Most efficient way to write Combination and Permutation calculator in Javascript

Question

I have a math website http://finitehelp.com that teaches students Finite Math. I thought it would be cool to include a calculator so I made one for combinations and permutat

Answer 1

I would prefer recursive function, tail recursive may cause stackoverflow for functions like fibonacci.

Math._factorial = function(n){
  return Math._fact(n,1);
}

Math._fact= function(n,res){
  n = Number(n);
  if (n == null) {
    alert("Factorial requires a numeric argument.");
    return null;
  } else if (n < 2){
    return res;
  } else {
    return Math._fact(n-1, res*n);
  }
}

Answer 2

If you're concerned about efficiency, you'd probably want to re-implement the factorial as an iterative function rather than a recursive one. The recursive version will use a lot more memory and CPU time than the iterative version.

function factorial(n) { 
  var x=1; 
  var f=1;
  while (x<=n) {
    f*=x; x++;
  }
    return f;
}

You also shouldn't be adding your own functions to the Math namespace. It's not a good habit to get into.

Answer 3

Well, here we go!

First of all, why would you ever need to write this?

Math.divide = function(a,b)
{
    return a/b;
}

I would do away with it completely.

You can also clean up your Math.factorial a little bit:

Math.factorial = function(n)
{
    n = Number(n);

    if (isNAN(n)) {
        alert("Factorial requires a numeric argument.");
        return null;
    } else if (n < 2) {
        return 1;
    } else {
        return (n * Math.factorial(n - 1));
    }
}

But the main problem is your onclick() code:

onclick="var n = T1.value; var r = T2.value; var n_minus_r = parseFloat(n) - parseFloat(r); var numerator = Math.factorial(T1.value); var n_minus_r_fact = Math.factorial(n_minus_r); var r_fact = Math.factorial(r); var denominator = n_minus_r_fact * r_fact; T3.value = Math.divide(numerator,denominator); return true;

This is way too complicated. I'd make it a function and bind it to the element, which would get rid of all of the crap in your HTML and make it a bit easier to work with:

window.onload = function()
{
    document.getElementById('calculate').onclick = function() {
        var n = T1.value,
            r = T2.value;

        T3.value = Math.factorial(n) / (Math.factorial(r) * Math.factorial(n - r));
    }
}

And just get rid of the onclick= code.

Answer 4

As we know, combinations is short for:

So the fastest combinations implement is below:

function factorial(n) {
  let r = 1;
  while (n > 1) r *= n--;
  return r;
}
function combinations(n,r){
    let s = 1;
    let i = r;
    while(i<n) s*=++i;
    return s/factorial(n-r)
}
combinations(5,2)

Answer 5

Math.factorial= function(n){
    var i= n;
    while(--i) n*= i;
    return n;
}

Math.combinations= function(n, r, repeats){
    if(n< r) return 0;
    if(n=== r) return 1;
    if(repeats){
        return Math.factorial(n+r-1)/((Math.factorial(r)*Math.factorial(n-1)));
    }
    return Math.factorial(n)/((Math.factorial(r)*Math.factorial(n-r)));
}


var a= [
    'aqua', 'black', 'blue', 'fuchsia', 'gray', 'green', 'lime', 'maroon',
    'navy', 'olive', 'orange', 'purple', 'red', 'silver', 'teal', 'white',
    'yellow'
]
//how many 3 color combinations are there?
//[red,green,blue] is different than [green,red,blue]
// Math.combinations(a.length,3,true) >>969
// how many unique combinations (ignoring order) are there?
// Math.combinations(a.length,3)>>680