The document provides instructions for Assignment 09, which involves implementing four functions that use a stack data structure: 1. doParenthesisMatch() checks if a string of parentheses is properly matched and returns a boolean. 2. decodeIDSequence() decodes a string of 'I's and 'D's into a minimum number string without repeated digits. 3. insertItemOnSortedStack() inserts an item into a sorted stack. 4. sortStack() sorts an unsorted stack recursively. Students are provided header and implementation files for a Stack ADT and tests, and must implement the functions in the given files while following style guidelines. The assignment evaluates correct implementation of the functions and stack usage,

1. 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

2. 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.

3. 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.
1
The general approach you should take for this assignment, and
all assignment is:
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.
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.
AddthecorrectfunctionprototypeforthedoParenthesisMatch()mem
berfunctionintheassg09-stackfun.hpp header file. The prototype

4. consists of the name of the function, its input parameters and
their types, and the return value of the function.
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.
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.
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.
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.

5. 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

6. 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:
2
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

7. 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

8. 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.

9. 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:
3
given inputStack
and create temporaryStack for this algorithm

10. 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 (a stack of
integers) for the tests. You can originally create your function
to use a Stack & as its second input parameter. It is important
that the stack be a reference parameter here. Also notice that
instead of specifying an AStack &, we specify the abstract base

11. class Stack &. 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 &, 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 to to templatize. Once you
do this, you function should still
work and pass the tests using an 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 & (a reference to a Stack of 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

12. 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)
4
Once you have it working for type stacks, also templatize your

13. 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
---------------------------------------------------------------------------
----
test doParenthesismatch function -----------------------------------
-------------------------------------------- assg09-tests.cpp:28
...............................................................................
assg09-tests.cpp:33: PASSED: CHECK( doParenthesisMatch("")
)

14. 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

15. 5
Requirements and Grading Rubrics
Program Execution, Output and Functional Requirements
Your program must compile, run and produce some sort of
output to be graded. 0 if not satisfied.
(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.
(25 pts.) decodeIDSequence() implemented and correct. Used a
stack from our class Stack.hpp stack
implementation to implement the asked for algorithm.
(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.
(25 pts.) sortStack() implemented as described and working.
The function was implemented using recursion
as required. The function was templatized as asked for. The

16. 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.
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.
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.
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.
Do not include any statements (such as system("pause") or

17. 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.