moduli-number.js

/*
A number system with moduli is defined by a vector of k moduli, [m1,m2, ···,mk].
The moduli must be pairwise co-prime, which means that, for any pair of moduli, the only common factor is 1.

In such a system each number n is represented by a string "-x1--x2-- ... --xk-" of its residues, one for each modulus. The product m1 ... mk must be greater than the given number n which is to be converted in the moduli number system.

For example, if we use the system [2, 3, 5] the number n = 11 is represented by "-1--2--1-",
the number n = 23 by "-1--2--3-". If we use the system [8, 7, 5, 3] the number n = 187 becomes "-3--5--2--1-".

You will be given a number n (n >= 0) and a system S = [m1,m2, ···,mk] and you will return a string "-x1--x2-- ...--xk-" representing the number n in the system S.

If the moduli are not pairwise co-prime or if the product m1 ... mk is not greater than n, return "Not applicable".

Examples:

fromNb2Str(11 [2,3,5]) -> "-1--2--1-"
fromNb2Str(6, [2, 3, 4]) -> "Not applicable", since 2 and 4 are not coprime
fromNb2Str(7, [2, 3]) -> "Not applicable" since 2 * 3 < 7
*/

function fromNb2Str(n,sys) {
  if (sys.reduce(function(p,c) { return p * c; }) < n) return 'Not applicable';

  var min = Math.min.apply(null, sys);
  for(var i = 2, k; i <= min; i++) {
    k = 0;
    for(var j = 0; j < sys.length; j++) {
      if (sys[j] % i === 0) {
        k++;
      } 
    }  
    if (k > 1) return 'Not applicable';
  }

  return '-' + sys.map(function(i) { return n % i; }).join('--') + '-';
}

fromNb2Str(187, [8, 7, 5, 3]);

// -3--5--2--1-

/*
Can be optimized by using 

function gcd(a, b) {
  if(!b) return a;
  return gcd(b, a % b);
}
*/