Changing a function from iterative to recursive?

Question

projectEuler3(600851475143);

var projectEuler3 = function (composite) {
    var result = 2;
    while(composite > 1)
    {
        if (composite % result)
        {
            result++
        } else {
            composite = composite / result;
            console.log(result);
        }
    }
};

it's not homework... i'am trying to make my brain think recursively and this is helpful. — shawndumas, Feb 10 '09 at 19:52
As an aside, a great way to get your brain around recursion is traversing a binary tree. It's one of those cases were recursion is usually the best, and most elegant, solution. — Beska, Feb 10 '09 at 20:40

Beska · Answer 1 · 2009-02-10T20:34:09.093

2

EDIT: Turns out this question is designed to be a how to change an algorithm (in general) from iterative to recursive...not, as I assumed, how to get an answer to a particular problem.

This is for Project Euler! Project Euler is purely for your own benefit...if you're going to have someone else do the work for you, you could probably just look up the answer on google somewhere and type it in.

I can only guess you've decided that your program is correct, but that it is too slow, and you're hoping to speed it up. Making your function recursive won't help.

The site points out that if your program doesn't solve the question quickly, there's a better approach...try a different tact.

edited Feb 10 '09 at 20:34

answered Feb 09 '09 at 20:45

Beska

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Recursion is *definitely* not the first place to look to in speeding up code... Lol - +1 – Erik Forbes Feb 09 '09 at 23:21
yes it's from project euler. that's why i tagged it as such. but no, i am not trying to speed it up. run it, it's very fast. i want to make my brain think recursively and this is helpful to that end. – shawndumas Feb 10 '09 at 19:54
@ShawnDumas...okay, that makes sense! (I'm glad I didn't jump on the bandwagon to ding the question!) Next time, give a bit more information to hopefully keep the dings away. Check out Ben Blank's response...he's got a generic template you might be able to apply. – Beska Feb 10 '09 at 20:31
it was definitely a case of me not being clear! – shawndumas Feb 11 '09 at 12:02

score 2 · Answer 2 · answered Feb 09 '09 at 20:51

2

Hopefully in the spirit both of Project Euler (learn-by-doing) and SO (learn-by-asking), here's a fairly generic template for making a loop into tail-call recursion:

var projectEuler3 = function(n) {
    var pE3_inner = function(n, i) {
        // magic happens here

        // if neither n nor i has changed, this is an
        // infinite recursion (and usually a stack overflow)
        pE3_inner(n, i);
    }

    pE3_inner(n, 2);
}

answered Feb 09 '09 at 20:51

Ben Blank

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var pe3 = function (o) { o = o || { composite: 600851475143, result: 2 }; if (o.composite < 1) return o.result; (o.composite % o.result) ? o.result++ : o.composite = o.composite / o.result; return pe3(o); }; pe3(); this is getting me an InternalError: too much recursion... – shawndumas Feb 10 '09 at 20:17
Yep! That's one of the big drawbacks to recursion...it can generate a lot of stack. Still, that shouldn't matter in your case. Just pick a smaller number that will work, so that you can verify your code is doing what you expect. – Beska Feb 10 '09 at 20:36
Try changing your "< 1" to "< 2". At some point, o.composite and o.result will be the same and o.composite will be changed to 1. It will never be divided again, however, so it will never drop below one (barring rounding errors) and your function will overflow the stack. – Ben Blank Feb 10 '09 at 21:29
i think the object sucks so i used a closure: var pe3 = function (composite) { var result = 2; return (function () { if (composite <= 1) return result; (composite % result) ? result++ : composite = composite / result; return arguments.callee(result); })(); }; – shawndumas Feb 11 '09 at 13:01
...that works up till 9999995. any bigger and it blows... – shawndumas Feb 11 '09 at 13:02

score 2 · Answer 3 · answered Feb 25 '09 at 22:15

Structure and Interpretation of Computer Programs introduces the difference between iterative and recursive algorithms, how to identify which is which (in some languages it's not so obvious!), and how to convert from one to the other.

In addition to being an excellent textbook.

Changing a function from iterative to recursive?

3 Answers3