Objectives 

Assignment 09: Applications of Stacks 

COSC 2336: Data Structures and Algorithms Fall 2020 

• More practice with recursion.
• Practice writing some template functions.
• Use stack ADT to implement given algorithms.
• Practice using Stack class container given as a library in a separate file. • Look at some common applications of stacks. 

Description 

In this assignment, you will be using the Stack abstract data type we developed for this unit and discussed in our lectures, to implement 4 functions that use a stack data type to accomplish their algorithms. The functions range from relatively simple, straight forward use of a stack, to a bit more complex. But in all 4 cases, you should only need to use the abstract stack interface functions push(), pop(), top(), and isEmpty() in order to successfully use our Stack type for this assignment and the function you are asked to write. 

NOTE You are to use the Stack ADT abstraction give to you for this assignment. If you are familiar with STL stack containers, you are not to use them for this assignment. Part of the assignment is to look over and learn the Stack ADT implementation we give you here based on our textbook Stack examples. 

Setup 

For this assignment you will be given the following files: 

File Name 

assg09-tests.cpp assg09-stackfun.hpp assg09-stackfun.cpp Stack.hpp 

Stack.cpp 

Description 

Unit tests for the member functions
you are to write.
Header file where function prototypes for the functions you write using stacks should go. Implementaiton file, the implementation of the 4 functions you write for this assignment go here. Header file defining a Stack ADT for use in implementing the functions for this assignment. You will not make any modifications in this file, you are only going to be using the given Stack. Implementation file for the Stack ADT
template class. You also do not make any changes in this file either. 

Set up a multi-file project to compile the .cpp source files and run them as shown for the class. The Makefile you were given should be usable to create a build project using the Atom editor as required in this class. You will only be adding code to the assg09-stackfun.[hpp|cpp] file in this assignment. The Stack.[hpp|cpp] file contains a Stack container. You are to use this Stack ADT for the 4 functions you are to write for this assignment. 

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The general approach you should take for this assignment, and all assignment is: 

1. Set up your project with the given starting code. The files should compile and run, but either no tests will be run, or tests will run but be failing.
    
2. For this project, start by uncommenting the first TEST_CASE in the assg09-tests.cpp file. These are the unit tests to test the functionality of your doParenthesisMatch() function, the member function you are to implement.
    
3. AddthecorrectfunctionprototypeforthedoParenthesisMatch()memberfunctionintheassg09-stackfun.hpp header file. The prototype consists of the name of the function, its input parameters and their types, and the return value of the function.
    
4. Add a stub for your doParenthesisMatch() member function to the assg09-stackfun.cpp implementation file. The function should have the same signature as the prototype you gave in the header file. Documentation for the function has not been given for you this time, so add documentation of your function first. This function is supposed to return a bool result, so you should just initially return true so you can get your code to compile.
    
5. Your code should compile and run now. Make sure after adding the function prototype and stub your code compiles and runs. However, your unit tests will be failing initially.
    
6. Incrementally implement the functionality of your doParenthesisMatch() member function. You should try to add no more than 2 or 3 lines of code, and then make sure your program still compiles and runs. Start by adding code to get the first failing test to pass. Then once that test passes, move on to the next failing tests until you have all tests passing. If you write something that causes a previously passing test to fail, you should stop and figure out why, and either fix it so that the original test still passes, or remove what you did and try a new approach.
    
7. Once you have the doParenthesisMatch() member function implemented and all unit tests passing, you should then move on to the other functions in the order suggested. Some functions use previous ones in this assignment, so do them in the order given for you in the tasks below.
    

Tasks 

You should set up your project/code as described in the previous section. In this section we give some more details on implementing the member functions for this assignment. You should perform the following tasks for this assignment: 

1. In the first task, we will write a function that will check if a string of parenthesis is matching. Strings will be given to the function of the format “(()((())))”, using only opening “(” and closing “)”. Your function should be named doParenthesisMatch(). It takes a single string as input, and it returns a boolean result of true if the parenthesis match, and false otherwise. 

