" [label="(cc 10 0)", color=gray85];
+  "[5] (cc 10 1)" -> "[6] (cc 9 1)"; "[6] (cc 9 1)" [label="(cc 9 1)", ];
+  "[6] (cc 9 1)" -> "[7] (cc 9 0)"; "[7] (cc 9 0)" [label="(cc 9 0)", color=gray85];
+  "[6] (cc 9 1)" -> "[7] (cc 8 1)"; "[7] (cc 8 1)" [label="(cc 8 1)", ];
+  "[7] (cc 8 1)" -> "[8] (cc 8 0)"; "[8] (cc 8 0)" [label="(cc 8 0)", color=gray85];
+  "[7] (cc 8 1)" -> "[8] (cc 7 1)"; "[8] (cc 7 1)" [label="(cc 7 1)", ];
+  "[8] (cc 7 1)" -> "[9] (cc 7 0)"; "[9] (cc 7 0)" [label="(cc 7 0)", color=gray85];
+  "[8] (cc 7 1)" -> "[9] (cc 6 1)"; "[9] (cc 6 1)" [label="(cc 6 1)", ];
+  "[9] (cc 6 1)" -> "[10] (cc 6 0)"; "[10] (cc 6 0)" [label="(cc 6 0)", color=gray85];
+  "[9] (cc 6 1)" -> "[10] (cc 5 1)"; "[10] (cc 5 1)" [label="(cc 5 1)", ];
+  "[10] (cc 5 1)" -> "[11] (cc 5 0)"; "[11] (cc 5 0)" [label="(cc 5 0)", color=gray85];
+  "[10] (cc 5 1)" -> "[11] (cc 4 1)"; "[11] (cc 4 1)" [label="(cc 4 1)", ];
+  "[11] (cc 4 1)" -> "[12] (cc 4 0)"; "[12] (cc 4 0)" [label="(cc 4 0)", color=gray85];
+  "[11] (cc 4 1)" -> "[12] (cc 3 1)"; "[12] (cc 3 1)" [label="(cc 3 1)", ];
+  "[12] (cc 3 1)" -> "[13] (cc 3 0)"; "[13] (cc 3 0)" [label="(cc 3 0)", color=gray85];
+  "[12] (cc 3 1)" -> "[13] (cc 2 1)"; "[13] (cc 2 1)" [label="(cc 2 1)", ];
+  "[13] (cc 2 1)" -> "[14] (cc 2 0)"; "[14] (cc 2 0)" [label="(cc 2 0)", color=gray85];
+  "[13] (cc 2 1)" -> "[14] (cc 1 1)"; "[14] (cc 1 1)" [label="(cc 1 1)", ];
+  "[14] (cc 1 1)" -> "[15] (cc 1 0)"; "[15] (cc 1 0)" [label="(cc 1 0)", color=gray85];
+  "[14] (cc 1 1)" -> "[15] (cc 0 1)"; "[15] (cc 0 1)" [label="(cc 0 1)", color=gray85];
+  "[3] (cc 11 2)" -> "[4] (cc 6 2)"; "[4] (cc 6 2)" [label="(cc 6 2)", ];
+  "[4] (cc 6 2)" -> "[5] (cc 6 1)"; "[5] (cc 6 1)" [label="(cc 6 1)", ];
+  "[5] (cc 6 1)" -> "[6] (cc 6 0)"; "[6] (cc 6 0)" [label="(cc 6 0)", color=gray85];
+  "[5] (cc 6 1)" -> "[6] (cc 5 1)"; "[6] (cc 5 1)" [label="(cc 5 1)", ];
+  "[6] (cc 5 1)" -> "[7] (cc 5 0)"; "[7] (cc 5 0)" [label="(cc 5 0)", color=gray85];
+  "[6] (cc 5 1)" -> "[7] (cc 4 1)"; "[7] (cc 4 1)" [label="(cc 4 1)", ];
+  "[7] (cc 4 1)" -> "[8] (cc 4 0)"; "[8] (cc 4 0)" [label="(cc 4 0)", color=gray85];
+  "[7] (cc 4 1)" -> "[8] (cc 3 1)"; "[8] (cc 3 1)" [label="(cc 3 1)", ];
+  "[8] (cc 3 1)" -> "[9] (cc 3 0)"; "[9] (cc 3 0)" [label="(cc 3 0)", color=gray85];
+  "[8] (cc 3 1)" -> "[9] (cc 2 1)"; "[9] (cc 2 1)" [label="(cc 2 1)", ];
+  "[9] (cc 2 1)" -> "[10] (cc 2 0)"; "[10] (cc 2 0)" [label="(cc 2 0)", color=gray85];
+  "[9] (cc 2 1)" -> "[10] (cc 1 1)"; "[10] (cc 1 1)" [label="(cc 1 1)", ];
+  "[10] (cc 1 1)" -> "[11] (cc 1 0)"; "[11] (cc 1 0)" [label="(cc 1 0)", color=gray85];
+  "[10] (cc 1 1)" -> "[11] (cc 0 1)"; "[11] (cc 0 1)" [label="(cc 0 1)", color=gray85];
+  "[4] (cc 6 2)" -> "[5] (cc 1 2)"; "[5] (cc 1 2)" [label="(cc 1 2)", ];
+  "[5] (cc 1 2)" -> "[6] (cc 1 1)"; "[6] (cc 1 1)" [label="(cc 1 1)", ];
+  "[6] (cc 1 1)" -> "[7] (cc 1 0)"; "[7] (cc 1 0)" [label="(cc 1 0)", color=gray85];
+  "[6] (cc 1 1)" -> "[7] (cc 0 1)"; "[7] (cc 0 1)" [label="(cc 0 1)", color=gray85];
+  "[5] (cc 1 2)" -> "[6] (cc -4 2)"; "[6] (cc -4 2)" [label="(cc -4 2)", color=gray85];
+  "[2] (cc 11 3)" -> "[3] (cc 1 3)"; "[3] (cc 1 3)" [label="(cc 1 3)", ];
+  "[3] (cc 1 3)" -> "[4] (cc 1 2)"; "[4] (cc 1 2)" [label="(cc 1 2)", ];
+  "[4] (cc 1 2)" -> "[5] (cc 1 1)"; "[5] (cc 1 1)" [label="(cc 1 1)", ];
+  "[5] (cc 1 1)" -> "[6] (cc 1 0)"; "[6] (cc 1 0)" [label="(cc 1 0)", color=gray85];
+  "[5] (cc 1 1)" -> "[6] (cc 0 1)"; "[6] (cc 0 1)" [label="(cc 0 1)", color=gray85];
+  "[4] (cc 1 2)" -> "[5] (cc -4 2)"; "[5] (cc -4 2)" [label="(cc -4 2)", color=gray85];
+  "[3] (cc 1 3)" -> "[4] (cc -9 3)"; "[4] (cc -9 3)" [label="(cc -9 3)", color=gray85];
+  "[1] (cc 11 4)" -> "[2] (cc -14 4)"; "[2] (cc -14 4)" [label="(cc -14 4)", color=gray85];
+  "[0] (cc 11 5)" -> "[1] (cc -39 5)"; "[1] (cc -39 5)" [label="(cc -39 5)", color=gray85];
+}

