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To understand the workings of a stack as well as postfix notation, and to be introduced to the C++ Standard Template Library (STL).
A stack is a basic data structure similar in use to a physical stack of papers. You can add to the top (push) and take from the top (pop), but you are not allowed to access the middle or bottom. A stack adheres to the LIFO property.
Go through Tutorial 3: Unix, part 1, which is the introduction and sections 1-4. This tutorial is originally from the department of Electrical Engineering at the University of Surrey, and is available online here. You should complete the introductory part and sections 1-4. You should already be somewhat familiar with some of the materials in the first few of these tutorials, as they were covered in the Unix tutorial from the first lab. The rest of the tutorial (sections 5-8) are for next week’s lab, but feel free to go through it this week, if you are interested.
In this lab, you will:
The various parts of this lab develop the entire program:
Note that the program should be able to fully run after each lab portion.
A stack is a container that implements the LIFO (last in, first out) property. Often it internally uses a linked list, array, vector, or a doubly-linked list to contain the elements. In general, a stack needs to implement the following interface and functionality:
void push(int e): This adds the passed element to the
top of the stack.int top(): This returns the element on the top of the
stack. It does not remove that element from the top. If the stack is
empty, then somehow an error must be indicated – printing an error
message and exiting is fine for reporting errors for this lab.void pop(): This removes the element on the top of the
stack, but does not return it. If the stack is empty, then somehow an
error must be indicated – for this lab, you can just print out an error
message and then exit.bool empty(): This tells whether there are any elements
left in the stack (false) or not (true).Often, the top() and pop() functionality
are joined as an int pop() function, but in this lab, it is
beneficial to separate them, as that is what the STL stack does.
If pop() or top() are called on an empty
stack, terminate the program with the function call
exit(-1), which is from the <cstdlib>
library.
For this lab, you will use a stack of int values.
Postfix notation (also known as reverse Polish notation) involves writing the operators after the operands. Note how parentheses are unnecessary in postfix notation.
An online description of postfix calculators can be found on Wikipedia.
We will be using the C++ STL stack to implement our postfix calculator. The stack class’s documentation can be found here.
Your calculator must implement the following arithmetic operations:
+: addition (prelab)-: subtraction (prelab)*: multiplication (inlab)/: division (inlab)~: unary negation (inlab)Notes:
left_operand
right_operand operator. For example, 1 2 -
translates to 1 - 2.For your keyboard input, your program should read in a single line of
space-delimited tokens from standard input. You should read this in
using strings (if you are looking at building a tokenizer,
then you are making it much more difficult than it need be). When
processing input, you can’t know before you read something if it will be
an operand (a numeric value) or an operator (a character), so you must
read in each space-separated part into a string variable before parsing
it. No values, nor intermediate computational results, will exceed what
can be stored in an int.
We provide you with a number of input files that match the input shown at the end of this lab document. Recall that you can supply the contents of a file as input to your program via input redirection (as described in the Unix tutorial):
./a.out < addition.txtHow should the program know when you are finished providing input? There are a couple of ways to do this.
cin. This will
require entering a Control-D at the end of the provided input
(i.e., enter the postfix expression, hit Enter, and then hit Control-D).
The input we provide during the execution will provide the Control-D at
the end of said input.getline() method, but
this is likely the harder way to deal with it.As mentioned in the Unix tutorial, Control-D stands for “end of
file”, which lets cin know that there is no more input to
read.
NOTE: When hitting Control-D, you have to enter it on its own line. This means that you first have to hit Enter, then Control-D.
Below is a sample execution run to show you the input and output format we are looking for.
Input
1 2 + 3 -Output
0You do not need to supply any input prompting for this assignment. When the program runs, nothing should print out to the terminal and the user should be able to input a postfix expression.
cin is the opposite of cout – rather than
printing to standard output, it reads from standard input. When you type
a line and press enter, that entire line gets sent to cin,
which then automatically splits on whitespace to produce multiple
tokens. Therefore, if we were to supply + 2 3 isn't 2150
great?? as input, we would get six tokens back. This is very
helpful as the postfix expressions are already space-delimited.
A sample code snippet to continuously read from standard input would look something like this:
string token;
while (cin >> token) {
// Do stuff with `token`!
// For example, we can print each token back out on its own line:
cout << token << endl;
}There are two cases you will need to handle when parsing each token: operators and numbers.
C++ allows you to compare strings for equality with ==.
For example, you can check if s is the division operator
with if (s == "/").
Hint: we can check for all the operators, since there are only five of
them. If all the checks fail, what does that mean the token has to
be?
cin takes in all input as strings, but we need to convert those to
ints so that we can push them into the stack. Perhaps you should take a
look at the
string documentation to see if anything can help you
out.
The C++ stack class is templated, which means it can
hold whatever type you specify (think back to ArrayLists in Java). Since
we will be using ints for our postfix calculator, we can
specify that by saying stack<int> when declaring our
stack.
Given that you will need to check if the stack is empty before every
top and pop call, it may be worth it to add
helper methods to your postfix calculator that, when called, will
perform the necessary checks before top/pop.
When compiling your code, remember to compile ALL of your cpp files in the compile command:
clang++ postfixCalculator.cpp testPostfixCalc.cppYou can also use clang++ *.cpp if there are no other C++
files in your directory.
The purpose of the in-lab is first to ensure that your pre-lab code (the postfix calculator) is working properly. Then, you will need to handle negative integer inputs and add the remaining three operators: multiplication, division, negation. By the end of the in-lab, your postfix calculator should be able to read in a single line of space-delimited tokens representing a postfix expression and print out the result of the expression before exiting.
The core functionality of user input should be completed in the
pre-lab. For this section, you must add code that allows the program to
accept negative numbers (e.g -1, -10) for use with the calculator. In
addition to handling negative numbers, you must also add functionality
that allows the user to enter the symbols for multiplication, division,
and negation, which are respectively: *, /,
~
See the Sample Execution Run section of the pre-lab for specifications.
By expanding the integer input to also include negative numbers, you
must be careful not to accidentally parse a negative number as the
subtraction operator. For example, if your code were to only check the
first character of every token, then it may mistake a number like
-5 as the subtraction operator -. To handle
this, your code should check the length of tokens and their first
character in order to determine exactly what the user has just input to
your calculator.
For the post-lab, you will be implementing your own stack and then modifying your postfix calculator to use that stack instead of the STL stack.
Your stack class must:
void push(int e), void
pop(), int top(), and bool empty()
methods to perform the same functionality as the STL stackYou may modify and re-use your LinkedList code from Lab 2, or you may write your own code, as long as you satisfy the above requirements.
Depending on how you implement the stack class, you may just need the
stack.h/cpp files, in addition to the three postfix calculator files
(postfixCalculator.h/cpp and testPostfixCalc.cpp). Or you may need
stack.h/cpp and stacknode.h/cpp in addition to the three postfix
calculator files. Or you may want to include the six
List/ListItr/ListNode files from lab 2 as well as stack.h/cpp and the
three postfix calculator files. How you do this is up to you - as long
as it works, we don’t really care, provided that is compiles with
clang++ *.cpp
The following examples provide postfix expressions and their expected value.
addition.txt: 1 2 3 4 5 + + +
+; expected output: 15
subtraction.txt: 20 10 - -3
10 - - 2 -; expected output: 21
multiplication.txt: -1
-2 -5 3 * 2 -2 * * * *; expected output: 120
division.txt: -1512 -12 -2 / /
-2 / 3 /; expected output: 42
negation.txt: -1 ~ ~ ~;
expected output: 1