CSCI 2610
Spring 2000
Practice questions for quiz 2

The actual quiz will probably be a little shorter than this. These questions are a sample of the kind of questions that you will be asked to answer.

  1. Which of the following is an invariant for the loop inside function one? (Hint: Look at the values that the variables n and m take on.)
    1. n > 0
    2. m = 14
    3. 2n+m = 14
    4. n = n - 1 
       int one()
   {
     int n,m;
     n = 4;
     m = 6;
     while(n > 0) {
       n = n - 1;
       m = m + 2;
     }
     return m;
   }

  2. Given the following definition of function f, what are the values of f(1), f(f(1)) and f(f(f(1)))? 
       int f(int x)
   {
     if(x < 2) {
       return x + 1;
     }
     else {
       return 2*x + 1;
     }
   }

  3. If function t is called, what is printed. Be very careful with this question. 
       void r(int a, int x, int &z)
   {
     cout << r: a = " << a << " x = " << x << " z = " << z << endl;
     a = 2;
     x = 5;
     z++;
   }

   void t()
   {
     int a, b, x, z;
     a = 9;
     b = 20;
     x = 67;
     z = 92;
     r(a,b,x);
     r(a,b,x);
     cout << "t: a = " << a << " b = " << b
          << " x = " << x << " z = " << z << endl;
   }

  4. What is the value of mystery(4)? 
       int mystery(int n)
   {
     if(n == 0) return 0;
     else return mystery(n-1) + n;
   }

  5. Write a recursive function sevens so that sevens(n) returns 1 if n has any sevens in its decimal representation, and returns 0 otherwise. For example, sevens(3701) = 1, sevens(777) = 1 and sevens(42) = 0. Assume that n is not negative.

    Note that you can get the rightmost digit of a number n by taking the remainder when you divide n by 10, and you can remove the rightmost digit by dividing n by 10.

    For this problem, do not use any form of loop, and do not alter the value of any variable that already has a meaningful value. 

       int sevens(long n)