#lang racket
(define (fast-exp x n)
  (cond [(= n 0) 1]
        [(= n 1) x]
        [(even? n) (fast-exp (* x x) (/ n 2))]
        [else (* x (fast-exp (* x x) (quotient n 2)))]))

(define (fast-exp2 x n)
  (define (sqr x) (* x x))
  (define half (quotient n 2))
  (cond [(= n 0) 1]
        [(= n 1) x]
        [(even? n) (fast-exp2 (sqr x) half)]
        [else (* x (fast-exp2 (sqr x) half))]))

(define (roots a b c)
  (define discriminant (- (fast-exp b 2) (* 4 (* a c))))
  (cond [(and (= a 0) (= b 0))
         (if (= c 0) +inf.0 0)]
        [(= discriminant 0) 1]
        [(< discriminant 0) 0]
        [(> discriminant 0) 2]))

(define (fact n)
  (define (loop i res)
    (if (> i n)
        res
        (loop (+ i 1) (* res i))))
  (loop 1 1))

(define (fib n)
  (define (loop i prev curr)
    (if (= i n)
        curr
        (loop (+ i 1) curr (+ prev curr))))
  (if (= n 0) 0
    (loop 1 0 1)))

(define (reverse-int n)
  (define (loop temp newN)
    (if (= newN 0)
        temp
        (loop (+ (* temp 10) (remainder newN 10)) (quotient newN 10))))
    (loop 0 n))