chapter-1/1.2/1.14.py

@@ -2,18 +2,21 @@
 # using GraphViz
 coins = [50, 25, 10, 5, 1]
 
+
 # return (node string, label string)
 def get_str(level, amount, kind):
   return (f"[{level}] (cc {amount} {kind})", f"(cc {amount} {kind})")
 
+
 def is_leaf(amount, kind):
   return amount <= 0 or kind == 0
 
+
 def cc(level, amount, kind):
-  (ns, ls) = get_str(level, amount, kind)
+  (node_name, label) = get_str(level, amount, kind)
 
   if level == 0:
-    print(f'  "{ns}" [label = "{ls}"];')
+    print(f'  "{node_name}" [label = "{label}"];')
 
   if amount < 0:
     return 0
@@ -25,28 +28,36 @@ def cc(level, amount, kind):
   left_amount = amount
   left_kind = kind - 1
   left_is_leaf = is_leaf(left_amount, left_kind)
-  (left_ns, left_ls) = get_str(level+1, left_amount, left_kind)
-  print(f'  "{ns}" -> "{left_ns}"; "{left_ns}" [label="{left_ls}", {"color=gray85" if left_is_leaf else ""}];')
-  left = cc(level+1, left_amount, left_kind)
+  (left_node, left_label) = get_str(level + 1, left_amount, left_kind)
+  print(
+    f'  "{node_name}" -> "{left_node}"; "{left_node}" [label="{left_label}", {"color=gray85" if left_is_leaf else ""}];'
+  )
+  left = cc(level + 1, left_amount, left_kind)
 
-  right_amount = amount - coins[5-kind]
+  right_amount = amount - coins[5 - kind]
   right_kind = kind
   right_is_leaf = is_leaf(right_amount, right_kind)
-  (right_ns, right_ls) = get_str(level+1, right_amount, right_kind)
-  print(f'  "{ns}" -> "{right_ns}"; "{right_ns}" [label="{right_ls}", {"color=gray85" if right_is_leaf else ""}];')
-  right = cc(level+1, right_amount, right_kind)
+  (right_node, right_label) = get_str(level + 1, right_amount, right_kind)
+  print(
+    f'  "{node_name}" -> "{right_node}"; "{right_node}" [label="{right_label}", {"color=gray85" if right_is_leaf else ""}];'
+  )
+  right = cc(level + 1, right_amount, right_kind)
 
   return left + right
 
+
 def run():
-  print("""digraph G {
+  print(
+    """digraph G {
   graph [ranksep=0.25];
   node [color=gray95, style=filled, fontsize=9, shape=box, margin=.08, width=0, height=0 ];
   edge [penwidth=.5, arrowsize=0.5];
-""")
+"""
+  )
 
   cc(0, 11, 5)
 
   print("}")
 
