Assg 10: Applications of Stacks

Assg 10: Applications of Stacks

Description

In this assignment, you will be using the Stack abstract data type we devel- oped this week and discussed in our weeks 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 suc- cessfully use our Stack type for this assignment and the function you are asked to write.

For this assignment you need to perform the following tasks.

1. In the �rst 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

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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 migth be

for each charcter c in expression

do

if c is an open paren ‘(‘

push it on stack

if c is a close paren ‘)’:

do

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 ‘)’

done

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:

s = “(())”;

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

{

char c = s[index];

// handle char c of the string expression s here

}

1. 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”.

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sequence output

IIII -> 12345

DDDD -> 54321

ID -> 132

IDIDII -> 1325467

IIDDIDID -> 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, becase in order to then decrease, and also only have 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 di�cult to think of any solution involving a simple iterative loop (though a recursive function is not too di�cult).

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

for each 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)

do

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

done

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.

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1. 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 �rst 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 accmplish the task. The pseudo-code to accomplish this insertion is relatively simple:

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

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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 in- stead of specifying an AStack &, we specify the abstract base 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

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.

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 �nal 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 �rst for strings, then try and templatize the function. This is a void funciton, 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 recursize algorithm is as follows:

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given inputStack as an input parameter