6.090 IAP '05 - Lecture 3 Solutions

Problem 1

(define abs
  (lambda (x)
    (if (< x 0)
        (- x)
        x)))

Problem 2:

(define sum-to-n
  (lambda (n)
    (if (= n 1)
        1
        (+ n (sum-to-n (- n 1))))))

(define sum-of-n-squared
  (lambda (n)
    (if (= n 1)
        1
        (+ (* n n) (sum-of-n-squared (- n 1))))))

Problem 3:

(define find-e
  (lambda (n)
    (if (= n 0)
        1
        (+ (/ 1 (fact n))
           (find-e (- n 1))))))

Problem 4:

(define loop
  (lambda ()
    (loop)))

Problem 5:

(define pad
  (lambda (s n)
    (if (= n 0)
	s
	(string-append (pad s (- n 1)) " "))))
or
(define pad
  (lambda (s n)
    (if (= n 0)
	s
	(pad (string-append s " ") (- n 1)))))

Problem 6:

(define gcd
  (lambda (a b)
    (if (= b 0)
        a
        (gcd b (remainder a b)))))

Hanoi

(define hanoi
  (lambda (n to from scratch)
    (if (= n 1)
        (move n to from)
        (begin
         (hanoi (- n 1) from scratch to)
         (move n to from)
         (hanoi (- n 1) scratch to from)))))

Problem 7:

See lecture 4 solutions.

Guessing Game

(define guess-a-number
  (lambda ()
    (play-loop (random-number 1 100))))

(define play-loop
  (lambda (number)
    (let ((guess (get-player-guess)))
      (if (= guess number)
	  (show-msg "You win!")
	  (if (< guess number)
	      (begin
		(show-msg "Too low!")
		(play-loop number))
	      (begin
		(show-msg "Too high!")
		(play-loop number)))))))