L-16 MCS 260 Wed 26 Sep 2001

Exam I on Chapters 1 to 4

1. Consider the following statements :

          int n = 9535;
          int s = 0;
          while (n > 0)
          {
             s += n % 10;
             n /= 10;
          }
   

   Replace the while with an equivalent do loop :

                                                           +--------+
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                                                           +--------+
   

2. Consider the following program :

          #include <stdio.h>
          int main(void)
          {
             int d,l,n = 4395;
             for (l = 0, d = n; d > 0; l++, d /= 10);
             printf("%d\n",l);
             return 0;
          }
   

   1. Rewrite the program into an equivalent one using while instead of a for loop :

   2. In this part we investigate what this program prints. Complete the table below with values for l and d for each step.

            -------------------------
            | step |    d   |   l   |
            =========================
            |   0  |  4395  |   0   |
            |      |        |       |
            |      |        |       |
            |      |        |       |
            |      |        |       |
            |      |        |       |
            |      |        |       |
            -------------------------
      

      So, what does the program finally print?

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                                                           +--------+
   

3. An integer number is prime if it is divisible only by 1 and itself. Consider the prototype of the function is_prime :

        int is_prime ( int n );
        /* returns 1 if n is prime, 0 otherwise */
   

   Write the definition of is_prime below :

        int is_prime ( int n )
   
   
                                                           +--------+
                                                           |    /15 |
                                                           +--------+
   

4. Consider a hat function defined by

       hat(x) = 0    if   x < 1    or  x < -1  
                1+x  if   x >= -1 and  x < 0 
                1-x  if   x >= 0  and  x < 1 
   

   The function hat takes a float x as input and returns hat(x) as defined above.

   Give the definition of hat in C :

                                                           +--------+
                                                           |    /15 |
                                                           +--------+
   

5. Write a program to sum the values of coins.

   The coins are represented by a sequence of characters, like pnqdpqnnppdqddpp.

   Each character stands for a coin:

         -------------------------------
         | character | meaning | value |
         ===============================
         |     p     | penny   | $0.01 |
         |     n     | nickel  | $0.05 |
         |     d     | dime    | $0.10 |
         |     q     | quarter | $0.25 |
         -------------------------------
   

   If the example input pnqdpqnnppdqddpp is put in the file /tmp/input and the program has the name coins, then the program runs like

            [jan@galois]% ./coins < /tmp/input
            value of coins : $1.36
            [jan@galois]% 
   

   Observe that the output value is printed with two digits after the decimal point.

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                                                           |    /30 |
                                                           +--------+