Improving performance for converting numbers to lists, and base10 to base2

Question

Many Project Euler problems require manipulating integers and their digits, both in base10 and base2. While I have no problem with converting integers in lists of digits, or

Answer 1

Are you running these timings in DrRacket by any chance? The IDE slows down things quite a bit, especially if you happen to have debugging and/or profiling turned on, so I'd recommend doing these tests from the command line.

Also, you can usually improve the brute-force approach. For example, you can say here that we only have to consider odd numbers, because even numbers are never a palindrome when expressed as binaries (a trailing 0, but the way you represent them there's never a heading 0). This divides the execution time by 2 regardless of the algorithm.

Your code runs on my laptop in 2.4 seconds. I wrote an alternative version using strings and build-in functions that runs in 0.53 seconds (including Racket startup; execution time in Racket is 0.23 seconds):

#!/usr/bin/racket
#lang racket

(define (is-palindrome? lon)
  (let ((lst (string->list lon)))
    (equal? lst (reverse lst))))

(define (sum-them max)
  (for/sum ((i (in-range 1 max 2))
             #:when (and (is-palindrome? (number->string i))
                         (is-palindrome? (number->string i 2))))
    i))

(time (sum-them 1000000))

yields

pu@pumbair: ~/Projects/L-Racket  time ./speed3.rkt
cpu time: 233 real time: 233 gc time: 32
872187

real    0m0.533s
user    0m0.472s
sys     0m0.060s

and I'm pretty sure that people with more experience in Racket profiling will come up with faster solutions.

So I could give you the following tips:

• Think about how you may improve the brute force approach
• Get to know your language better. Some constructs are faster than others for no apparent reason
  • see http://docs.racket-lang.org/guide/performance.html and http://jeapostrophe.github.io/2013-08-19-reverse-post.html
• use parallelism when applicable
• Get used to the Racket profiler

N.B. Your 10->bin function returns #f for the value 0, I guess it should return '(0).