Question

This code is supposed to simplify fractions and convert decimals to fractions but when I put in fractions with larger dividens (numbers more than 7 or 8 digits) it lags a great amount.

http://jsfiddle.net/SuperBoi45/vQjgx/

var fraction = {};

fraction.simplify = function( frac ) {
    if ( frac.indexOf('/') < 0 ) return frac;
    var numbers = frac.split('/'),
        factor = null,
        parsed = null;

    return (function run( nums ) {
        factor = fraction.factor( nums[0], nums[1] );

        if ( factor === 1 ) {
            parsed = [ Math.abs(nums[0]), Math.abs(nums[1]) ];

            if ( nums[1] === 1 ) return nums[0];
            else if ( nums[1] === -1 ) return -nums[0];
            else if ( nums[0] < 0 && nums[1] < 1 ) return parsed[0] + '/' + parsed[1];
            else if ( nums[0] < 0 || nums[1] < 0 ) return '-' + parsed[0] + '/' + parsed[1];
            else return nums[0] + '/' + nums[1];
        }

        return run( [ nums[0] / factor, nums[1] / factor ] );
    })( numbers );
};
fraction.convert = function( decimal ) {
    var j = decimal.length - 1,
        b = "1";

    if ( decimal.indexOf(".") >= 0 && decimal.length > 1 ) {

        while ( decimal.charAt( j ) != "." ) {
            b += "0";
            j--;
        }

        decimal *= b;
        decimal += "/" + b;

    }

    return decimal;

};
fraction.factor = (function() {

    var greater = function( a, b ) {
        return a > b ? a : b;
    };

    return function( x, y ) {
        x = Math.abs( x );
        y = Math.abs( y );

        var a = greater( x, y ),
            i = a,
            b = ( i === x ) ? y : x;

        for ( ; i >= 1; i-- ) {
            if ( a % i === 0 && b % i === 0 ) return i;
        }

        return 1;
    };

})();​

I’m trying to make it work like Wolfram Alpha because you can put in fractions with large dividens and it doesn’t freeze one bit when showing you its quick-rendered result.

http://wolframalpha.com/

Can anyone fix this code to work with larger numbers. I’d figure you’d have to use a different algorithm than mine. On the other hand, does anyone know WA’s algorithm or can direct me to a site where I can find out?

Answer 1

Replace fraction.factor() with this:

function gcd(a, b) {
    if (b > a) return gcd(b, a);
    if (b === 0) return a;
    return gcd(b, a % b);
};

That’s Euclid’s algorithm, which can serve as a great introduction to Number Theory. It’ll run way faster than your iterative approach.