Created 01/07/03

# on More Recursion

Instructions: For each question, choose the single best answer. Make your choice by clicking on its button. You can change your answers at any time. When the quiz is graded, the correct answers will appear in the box after each question.

1. Here is another recursive definition involving 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 involving 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? (Assume that all the usual methods are available.)

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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