Created 01/07/03

on Examples of Recursion

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1. Consider a definition of mystery(): 

mystery(0,N) = N
mystery(P,Q) = mystery(P-1, Q+1)

According to this definition, what is mystery(2,4)?

A.    0
B.    2
C.    4
D.    6

2. Look at mystery() again: 

mystery(0,N) = N
mystery(P,Q) = mystery(P-1, Q+1)

Which of the following Java methods correctly implements it?

A.    
int mystery( int P, int Q )
{
  if ( Q==0 )
  {
    return Q;
  }
  else
  {
    return mystery(P-1, Q-1);  
  }
}
B.    
int mystery( int P, int Q )
{
  if ( P==Q )
  {
    return Q;
  }
  else
  {
    return mystery(P-1, Q);  
  }
}
C.    
int mystery( int P, int Q )
{
  if ( P==0 && Q==0)
  {
    return 1;
  }
  else
  {
    return mystery(P-1, Q+1);  
  }
}
D.    
int mystery( int P, int Q )
{
  if ( P==0 )
  {
    return Q;
  }
  else
  {
    return mystery(P-1, Q+1);  
  }
}

3. Say that you have a recursive Java method, funct(). Is it always possible to write an iterative version of funct()?

A.    Yes.
B.    Usually, but not always.
C.    Almost never.
D.    No.

4. Say that you have an iterative Java method, foo(). Is it always possible to write a recursive version of foo()?

A.    Yes.
B.    Usually, but not always.
C.    Almost never.
D.    No.

5. Say that you have an recursive Java method, compute(). Is it always possible to write a method that implements compute() with a one line formula?

A.    Yes.
B.    Usually, but not always.
C.    Almost never.
D.    Never.

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