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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