5kyu_FactorialDecomposition.js

// 5kyu - Factorial Decomposition

// The aim of the kata is to decompose n! (factorial n) into its prime factors.

// Examples:

// n = 12; decomp(12) -> "2^10 * 3^5 * 5^2 * 7 * 11"
// since 12! is divisible by 2 ten times, by 3 five times, by 5 two times and 
// by 7 and 11 only once.

// n = 22; decomp(22) -> "2^19 * 3^9 * 5^4 * 7^3 * 11^2 * 13 * 17 * 19"

// n = 25; decomp(25) -> 2^22 * 3^10 * 5^6 * 7^3 * 11^2 * 13 * 17 * 19 * 23
// Prime numbers should be in increasing order. When the exponent of a prime 
// is 1 don't put the exponent.

// Notes

// the function is decomp(n) and should return the decomposition of n! into 
// its prime factors in increasing order of the primes, as a string.
// factorial can be a very big number (4000! has 12674 digits, n will go from 
// 	300 to 4000).
// In Fortran - as in any other language - the returned string is not permitted 
// to contain any redundant trailing whitespace: you can use dynamically 
// allocated character strings.

function decomp(n) {
  let arr = {}, ans = [];
  for(let i = 2 ;i <= n;i++){
    let idx = i;
    for(let x in arr)
      while(idx % x === 0){
        idx /= x;
        arr[x]++;
      }
    if(idx > 1 ) arr[idx] = 1;
  }
  for(let x in arr)
    (arr[x] === 1) ? ans.push(x) : ans.push( x + "^" + arr[x] );
  return ans.join(" * ");