Arthur Barraux
159 lines
3.6 KiB
Scheme
159 lines
3.6 KiB
Scheme
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; A collection of SICP excercises
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; these are all my solutions from reading
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; the book
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; 1.01 - basic expressions
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(assert (= (+ (* 2 4) (- 4 6)) 6))
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(define a 3)
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(define b (+ a 1))
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(assert (= (+ a b (* a b)) 19))
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(assert (= (if (and (> b a) (< b (* a b)))
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b
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a) 4))
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(assert (= (cond ((= a 4) 6)
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((= b 4) (+ 6 7 a))
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(else 25)) 16))
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(assert (= (+ 2 (if (> b a) b a )) 6))
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(assert (= (* (cond ((> a b) a)
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((< a b) b)
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(else -1))
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(+ a 1)) 16))
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; 1.03 - largest squares
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(define (sqr x) (* x x))
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(define (largest-squares x y z)
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(cond ((and (< z x) (< z y)) (+ (sqr x) (sqr y)))
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((and (< y x) (> y z)) (+ (sqr x) (sqr z)))
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(else (+ (sqr y) (sqr z)))
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))
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(assert (= (largest-squares 3 4 5) (+ 25 16)))
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(assert (= (largest-squares 3 5 4) (+ 25 16)))
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; 1.14 change counter
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(define (count-change amount) (cc amount 5))
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(define (cc amount kinds-of-coins)
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(cond ((= amount 0) 1)
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((or (< amount 0) (= kinds-of-coins 0)) 0)
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(else (+ (cc amount
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(- kinds-of-coins 1))
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(cc (- amount
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(first-denomination kinds-of-coins))
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kinds-of-coins)))))
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(define (first-denomination kinds-of-coins)
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(cond ((= kinds-of-coins 1) 1)
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((= kinds-of-coins 2) 5)
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((= kinds-of-coins 3) 10)
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((= kinds-of-coins 4) 25)
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((= kinds-of-coins 5) 50)))
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(display "counting change: ")
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(display (count-change 75))
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(newline)
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; 1.16 - fast powers
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(define (exp-fast b n) (exp-iter b n 1))
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(define (exp-iter b n product)
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(cond ((= n 0) product)
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; b^n = (b^2) n/2
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((even? n) (exp-iter (* b b) (/ n 2) product))
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; b^n = b * b^n-1
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(else (exp-iter b (- n 1) (* product b)))))
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(assert (= (exp-fast 5 4) 625))
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(assert (= (exp-fast 2 8) 256))
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; 1.17 - fast multiply
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(define (double a) (+ a a))
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(define (halve a) (/ a 2))
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(define (fast-mul a b) (fast-mul-iter a b 0))
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(define (fast-mul-iter a b sum)
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(cond ((= b 0) sum)
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((even? b) (fast-mul-iter (double a) (halve b) sum))
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(else (fast-mul-iter a (- b 1) (+ sum a)))))
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(assert (= (fast-mul 3 4) 12))
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(assert (= (fast-mul 100 10) 1000))
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; 1.19 fibonacci
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(define (fib-helper n a b p q)
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(cond
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((= n 0) b)
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((even? n) (fib-helper (/ n 2)
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a
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b
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(+ (* p p) (* q q))
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(+ (* 2 q p) (* q q ))
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))
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(else
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(fib-helper
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(- n 1)
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(+ (* b q) (* a q) (* a p))
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(+ (* b p) (* a q))
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p
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q))))
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(define (fib n)
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(fib-helper n 1 0 0 1))
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(assert (= (fib 5) 5))
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(assert (= (fib 7) 13))
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(assert (= (fib 8) 21))
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; 2.21 - square list
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(define (square-list items)
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(if (null? items)
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items
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(cons (* (car items) (car items)) (square-list (cdr items)))))
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(define (square-list2 items)
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(map (lambda (x) (* x x)) items))
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(display (square-list (list 1 2 3 4)))
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(newline)
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(display (square-list2 (list 4 5 6 7)))
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; bank accounts
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(define (make-account val)
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(lambda (action)
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(if (eq? action 'deposit)
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(lambda (n) (set! val (+ val n)))
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(lambda (n) (set! val (- val n))))))
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(define justin (make-account 100))
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(define ryan (make-account 200))
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((justin 'deposit) 20)
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((ryan 'withdraw) 20)
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(gc-flip)
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(assert (= ((justin 'withdraw) 0) 120))
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(assert (= ((ryan 'deposity) 0) 180))
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; and or expansion
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(let ((a 1))
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(if (and (= a 0) (garbage here))
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(assert 0)
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'pass)
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(if (or (= a 1) (garbage here))
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'pass
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(assert 0)))
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