The algorithm to check for matching parenthesis using a stack is fairly simple. A pseudo-code description might be 

    for each charcter c in expression
    do

       if c is an open paren '('
         push it on stack

       if c is a close paren ')':
       then

          if stack is empty
             answer is false, because we can't match the current ')'

          else
             pop stack, because we just matched an open '(' with a close ')'

endif done 

Your function will be given a C++ string class as input. It is relatively simple to parse each character of a C++ string. Here is an example for loop to do this: 

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s = “(())”;
for (size_t index = 0; index < s.length(); index++) { 

char c = s[index];
// handle char c of the string expression s here 

} 

2. In the next task, we will also write a function that decodes a string expression. Given a sequence consisting of ‘I’ and ‘D’ characters, where ‘I’ denotes increasing and ‘D’ denotes decreasing, decode the given sequence to 

construct a “minimum number” without repeated digits.
An example of some inputs and outputs will make it clear what is meant by a “minimal number”. 

sequence IIII -> DDDD -> ID -> IDIDII -> IIDDIDID -> 

output
12345
54321
132
1325467
125437698

If you are given 4 characters in the input sequence, the result will be a number with 5 characters, and further only the digits ‘12345’ would be in the “minimal number” output. Each ‘I’ and ‘D’ in the input denotes that the next digit in the output should go up (increase) or go down (decrease) respectively. As you can see for the input sequence “IDI” you have to accommodate the sequence, thus the output goes from 1 to 3 for the initial increase, because in order to then decrease, and also only use the digits ‘123’, we need 3 for the second digit so the third can decrease to 2. 

Take a moment to think how you might write an algorithm to solve this problem? It may be difficult to think of any solution involving a simple iterative loop (though a recursive function is not too difficult). 

However, the algorithm is relatively simple if we use a stack. Here is the pseudo-code: 

 for each index, character c in input sequence
 do

    push character index+1 onto stack (given 0 based index in C)

if we have processed all characters or c == ‘I’ (an increase) then 

       pop each index from stack and append it to the end of result
    endif

done 

Your function should be named decodeIDSequence(). It will take a string of input sequence, like “IDI” as input, and it will return a string type, the resulting minimal number. Notice we will be constructing a string to return here, so simply start with an empty string string result = “” and append the digits to the end when you pop them from the stack as described. 

3. In the third task, you will write two functions that will be able to sort a stack. First of all, you should write a simpler method that, given an already sorted stack as input, and an item of the same type as the stack type, the item should be inserted into the correct position on the sorted stack to keep it sorted. For example, the stacks will be sorted in ascending order, where the item at the bottom of the stack is the smallest value, and the item at the top is the largest, like this: 

 top: 8 7 5 3 1 :bottom

If we call the function to insert a 4 into this sorted stack, the result should be: 

top: 8 7 5 4 3 1 

Your function should be called insertItemOnSortedStack(). This function takes an item as its first parameter, and a reference to a Stack as its second parameter. You should create and use another temporary stack in your function in order to accomplish the task. The pseudo-code to accomplish this insertion is relatively simple: 

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 given inputStack
 and create temporaryStack for this algorithm

 while top of inputStack > item we want to insert
 do

    pop topItem from inputStack

    push topItem onto the temporaryStack
 done

at this point, items on inputStack are <= to the item we want to insert so push item onto inputStack 

 now put items back from temporaryStack to original inputStack
 while temporaryStack is not empty
 do

    pop topItem from temporaryStack

    push topItem onto the inputStack
 done

The tests given for the insert function use an AStack<int> (a stack of integers) for the tests. You can originally create your function to use a Stack<int> & as its second input parameter. It is important that the stack be a reference parameter here. Also notice that instead of specifying an AStack<int> &, we specify the abstract base class Stack<int> &. This is to demonstrate the power of using virtual classes and class abstractions. If you specify the base class, you can pass an AStack or an LStack or any class that is derived from the base Stack class, as long as that class implements all of the virtual functions of the abstract Stack interface. Once you have your function working for Stack<int> &, templatize your function. We practiced creating function templates in a previous assignment. Here it should be relatively simple, you simply need to add the 

template <class T>
before the function, and change the <int> to <T> to templatize. Once you do this, you function should still 

work and pass the tests using an <int> type. 

4. Once you have your insertItemOnSortedStack() template function working, it is even easier to use this function to create a sortStack() function. We could implement this function again using a temporary stack, but for this fourth and final function I want you instead to create a recursive function. A recursive function in this case is going to work in essentially the same way, but we will be using the OS/system function call stack implicitly to perform the algorithm, rather than explicitly creating and using our own temporary stack. 

