Created 01/07/03

on More Recursion

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1. Here is another definition for integers N and M. Assume 0<=N and 0<M. 

mod( N, M ) = N, if N < M
mod( N, M ) = mod( N-M, M ), if N >= M

What is the value of mod(2, 5)?

A.    2
B.    5
C.    7
D.    17

2. What is the value of mod(17, 5)?

A.    2
B.    5
C.    7
D.    17

3. Here (again) is the definition of mod() for integers N and M. Assume 0<=N and 0<M. 

mod( N, M ) = N, if N < M
mod( N, M ) = mod( N-M, M ), if N >= M

Which of the following methods correctly implements it?

A.    
int mod( int N, int M )
{
  if ( N > M )
    return M;
  else
    return mod( M-N, M );
}
B.    
int mod( int N, int M )
{
  if ( M < N )
    return 1;
  else
    return mod( N-M, M );
}
C.    
int mod( int N, int M )
{
  if ( N < M )
    return N;
  else
    return mod( N-M, M );
}
D.    
int mod( int N, int M )
{
  if ( N < M )
    return N;
  if ( N > M )
    return mod( N-M, M );
}

4. Here is another crazy definition, for integers N and M. Assume 0<=N and 0<M. 

div( N, M ) = 0, if N < M
div( N, M ) = 1 + div( N-M, M ), if N >= M

What is div( 7, 5 ) ?

A.    0
B.    1
C.    2
D.    5

5. What is div( 17, 5 ) ?

A.    1
B.    2
C.    3
D.    4

6. Here is our definition, again, for integers N and M. Assume 0<=N and 0<M. 

div( N, M ) = 0, if N < M
div( N, M ) = 1 + div( N-M, M ), if N >= M

Which one of the following correctly implements it ?

A.    
int div( int N, int M )
{
  if ( N < M )
    return N;
  else
    return div( N-M, M );
}
B.    
int div( int N, int M )
{
  if ( N < M )
    return 0;
  else
    return 1+div( N-M, M );
}
C.    
int div( int N, int M )
{
  if ( N == M )
    return N;
  else
    return div( N-M, M );
}
D.    
int div( int N, int M )
{
  if ( N < M )
    return 0;
  else
    return 1+div( N-M, N );
}

7. Which of the following correctly tests if str is the empty string?

A.    str == ""
B.    str == 0
C.    str.length = 0
D.    str.length() == 0

8. Which of the following evaluates to the first character of str?

A.    str[0]
B.    str[1]
C.    str.substring(0)
D.    str.charAt(0)

9. Here is another definition. Assume that x is a variable that represents a single character and that X represents a string. The operator "+" means concatenation. 

rev( "" ) = ""
rev( x+X ) = rev(X) + x

What is rev( "fooey" )?

A.    "ooeyf"
B.    "ooey"
C.    "Fooey"
D.    "yeoof"

10. Here is the definition. 

rev( "" ) = ""
rev( x+X ) = rev(X) + x

Which of the following correctly implements it?

A.    
String  rev( String str )
{
  if ( str == ""  )
    return str;
  else
    return rev( str.substring(1) ) + str.charAt(0);
}
B.    
String  rev( String str )
{
  if ( str.length() == 0 )
    return str;
  else
    return rev( str.substring(1) ) + str.charAt(0);
}
C.    
String  rev( String str )
{
  if ( str.length() == 0 )
    return str;
  else
    return rev( str.substring(0) ) + str.charAt(0);
}
D.    
String  rev( String str )
{
  if ( str.length() == 0 )
    return str;
  else
    return rev( str.substring(0) ) + str.charAt(1);
}

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