Problem 1 (25 points)
---------

Program a. (5 points)

What does the following program output ?

#include <iostream>

using namespace std;

int main()
{
  for(int i=0;i< 8;i ++)
     if(i%2 == 0) cout<< i+1 << "\t";
     else if(i %3 == 0) cout<< i*i << "\t";
     else if(i % 5 == 0) cout<<2*i - 1 << "\t";
     else cout<< i << "\t";
}


Program b. (5 points)
What does the following program ouput for input 6000

#include <iostream>

using namespace std;

int main()
{
   long bound;
   cin>> bound;

   long f = 1, i=1;
  
   do {
     f *= ++i;
     cout<<", "<<f;
   } while(f < bound)

}

Problem c. (2.5 points)

Is there anything wrong with the following piece of code ? If yes, what is it ?

if(x==0) 
  if(y==0) cout<<"x and y are both zero."<<endl;
  else cout<<" x is not zero "<<endl;


Problem d. (2.5 points)

What is the difference between the following two statements

Statement 1. if(n > 2) {if (n < 6) cout<< "OK" ; } else cout<< "NG";
Statement 2. if (n > 2) { if (n < 6) cout<< "OK" ; else cout<< "NG"; }


Problem e. (2.5 points)

What is wrong with the following program ?

int main()
{
   const double PI;
   int n;
   PI = 3.14159265358979;
   n = 22;
}

Problem f (2.5 points)

How is the following expression evaluated ? 

(x < y ? -1 : (x == y ? 0 : 1) );


Problem g. (5 points)

What is the output of the following program ?

int main()
{
  for(int i=0;i< 8;i ++)
   {
     if(i%2 == 0) cout<<i+1<<endl;
     else if(i%3 == 0) continue;
     else if(i%5 == 0) break;
     cout<< "End of program"<<endl;
   }

cout<<"End of program"<<endl;

}





Problem 2 (25 points)
---------------------
Write a program which reverses the digits of a given integer. For example, if the input to the program is 12345 the output should be 54321.
   
Program input and output


Please stick to this format. I will use a autograder to evaluate your programs. The autograder does understand anything (:() except the following format.


Sample input -- an integer
Sample output -- an integer which is the reverse of the input

For example,

12345 // sample input
54321 // sample output



Problem 3  (50 points)
----------------------

Implement the Euclidean Algorithm for finding the greatest common divisor of 
two given postive numbers. This algorithm transforms a pair of positive integers (m,n) into a pair (d,0) by repeatedly dividing the larger integer by the smaller number and replacing the smaller with the remainder and the larger number with the smaller number. When the remainder is 0, the other integer in the pair will be the greatest common divisor of the original pair (and of all the intermediate pairs). For example, if m is 532 and n is 112, then the Euclidean Algorithm reduces the pair (532,112) to (28,0) by 

       (532,112) --- (112,84) --- (84,28) ---- (28,0)

So, 28 is the greatest common divisor of 532 and 112. The result can be verified from the fact that 532 = 28*19 and 112=28*8. The reason that the Euclidean Algorithm works is that each pair in the sequence has the same set of divisors, which is precisely the factors of the greatest common divisor. In the example above, the common set of divisors is [1,2,4,7,14,28]. The reason that this set of divisors is invariant under the reduction process is that when m = n*q + r, a number is a common divisor of m and n if and only if it is common divisor of n and r.

Note : Since greatest common divisor can be calculated only for positive intergers, in case the input is a negative integer or 0 just print 0 as an output

Sample input and output format 
   Please stick to this format. I will use a autograder to evaluate your programs. The autograder does understand anything :( except the following format.


Sample input --- two integers 
Sample output --- greatest common divisor of the two integer
Your source file --- there should be only file called hw1_3.cpp.

For example,

532 112 // Sample input
28  // Sample output