Create a function called sortStack(). This function should take a Stack<string> & (a reference to a Stack of <string> types) as its only parameters. You will later templatize this function as well, but all of the tests of sortStack() use stacks of strings, so get it working first for strings, then try and templatize the function. This is a void function, it doesn’t return a result, but it implicitly causes the stack it is given to become sorted. 

The function, as the name implies, will take an unsorted stack, and will sort them in the same order we used previously, e.g. in ascending order with the smallest item at the bottom of the stack, and the largest at the top. The pseudo-code to accomplish this using a recursive algorithm is as follows: 

 given inputStack as an input parameter

 # the base case
 if inputStack is empty, do nothing (return)

 # the general case
 take top item from inputStack and save it in a local variable

 call sortStack(inputStack) recursively on this now smaller stack

 # on return, the stack should be sorted, so
 insertItemOnSortedStack(my item I popped, inputStack)

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Once you have it working for type stacks, also templatize your sortStack() function, so that it will actually work to sort a Stack of any type. 

Example Output 

Here is the correct output you should get from your program if you correctly implement all the class functions and successfully pass all of the unit tests given for this assignment. If you invoke your function with no command line arguments, only failing tests are usually shown by default. In the second example, we use the -s command line option to have the unit test framework show both successful and failing tests, and thus we get reports of all of the successfully passing tests as well on the output. 

$ ./test =============================================================================== All tests passed (47 assertions in 4 test cases) 

$ ./test -s 

——————————————————————————- 

test is a Catch v2.7.2 host application. Run with -? for options 

——————————————————————————- 

<doParenthesisMatch()> test doParenthesismatch function ——————————————————————————- assg09-tests.cpp:28 ……………………………………………………………………. 

assg09-tests.cpp:33: PASSED: CHECK( doParenthesisMatch(“”) ) 

with expansion:
 true

… output snipped … 

=============================================================================== All tests passed (47 assertions in 4 test cases) 

Assignment Submission 

A MyLeoOnline submission folder has been created for this assignment. There is a target named submit that will create a tared and gziped file named assg02.tar.gz. You should do a make submit when finished and upload your resulting gzip file to the MyLeoOnline Submission folder for this assignment. 

$ make submit
tar cvfz assg09.tar.gz assg09-tests.cpp assg09-main.cpp 

assg09-stackfun.hpp assg09-stackfun.cpp Stack.hpp Stack.cpp assg09-tests.cpp
assg09-main.cpp
assg09-stackfun.hpp 

assg09-stackfun.cpp Stack.hpp
Stack.cpp 

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Requirements and Grading Rubrics
Program Execution, Output and Functional Requirements 

1. Your program must compile, run and produce some sort of output to be graded. 0 if not satisfied.
    
2. (25 pts.) doParenthesisMatch() is implemented correctly and is passing all of the tests. Used a stack of from
   our class Stack.hpp to implement the algorithm.
    
3. (25 pts.) decodeIDSequence() implemented and correct. Used a stack from our class Stack.hpp stack
   implementation to implement the asked for algorithm.
    
4. (25 pts.) insertItemOnSortedStack() implemented and working. The function is correctly templatized. The
   function takes a reference to the Stack abstract class as it second parameter.
    
5. (25 pts.) sortStack() implemented as described and working. The function was implemented using recursion
   as required. The function was templatized as asked for. The function takes a reference to a Stack base class as its only parameter.
    

Program Style 

Your programs must conform to the style and formatting guidelines given for this class. The following is a list of the guidelines that are required for the assignment to be submitted this week. 

1. Most importantly, make sure you figure out how to set your indentation settings correctly. All programs must use 2 spaces for all indentation levels, and all indentation levels must be correctly indented. Also all tabs must be removed from files, and only 2 spaces used for indentation.
    
2. A function header must be present for member functions you define. You must give a short description of the function, and document all of the input parameters to the function, as well as the return value and data type of the function if it returns a value for the member functions, just like for regular functions. However, setter and getter methods do not require function headers.
    
3. You should have a document header for your class. The class header document should give a description of the class. Also you should document all private member variables that the class manages in the class document header.
    
4. Do not include any statements (such as system(“pause”) or inputting a key from the user to continue) that are meant to keep the terminal from going away. Do not include any code that is specific to a single operating system, such as the system(“pause”) which is Microsoft Windows specific.