VE 280Lab 5 - Solved

                                                             


Ex.1 Carole & Tuesday                                                                              
Related Topics: ADT, list.

A famous band Carole & Tuesday now decides to release an album. They want to maintain songs as a "list". Roddy, a friend of Carole and Tuesday, provides many starter files for this "list" and lets you complete all functions in files.

A "list" is a sequence of zero or more numbers in no particular order. A list is well-formed if: a) It is the empty list, or

b) It is an integer followed by a well‐formed list.

A list is an example of a linear‐recursive structure: it is "recursive" because the definition refers to itself. It is "linear" because there is only one such reference.

Here are some examples of well‐formed lists:

 

int dot(list_t v1, list_t v2);

// REQUIRES: Both "v1" and "v2" are non-empty

//

// EFFECTS: Treats both lists as vectors. Returns the dot

//          product of the two vectors. If one list is longer //          than the other, ignore the longer part of the vector.

list_t filter(list_t list, bool (*fn)(int));

 // EFFECTS: Returns a list containing precisely the elements of "list" //          for which the predicate fn() evaluates to true, in the //          order in which they appeared in list.

//

//          For example, if predicate bool odd(int a) returns true

//          if a is odd, then the function filter(list, odd) has //          the same behavior as the function filter_odd(list).

list_t filter_odd(list_t list);

// EFFECTS: Returns a new list containing only the elements of the

//          original "list" which are odd in value, 

//          in the order in which they appeared in list.

//

//          For example, if you apply filter_odd to the list //          ( 3 4 1 5 6 ), you would get the list ( 3 1 5 ).

Since  filter_odd is a special case of filter , you can use filter_odd as a function to test filter if you implement it with filter .

Hint

 You can think in the way that recursive.h provides an ADT for you and you need to implement the new functions declared in ex1.h using the methods provided.

Problem

 1. Implement the functions in ex1.cpp .

Requirements

1. If you define any helper functions yourself, be sure to declare them "static", so that they are not visible outside this file.

Testing

 Since you are only required to implement new methods, there is no IO requirements. However ex1Test.cpp is provided for you to test your correctness but you still need to design you own

test cases to get full score.

Ex2. Quadratic Functions in Standard Form                                       
Roddy is in charge of tuning for Carole & Tuesday. However, this reminds him of tough time dealing with quadratic functions in high school. As a student taking VE280, you can use your knowledge about abstract data types (ADT) to help Roddy with little knowledge in math play with quadratic functions.

Related Topics: ADT.

Problem: Roddy wants to represent a quadratic function in a standard form, which is

                                           (                  ). He decides that the following operations should be allowed on

quadratic functions:

1.  Evaluate       at a given int  value.

2.  Get the root(s) of       , which is the value of  such that  

3.   Check if two quadratic functions ( and ) intersects, which means whether there exists some real   such that    .

Therefore, he designed this interface to represent a quadratic function

 

Requirements:

1.     Look through file rootType.h , to make the output simple, we make the following restrictions:

 if           has two different real roots, then the smaller               should be in roots[0] and the bigger           should be in roots[1] .

                    If              has one real root, then                        should be in both roots[0] and roots[1] .

If                         has two complex roots, then              should be in root[0] and  should be in roots[1] , where   .

2.     Look through standardForm.h and implement the methods for QuadraticFunction class in standardForm.cpp .

3.     ex2.cpp is used to test your ADT, you can just read it and run it.

Input Format: Since you only need to implement the methods of this ADT, we just provide a

 

Output Format: Since you only need to implement the methods of this ADT, we just provide a

 

1 .

 

Ex3. Quadratic Functions in Factored Form                                        
Related Topics: ADT.

Problem: Roddy realizes that a quadratic function can also be represented in a factored form, which is  ).

This time, the interface looks the same, but the data members are different:
transformation so that they can fit into the new data members. Again, the output method is provided. So you needn't implement it.