Stacks and Their Operations

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Questions and Answers

What behavior characterizes a stack data structure?

The last item added is the first to be removed. (correct)

The first item added is the last to be removed.

Elements can only be added at the bottom of the stack.

Elements can be added or removed from both ends.

What will occur if an attempt is made to push an element onto a full stack?

An UNDERFLOW error message is displayed.

The stack pointer is reset to the bottom.

An OVERFLOW error message is displayed. (correct)

The new element is added successfully.

What is the purpose of the TOP pointer in a stack?

To mark the location of the last element added. (correct)

To store the maximum size of the stack.

To indicate the number of items in the stack.

To point to the bottom element of the stack.

During the POP operation, what happens if the stack is empty?

An UNDERFLOW error message is displayed. Signup and view all the answers

Which of the following operations would not be valid if TOP equals 0?

POP operation to remove an element. Signup and view all the answers

What is the primary characteristic of Polish notation regarding the placement of operators and operands?

Operators are placed before operands. Signup and view all the answers

What is the equivalent Polish notation for the Infix expression (A + B) * C?

*+ABC Signup and view all the answers

In which notation are parentheses not required to indicate the order of operations?

Both Polish and Reverse Polish notations. Signup and view all the answers

What is the outcome when translating the Postfix expression 5 6 2 + * 12 4 / - to Infix notation?

5 * (6 + 2) - (12 / 4) Signup and view all the answers

How does the process of transforming an Infix expression into Postfix typically begin?

By pushing the opening parenthesis onto the stack. Signup and view all the answers

In the expression A + (B * C - (D / E F) * G) * H, what is its equivalent Postfix expression?

ABCDEF/G-H*+ Signup and view all the answers

What is the function of the stack in the transformation of Postfix expressions?

To temporarily hold operators and operands. Signup and view all the answers

Which of the following transformations would use a stack for managing operations?

Postfix to Infix expression. Signup and view all the answers

What is the main advantage of Reverse Polish Notation over Infix notation?

It eliminates the need for parentheses. Signup and view all the answers

Which of the following statements about the Order of Operations in Polish Notation is true?

The order of operations is always determined by the placement of operators and operands. Signup and view all the answers

What defines an elementary item in data structures?

A data item that cannot be subdivided further. Signup and view all the answers

Which operation involves arranging all data elements in a specific sequence?

Sorting Signup and view all the answers

What is a record in the context of data structures?

A collection of field values of a specific entity. Signup and view all the answers

How can data structures be classified based on their organization?

By whether they are linear or non-linear. Signup and view all the answers

What is one of the primary functions of data structures?

To organize data for efficient processing and retrieval. Signup and view all the answers

Which characteristic defines a static data structure?

It has fixed formats and sizes along with memory locations. Signup and view all the answers

What does the term 'FILO' refer to in the context of data structures?

Elements are handled in a first-in, last-out order. Signup and view all the answers

Which situation describes the 'Worst Case' in execution time for data structures?

The circumstance in which a specific operation takes the longest time possible. Signup and view all the answers

Which of the following correctly describes an array in data structures?

A linear data structure stored in contiguous memory locations. Signup and view all the answers

In the context of a queue data structure, what does FIFO stand for?

First In, First Out. Signup and view all the answers

Which of the following best describes a directed edge in a graph?

A connection that represents a one-way relationship between vertices Signup and view all the answers

What is a key characteristic of linear data structures compared to non-linear data structures?

They allow for single-level organization of data elements Signup and view all the answers

Which application is most likely to utilize non-linear data structures?

Image processing tasks Signup and view all the answers

How does memory usage differ between linear and non-linear data structures?

Non-linear structures can become memory inefficient due to their complexity Signup and view all the answers

What happens to the time complexity of non-linear data structures as input size increases?

It always remains constant Signup and view all the answers

Study Notes

Stacks

A stack is a list where items are added and removed from one end, called the top.
Items are inserted using the "push" operation.
Items are removed using the "pop" operation.
The last item added is the first item removed (LIFO - Last-In, First-Out).

Basic Operations

Push: adds an element to the top of the stack.
Pop: removes the element from the top of the stack.
These terms are specific to stacks, not other data structures.

Array Representation of Stacks

Stacks can be represented using a linear array called STACK.
TOP is a pointer that holds the index of the top element.
MAXSTK is a variable specifying the maximum elements the stack can hold.
The stack is empty if TOP = 0 or TOP = NULL.

PUSH Operation

PUSH(STACK, TOP, MAXSTK, ITEM)
Checks if the stack is full (TOP = MAXSTK).
If full, prints "OVERFLOW" and returns.
Increments TOP by 1.
Places the ITEM at the new TOP position in the STACK array.
Returns.

POP Operation

POP(STACK, TOP, ITEM)
Checks if the stack is empty (TOP = 0).
If empty, prints "UNDERFLOW" and returns.
Assigns the value at the current TOP position to ITEM.
Decrements TOP by 1.
Returns.

Arithmetic Expressions: Polish Notation

Infix notation: operator symbol is placed between operands (e.g., A + B).
Polish notation (also called prefix notation): operator symbol is placed before its operands (e.g., +AB).
Reverse Polish notation (also called postfix notation): operator symbol is placed after its operands (e.g., AB+).
Polish notation eliminates the need for parentheses in expressions. Order of operation is unambiguous.

Quicksort

An application of stacks used to sort a list of data items (A) numerically or alphabetically.
Quicksort is a divide-and-conquer algorithm.

Quicksort (Reduction Step)

Finds the appropriate position for the first element.
Steps involve scanning the list and exchanging elements.
The process is repeated recursively to sort the sublists.
The first step involves comparing the last element in the array with the first element. Elements are then rearranged into sublists. These sublists are then processed recursively.
This specific step of finding the correct position for the first element is a stack-based operation.

Quicksort Complexity

Worst-case running time: n²/2
Average-case running time: n log n
Best-case running time: O(n log n)

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Description

This quiz covers the fundamental concepts of stacks, including the push and pop operations, and their array representation. It's designed to test your understanding of how items are added and removed in a stack data structure and the implementation details related to these operations.