Advanced Math/Algorithm

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Expert: - 11/15/2010


Question

Algorthm EXP 24 size
Please see the attached JPG file.

Thanks

Answer
// written in C++
#include <stdio.h>

int exp(int n)
{
 int i=0;  // counter

 while ((n % 2) == 0)  // the "n % 2" gives "mod(n,2)"
  {                    // that is, 1 if odd and 0 if even
   n = 1.0*n/2;   //  1.0 there to make n real, not an integer
   i++;
  }
  return (i);
 }


void main()
{
 printf ("%d", exp(24));
}

Now this procdure returned the number of times that two divides into the number.  For example, if we had passed n as 2, as in exp(2), we would have gotten 1.  Since mod(1,2) = 1, that is all it does and a 1 is returned.

If we passed 48 as n, n goes to 24 and i goes to 1;
n goes to 12 and i goes to 2,
n goes to 6 and i goes 3,
n goes to 3 and i goes to 4,
and that is when it ends.

From what is here, it can be seen that I passed it 24.

From math, I know that ln(n)/ln(2) is the same as log(base2)(n).
The integer portion of a number will be the power of 2 that is the highest and less than n.  This is the maximum number of times that 2 can divide, for if the number of times were any higher, the number would be at least one more power of 2.

Scott A Wilson

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