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 :

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

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

   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   |
            |   1  |   439  |   1   |
            |   2  |    43  |   2   |
            |   3  |     4  |   3   |
            |   4  |     0  |   4   |
            -------------------------
      

      So, what does the program finally print? 4

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

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 )
        {
           int i;
    
           for (i = 2; i < n; i++)
              if (n % i == 0) return 0;
   
           return 1;
        }
   
                                                           +--------+
                                                           |    /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 :

   
      float hat ( float x)
      {
         if (x < -1)
            return 0;
         else if (x < 0)
            return 1+x;
         else if (x < 1)
            return 1-x;
         else
            return 0;
      }
            
                                                           +--------+
                                                           |    /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.

   /* MCS 260 exam 1 question : counting coins
      Takes a sequence of characters on input, like pndqdnp
         p = penny   $0.01;
         n = nickel  $0.05;
         d = dime    $0.10; 
         q = quarter $0.25.
      Prints the value of the sum of the coins.   */
   
   #include<stdio.h>
   
   int main(void)
   {
      float sum = 0.0;
      char coin;
   
      while (scanf("%c", &coin) > 0)
         switch(coin)
         {
            case 'p': sum += 0.01; break;
            case 'n': sum += 0.05; break;
            case 'd': sum += 0.10; break;
            case 'q': sum += 0.25; break;
         }
   
      printf("value of coins : $%.2f\n", sum);
   
      return 0;
   }
                                                           +--------+
                                                           |    /30 |
                                                           +--------+