(define (sqrt x)
  (define (average x y) (/ (+ x y) 2))
  (define (square x) (* x x))
  (define (good-enough? guess)
    (< (abs (- (square guess) x)) 0.00001))
  (define (improve guess)
    (average guess (/ x guess)))
  (define (sqrt-iter guess)
    (if (good-enough? guess)
        guess
        (sqrt-iter (improve guess))))
  (sqrt-iter 1.0))

;(define (factorial n)
;  (if (= n 1) 1 (* n (factorial (- n 1)))))

(define (factorial n)
  (define (fact-iter product counter max-count)
    (if (> counter max-count)
        product
        (fact-iter (* counter product)
                   (+ counter 1)
                   max-count)))

  (fact-iter 1 1 n))


(define (A x y)
  (cond ((= y 0) 0)
        ((= x 0) (* 2 y))
        ((= y 1) 2)
        (else (A (- x 1)
                 (A x (- y 1))))))

;(define (fib n)
;  (cond ((= n 0) 0)
;        ((= n 1) 1)
;        (else (+ (fib(- n 1))
;                 (fib(- n 2))))))

(define (fib n)
  (define (fib-iter a b count)
    (if (= count 0)
        b
        (fib-iter (+ a b) a (- count 1))))
  
  (fib-iter 1 0 n))


(define (count-change amount)
  (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 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)))))
  
  (cc amount 5))


(define (ptri n)
  (if (< n 3) n
      (+
       (ptri (- n 1))
       (+ (* (ptri (- n 2)) 2)
          (* (ptri (- n 3)) 3)))))