[Algorithm] 2. Trailing Zeros

Description

Write an algorithm which computes the number of trailing zeros in n factorial.

Example

11! = 39916800, so the out should be 2

Challenge

O(log N) time

Answer

     /*
      * @param n: A long integer
      * @return: An integer, denote the number of trailing zeros in n!
      */
     long long trailingZeros(long long n) {
         // write your code here, try to do it without arithmetic operators.
         if(n<){
             return ;
         }
         else{
             return n/ + trailingZeros(n/);
         }
     }

Tips

This solution is implemented by a recursive method, we can also use a loop method to solve this problem.

     /*
      * @param n: A long integer
      * @return: An integer, denote the number of trailing zeros in n!
      */
     long long trailingZeros(long long n) {
         // write your code here, try to do it without arithmetic operators.
         long long result = ;
         while ( n > )
         {
             result += n/;
             n /= ;
         }

         return result;
     }