+
 run()

chapter-1/1.2/1.16.scm

@@ -1,6 +1,3 @@
-(define (square n) (* n n))
-(define (even? n) (= (remainder n 2) 0))
-
 (define (expt b n)
   (define (iter a b n)
     (cond
@@ -9,4 +6,4 @@
       (else (iter (* a b) (square b) (/ (- n 1) 2)))))
   (iter 1 b n))
 
-(display (expt 2 100))
+(display (expt 2 20))

chapter-1/1.2/1.18.scm

@@ -1,7 +1,5 @@
 (define (double x) (+ x x))
 (define (halve x) (/ x 2))
-(define (even? x) (= (remainder x 2) 0))
-
 
 (define (mul a b)
   (define (iter s a b)
@@ -14,4 +12,4 @@
 (display (mul 2 100))
 (newline)
 
-(display (mul 4 6))
+(display (mul 3 7))

chapter-1/1.2/1.19.scm

@@ -0,0 +1,15 @@
+(define (fib n)
+  (define (fib-iter a b p q count)
+     (cond ((= count 0) b)
+          ((even? count)
+            (fib-iter
+              a b (+ (square p) (square q)) (+ (square q) (* 2 p q)) (/ count 2)))
+          (else (fib-iter
+                  (+ (* b q) (* a q) (* a p))
+                  (+ (* b p) (* a q))
+                  p
+                  q
+                  (- count 1)))))
+  (fib-iter 1 0 0 1 n))
+
+(display (fib 100))

chapter-1/1.2/1.22.scm

@@ -1,13 +1,16 @@
 (define (prime? n)
   (define (smallest-divisor n)
     (find-divisor n 2))
+
   (define (find-divisor n test)
     (cond
      ((> (* test test) n) n)
      ((divide? test n) test)
      (else (find-divisor n (+ 1 test)))))
+
   (define (divide? test n)
     (= (remainder n test) 0))
+
   (if (= (smallest-divisor n) n) true false))
 
 (define (search-for-primes n count)
@@ -19,7 +22,7 @@
               (display "***")
               (display (- (real-time-clock) begin-time))
               (newline)
-              (search-for-primes (+ n 1) (- count 1)))
+              (search-for-primes (+ n 2) (- count 1)))
             (search-for-primes (+ n 1) count)))))
 
 (search-for-primes 1e6 3)
@@ -33,3 +36,33 @@
 
 (search-for-primes 1e9 3)
 (newline)
+
+### 1.23
+
+{empty}::
++
+--
+
+link:chapter-1/1.2/1.23.scm[] is almost identical to 1.22.scm.
+
+----
+1000003.***1
+1000033.***1
+1000037.***1
+
+10000019.***3
+10000079.***3
+10000103.***3
+
+100000007.***10
+100000037.***8
+100000039.***8
+
+1000000007.***24
+1000000009.***25
+1000000021.***24
+----
+
+We can see that the process runs basically twice as fast as exercise 1.22, so the expectation is confirmed.
+
+--

chapter-1/1.2/1.23.scm

@@ -1,14 +1,18 @@
 (define (prime? n)
   (define (next n) (if (= n 2) 3 (+ n 2)))
+
   (define (smallest-divisor n)
     (find-divisor n 2))
+
   (define (find-divisor n test)
     (cond
      ((> (* test test) n) n)
      ((divide? test n) test)
      (else (find-divisor n (next test)))))
+
   (define (divide? test n)
     (= (remainder n test) 0))
+
   (if (= (smallest-divisor n) n) true false))
 
 (define (search-for-primes n count)

chapter-1/1.2/1.28.scm

@@ -1,9 +1,6 @@
-(define (even? n)
-  (= (remainder n 2) 0))
-
 (define (checked-square x m)
   (if (and
-        (= (remainder (* x x) m) 1)
+        (= (remainder (square x) m) 1)
         (not (or (= x 1) (= x (- m 1)))))
       0
       (square x)))
@@ -29,6 +26,10 @@
     ((miller-rabin-test n) (fast-prime? n (- times 1)))
     (else false)))
 
+; real prime
+(display (fast-prime? 7919 10))
+(newline)
+
 ; Carmichael numbers: 561, 1105, 1729, 2465, 2821, 6601
 (display (fast-prime? 561 10))
 (newline)

chapter-1/1.2/fast-expt.scm

@@ -0,0 +1,6 @@
+(define (fast-expt b n)
+  (cond ((= n 0) 1)
+        ((even? n) (square (fast-expt b (/ n 2))))
+        (else (* b (fast-expt b (- n 1))))))
+
+(display (fast-expt 2 20))

chapter-1/1.2/fast-prime.scm

@@ -26,4 +26,8 @@
         ((fermat-test n) (fast-prime? n (- times 1)))
         (else false)))
 
+; wrong result, 6601 is not a prime, but it can fool the Fermat test
+(display (fast-prime? 6601 10))
+(newline)
+
 (display (fast-prime? 9677 10))

chapter-1/1.2/prime.scm

@@ -9,3 +9,5 @@
 (define (divides? a b) (= (remainder b a) 0))
 
 (define (prime? n) (= n (smallest-divisor n)))
+
+(display (prime? 7919))

ruff.toml

@@ -0,0 +1 @@
+indent-width = 2