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2013-08-19: SIQ: Reversing Strings

The source for this post is online at 2013-08-19-reverse.rkt.

A common interview question is reversing the characters in a string. In this post, I present three ways to do this and measure the performance of the various approaches in Racket, as well as show how to verify the correctness of the algorithms.


First, let’s look at the simplest and most obviously correct way to do it: turn the string into a list and then reverse the list, and go back to a string:

<slow> ::=
(define (reverse-string/slow s)
  (list->string (reverse (string->list s))))

This version is likely to be slow because, for a n character string, it processes (* 3 n) characters, allocates one n string, and (* 2 n) cons cells.

A faster method would just process each character once and only allocate the new string once. We could do that by directly computing the characters to "swap".

(define (reverse-string s)
  (define len (string-length s))
  (build-string len (λ (i) (string-ref s (- len i 1)))))

You may think this version traverses the string a second time to compute the length, but in Racket this value is built-in to the string, so it is immediately available.

We might be able to go a lot faster if we did the reversal "in-place" by just swapping the characters. Since we’re just reversing the string, we could go from the outside to inside and swap the characters.

(define (reverse-string/really-fast s)
  (define len (string-length s))
  (for ([c (in-string s)]
        [i (in-range (quotient len 2))])
    (define ni (- len i 1))
    (define nc (string-ref s ni))
    (string-set! s ni c)
    (string-set! s i nc))

The only unfortunate part of this implementation is that it permanently mutates the string. If we made a copy of the string first, which is a faster operation than copying the characters one-by-one, we could probably beat the performance of the medium version but preserve its semantics.

<fast> ::=
(define (reverse-string/fast s)
  (reverse-string/really-fast (string-copy s)))

If we test these implementations on 40,000 random strings of length 1000, then the performance is pretty clear:

I am most interested in the speed of the "fast" version, because it is a drop-in replacement for the "slow" and "medium" versions, but almost three times faster.

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But first let’s remember what we learned today!

You can do performance engineering in Racket, just like you can in C.

Validating optimizations and performance is much simpler with Racket.

If you’d like to run this exact code at home, you should put it in this order:

<*> ::=
(require rackunit
(define (random-char)
  (if (zero? (random 5))
    (integer->char (+ (char->integer #\A) (random 26)))))
(define (random-string N)
  (list->string (build-list N (λ (i) (random-char)))))
(define N 100)
(define ss (build-list N (λ (i) (random-string 100))))
  (time-exp exp)
  (let-values ([(as cpu real gc) (time-apply (λ () exp) empty)])
    (collect-garbage) (collect-garbage) (collect-garbage)
    (values (first as)
  (slows st)
   (for/list ([s (in-list ss)])
     (reverse-string/slow s))))
  (mediums mt)
   (for/list ([s (in-list ss)])
     (reverse-string s))))
  (fasts ft)
   (for/list ([s (in-list ss)])
     (reverse-string/fast s))))
  (reallys rt)
   (for/list ([s (in-list ss)])
     (reverse-string/really-fast s))))
(for ([s (in-list slows)]
      [l (in-list slows)]
      [m (in-list mediums)]
      [f (in-list fasts)]
      [r (in-list reallys)])
  (check-equal? m l)
  (check-equal? f l)
  (check-equal? r l))
(printf "~a\n" (list st mt ft rt))