Data Structures CS 315 Spring 2017

Transcription

1 Data Structures CS 315 Spring 2017 First Exam Given on Monday, 6 March 2017 There are five problems on this exam spread over six pages. The last page contains the definition of class Token as it appeared in your first programming project. Please do not hesitate to ask for help if you are not sure what you have been asked to do. Problem 1; (10 points) Determine the running of the following operations: 1. Sequential search in an un-ordered array with n elements. 2. Binary search in an ordered array with n elements. 3. Delete from an un-ordered array with n elements. The element needs to be located before deletion. 4. Delete from an ordered array with n elements. The element needs to be located before deletion. 5. Sequential search in an un-ordered linked-list with n elements. 6. Delete from an un-ordered linked-list with n elements. The element needs to be located before deletion. 7. Delete from an ordered linked-list with n elements. The element needs to be located before deletion. 8. Insertion (of one element) into an ordered array with n elements.

2 Problem 2 (20 points) Write a recursive function to, given an array with n elements, reverses its elements. Here is the function prototype. void reverse(int a[], int n); // "a" has "n" elements. Write a recursive function to reverse its // elements. For example, if "a" contains 4, 10, 43, 19, 33, // once your function is complete, "a" should contains 33, 19, 43, 10, 4. 2

3 Problem 3 (20 points) Using the primitive functions (null, is_null, atom, eq, car, cdr, cons) and recursion, write a function to fatten a list. A few examples. 1. Let p be the list (()). The list that is the result of having flattened p is ( () () ). 2. ((())) flattened is ( () () () ). 3. (((((()))))) flattened is ( () () () () () () ). 4. () flattened is ( () ). list flatten( list p ) // pre-conditions: // p is not an atom and doesn t contain any atomes either. In addition, // the cdr of p is always a null list. So, it is like () or (()) or // ((())), etc. // The function returns a list that contains null lists. The number of // null lists in this list is the same as the depth of p. So, if p is // (), the result become a list that contains (), which is ( () ). If p // is (()), the function returns ( () () ), a list with two null // lists, one for each layer of (()), etc. 3

4 Problem 4 (25 points) Using the primitive functions (null, is_null, atom, eq, car, cdr, cons) and recursion, write a function to count the number of atoms in a recursive list. int countatoms( list p ) // pre-conditions: // p is a recursive-list, but it is not an atom. // The function counts and returns the number of atoms in p. // For example, given ( ((( a b ) (c) d ) (e f) ) ( gh i) ), // countatoms should return 8. Given ( ((( ) () ) () ) ( ) ), // countatoms should return zero. Note that an atom can appear // anywhere in the input list. 4

5 Problem 5 (25 points) For this problem, you are to write a function that creates one token from a string that contains a Roman expression. Token gettoken(std::string romanexpr); // romanexpr contains a potentially partial infix Roman // expression. For example, "III + II * a" or " + II * a". This function // finds the first token in romanexpr and returns it in an instance of // Token. For example, if the input contained "III + II * a", then the // function returns an instance of Token whose isromannumber() returns // true and whose romannumber() return "III". On the other hand, if // romanexpr contained " + II * a", then gettoken will return an instance // of Token whose isadditionoperator() returns true. // Variables in romanexpr consist of lower-case letters. Roman numbers // are strings that consist of M, D, C, X, V, and I. Operators are *, // +, -, /, and %. Finally, the expression could contain parentheses; ( and ). // The definition of Token appears on the last page of this exam. 5

6 class Token { public: Token() { init(); } Token(char c) { init(); _symbol = c; } Token(const std::string s) { init(); _romannumber = s; } std::string romannumber() const { return _romannumber; } void romannumber( std::string str ) { _romannumber = str; } bool eof() const { return _eof; } void eof(bool v) { _eof = v; } bool eol() const { return _eol; } void eol(bool v) { _eol = v; } bool isopenparen() const { return _symbol == ( ; } bool iscloseparen() const { return _symbol == ) ; } bool isequalsign() const { return _symbol == = ; } bool ismultiplicationoperator() const { return _symbol == * ; } bool isadditionoperator() const { return _symbol == + ; } bool issubtractionoperator() const { return _symbol == - ; } bool ismodulooperator() const { return _symbol == % ; } bool isdivisionoperator() const { return _symbol == / ; } bool isavariable() const { return _symbol >= a && _symbol <= z ; } char getvariable() const { return _symbol; } bool isromannumber() const { return _romannumber.length() > 0; } void print() const; private: void init() { _romannumber = ""; _eof = _eol = false; _symbol = \0 ; } }; std::string _romannumber; bool _eof, _eol; char _symbol; 6