Comleted 2.20

2_17.sch

@@ -0,0 +1,5 @@
+(define (last-pair l)
+  (if (null? (cdr l))
+      (list (car l))
+      (last-pair (cdr l))))
+

2_18.sch

@@ -0,0 +1,6 @@
+(define (reverse l)
+  (define (reverse-acc l acc)
+    (if (null? l)
+      acc
+      (reverse-acc (cdr l) (cons (car l) acc))))
+  (reverse-acc l '()))

2_19.sch

@@ -0,0 +1,45 @@
+;; Counting change
+
+(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)))
+
+;; EXERCISE 2.19
+;; The order of the coin values doesn't matter because we recurse
+;; over all coins.
+(define us-coins (list 50 25 10 5 1))
+
+(define uk-coins (list 100 50 20 10 5 2 1 0.5))
+
+;: (cc 100 us-coins)
+
+(define (cc amount coin-values)
+  (cond ((= amount 0) 1)
+        ((or (< amount 0) (no-more? coin-values)) 0)
+        (else
+         (+ (cc amount
+                (except-first-denomination coin-values))
+            (cc (- amount
+                   (first-denomination coin-values))
+                coin-values)))))
+
+(define (first-denomination coins) (car coins))
+
+(define (except-first-denomination coins) (cdr coins))
+
+(define (no-more? coins) (null? coins))

2_20.sch

@@ -0,0 +1,8 @@
+(define (same-parity x . xs)
+  (define (take-if-par l par)
+    (cond ((null? l) '())
+	  ((= (remainder (car l) 2) par) 
+	   (cons (car l) (take-if-par (cdr l) par)))
+	  (else
+	   (take-if-par (cdr l) par))))
+  (cons x (take-if-par xs (remainder x 2))))

2_7.sch

@@ -0,0 +1,64 @@
+(define (add-interval x y)
+  (make-interval (+ (lower-bound x) (lower-bound y))
+                 (+ (upper-bound x) (upper-bound y))))
+
+(define (mul-interval x y)
+  (let ((p1 (* (lower-bound x) (lower-bound y)))
+        (p2 (* (lower-bound x) (upper-bound y)))
+        (p3 (* (upper-bound x) (lower-bound y)))
+        (p4 (* (upper-bound x) (upper-bound y))))
+    (make-interval (min p1 p2 p3 p4)
+                   (max p1 p2 p3 p4))))
+
+;;(define (mul-interval x y)
+  ;;(cond ((and (> (lower-bound x) 0)
+	      ;;(> (lower-bound y) 0))
+	 ;;(make-interval 
+	  ;;(* (lower-bound x))))))
+
+(define (div-interval x y)
+  (if (not (= (upper-bound y) (lower-bound y)))
+    (mul-interval x 
+		  (make-interval (/ 1.0 (upper-bound y))
+				 (/ 1.0 (lower-bound y))))
+    (begin
+      (error "Error: second interval spans 0")
+      (newline))))
+
+(define (make-interval a b) (cons a b))
+
+(define (lower-bound x) (car x))
+(define (upper-bound x) (cdr x))
+
+(define (sub-interval x y)
+  (make-interval (- (lower-bound x) (upper-bound y))
+		 (- (upper-bound x) (lower-bound y))))
+
+;; 2.12
+(define (make-centre-percent c p)
+  (make-interval (- c (/ (* c p) 100))
+		 (+ c (/ (* c p) 100))))
+
+(define (center i)
+  (/ (+ (lower-bound i) (upper-bound i)) 2))
+
+(define (width i)
+  (/ (- (upper-bound i) (lower-bound i)) 2))
+
+(define (percent i)
+  (* (/ (width i) (center i)) 100))
+
+
+;; 2.14
+;; parallel resistors
+
+(define (par1 r1 r2)
+  (div-interval (mul-interval r1 r2)
+                (add-interval r1 r2)))
+
+(define (par2 r1 r2)
+  (let ((one (make-interval 1 1))) 
+    (div-interval one
+                  (add-interval (div-interval one r1)
+				(div-interval one r2)))))
+