CSE 130   Spring 2010

                                 Lab 9


 DO NOT SUBMIT THIS. THIS IS FOR YOUR PRACTICE ONLY.

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 1. Recursive function mystery

 a.   Look at the lab9 document using your browser and  try  to  under-
      stand  how  recursive  function mystery works.  TA will write the
      recursive function mystery on the board and explain what it does.

 b.   Function mystery returns 1 if b = 0. Otherwise  it  calls  itself
      recursively, and returns the product a*mystery(a , b-1). The next
      call would calculate mystery(a, b-2), and  return  a*a*mystery(a,
      b-2).

 c.   When the second parameter becomes zero, mystery would  return  1.
      But  it  has  already  accumulated the product a*a*a.... b times.
      This product is a^b or a raised to b.

 2. Program for lab9.c

 d.   Copy lab9.c from this page. Cut and paste it in your pico window.
      Save it as lab9.c.

// lab9.c
// CSE 130 Spring 2010. Lab 9, April 7, 2010.
// Sample program for studying recursive functions

   #include <stdio.h>
   int mystery (int a, int b)
     {
       if (b == 0) return 1;
           else return (a*mystery (a, b-1));
     }


   int main (void)
     {
       int i, m, n;
       printf("Type in m > 0, and n >= 0\n");
       scanf("%d%d", &m, &n);
       printf("\nm is %d and n is %d\n", m, n);

       i = mystery(m, n);  // Call to function mystery
       printf ("Function mystery returns %d\n", i);

       return 0;
     }

 e.   Save and compile lab9.c. Execute with m = 4 and n = 3.  It should
      print 64. Function mystery computes m raised to power n. (m^n).

 3. Remove recursion

 f.   Remove recursion from the function mystery and rewrite it using a
      loop.  Here a for loop will be useful. But keep the function.

 g.   Declare and initialize product to 1 before the for-loop.

 h.   The header for the for loop: for ( ; b > 0; b--)

 i.   Inside the loop, accumulate product = product*a;

 j.   At the end return product.

 k.   Save your program lab9.c. Compile and execute.  Try m = 4, and  n
      = 3. You should get 64 as answer.

 4. Another example

 l.   Suppose now we want to calculate the product m*n using  a  recur-
      sive function int mystery(int a, int b).

 m.   Here we can calculate product  a*b  =  a+a+a+....  b  times.   We
      assume that both a, b can be zero (0).

 n.   What is the product when b is 0, or a = 0?  If b is not zero  AND
      a  is not zero, then what is the expression for product that uses
      recursion ?

 o.   Remove the for-loop from function mystery. Delete variables  that
      you  do  not need. Write recursive function mystery using a and b
      only, for calculating product  a*b.  This  would  be  an  if-else
      statement.

 p.   Save your program as lab9.c. Compile and execute.  Try m = 4  and
      n = 3. You get 12 as an answer from main program. Try m = 0 and n
      = 0 to see if you get 0 as an answer.

 5. Modification-I

 q.   Rewrite the if-else statement of function mystery  such  that  it
      uses not-equal-to (!=) check instead of equal-to (==) check.

 r.   Save your program, compile and execute.  Again  check  with  dif-
      ferent values of m and n. Let at least one of them be zero.

 6. Modification-II (nested function calls)

 s.   Remove i = mystery(m, n); statement from main (  ).   Change  the
      printf statement that now prints mystery(m, n) instead of i.

 t.   Save your program, compile and run for m = 4  and  n  =  3.   You
      should  get  the  same  answer.  What we have is a case of nested
      function calls. Main calls printf, and printf calls mystery.