codewars #21 Number of trailing zeros of N! (5kyu)

 #21  Number of trailing zeros of N! 

Write a program that will calculate the number of trailing zeros in a factorial of a given number.

N! = 1 * 2 * 3 * ... * N

Be careful 1000! has 2568 digits...

For more info, see: http://mathworld.wolfram.com/Factorial.html

Examples

zeros(6) = 1

# 6! = 1 * 2 * 3 * 4 * 5 * 6 = 720 --> 1 trailing zero

zeros(12) = 2

# 12! = 479001600 --> 2 trailing zeros

Hint: You're not meant to calculate the factorial. Find another way to find the number of zeros.

팩토리얼을 구하고 0의 갯수를 세면... 타임 초과가 난다 이틀 연속 타임 초과

	  public static int zeros(int n) {
		    if(n==0) return 0;
			BigInteger ten = new BigInteger("10");
			BigInteger fact = Stream.iterate(BigInteger.ONE, x->x.add(BigInteger.ONE)).limit(n).reduce(BigInteger::multiply).get();
				
			int trail = 0; 
			while(fact.divideAndRemainder(ten)[1] == BigInteger.ZERO) {
				fact = fact.divide(ten);
				trail++;
			}
		    return trail;
    }

시간 고려해서 한 풀이

	 public static int zeros(int n) {
		 
	     int trail = 0; 
		 int i = 1;
		 double temp = 0d;
		 
		 do {
			 temp = n / Math.pow(5, i++);
			 trail += Math.floor(temp);
		 }while(temp  > 0);
			 
		return trail;
	}