export var isprime = function(num)
{
  if (num == 2 || num == 3)
    return true;
  if (num <= 1 || num % 2 == 0 || num % 3 == 0)
    return false;  
  for (let i = 5; i * i <= num ; i+=6) {
    if (num % i == 0 || num % (i + 2) == 0)
      return false;
  }
  return true;
}

export function isodd(n) { return n%2; }
export function iseven(n) { return !isodd(n); }

export var divisors = function(n)
{
  var d = [];
  var high = Math.sqrt(n);
  for (var i = 2; i < high; i++)
    if (n%i === 0)
      d = d.concat([i, n/i]);

  d.push(1);
  return d;
}

export function rotate_num(n)
{
  var dig = digits(n);
  return Math.trunc((n%10)*Math.pow(10,dig-1)+(n/10));
}

function arr_swap(A,i,j)
{
  var a = A[i];
  var b = A[j];
  A[i] = b;
  A[j] = a;
}


export function permutate_num(n)
{
  var perms = [];
function arr_gen(k, A)
{
  if (k === 1) {
    perms.push(A.slice());
    return;
  }

  arr_gen(k-1, A);
  
  for (var i = 0; i < k-1; i++) {
    if (k%2 === 0)
      arr_swap(A,i,k-1);
    else
      arr_swap(A,0,k-1);

    arr_gen(k-1,A);
  }
}

  var d = digitize(n);
  d = d.map(x=>String(x));
  arr_gen(d.length, d);
  perms = perms.map(function(p) {
    var n = "";
    for (var i = 0; i < p.length; i++)
      n += p[i];

    return Number(n);
  });
    
  return perms;
}

export function is_pandigital(n)
{
  var s = n;
  if (typeof s === 'number')
    s = String(s);
  var nums = s.split('').sort();
  return nums.every((x,i) => x == i+1);
}

export var digitize = function(n)
{
  var d = [];
  while (n) {
    d.push(n%10);
    n = Math.trunc(n/10);
  }
  return d.reverse();
}

export var digits = function(n) { return Math.floor(Math.log10(Math.abs(n)))+1; }

export var factorial = function(n)
{
  var s = 1;
  for (var i = n; i > 0; i--)
    s *= i;

  return s;
}

export var combination = function(n,k) { return factorial(n)/(factorial(k)*factorial(n-k)); }

export var permutation = function(n,k) { return factorial(n)/factorial(n-k); }

export function euler39(n) {
  if (n < 0 || n > 39) return undefined;
  return (n*n) + n + 41;
}

export function euler79(n) {
  if (n < 0 || n > 79) return undefined;
  return (n*n)-79*n+1601;
}