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Questions and Answers
What is the primary condition that allows the PUSH operation on a stack?
What is the primary condition that allows the PUSH operation on a stack?
In which situation does the term 'Underflow' apply to a stack?
In which situation does the term 'Underflow' apply to a stack?
What does the variable 'TOP' in a stack's array representation indicate?
What does the variable 'TOP' in a stack's array representation indicate?
Which of the following statements is TRUE regarding the array representation of a stack?
Which of the following statements is TRUE regarding the array representation of a stack?
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Which data structure feature is characteristic of the Stack?
Which data structure feature is characteristic of the Stack?
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What happens if the Top pointer is null when attempting to delete an element from the stack represented by an array?
What happens if the Top pointer is null when attempting to delete an element from the stack represented by an array?
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Which step is NOT performed when inserting a new element in the stack using a linked list?
Which step is NOT performed when inserting a new element in the stack using a linked list?
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What is one key advantage of using a linked list representation for a stack over an array implementation?
What is one key advantage of using a linked list representation for a stack over an array implementation?
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During the POP operation of a linked list stack, what is done with the node that is deleted?
During the POP operation of a linked list stack, what is done with the node that is deleted?
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Which application of stacks is particularly important in programming languages?
Which application of stacks is particularly important in programming languages?
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Study Notes
Stack Data Structure
- A stack is a linear data structure of variable size where elements are inserted and deleted only from one end, known as the "TOP."
- Known as LIFO (Last In First Out), the last element added is the first to be removed.
- Insertion is called "PUSH" and deletion is termed "POP."
Operations on Stack
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PUSH:
- Inserts a new element at the top of the stack.
- Possible only if there is space; can cause an Overflow condition if the stack is full.
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POP:
- Removes the element from the top of the stack.
- Possible only if the stack is not empty; can lead to an Underflow condition if the stack is empty.
Memory Representation
- A stack can be implemented using two methods:
- Array: Requires predetermined size; uses the index variable TOP to track the top element. Overflow and underflow must be managed.
- Linked List: Offers flexible size, allowing dynamic growth without prior limits.
Array Representation of Stack
- Homogeneous data elements are required.
- Maximum stack size must be defined before use.
- TOP starts at 0 when empty. Increment for PUSH, decrement for POP.
Linked List Representation of Stack
- Allows stack growth without a fixed limit.
- PUSH involves inserting at the start, while POP removes from the start.
Applications of Stack
- Used in evaluating arithmetic expressions by converting infix expressions to postfix or prefix notations.
Notations for Arithmetic Expressions
- Infix Notation: Operators between operands (e.g., m + n). Prefers operator precedence and associativity.
- Prefix Notation: Operators placed before operands (e.g., +mn).
- Postfix Notation: Operators placed after operands (e.g., mn+).
Evaluating Expressions
- Postfix expressions are evaluated using a stack to manage operands and operators systematically.
Recursion
- A recursive function calls itself to solve problems. Useful for repetitive computations.
- Examples include calculating sums, factorials, and the Fibonacci series.
Factorial Function
- The product of positive integers from 1 to n, represented as n!.
- Defined recursively:
- n! = n × (n-1)! with 0! = 1.
Fibonacci Series
- Sequence defined as F0 = 0, F1 = 1, with each subsequent term being the sum of the two preceding ones.
- Defined recursively:
- Fibo(n) = Fibo(n-1) + Fibo(n-2) with base cases for n = 0 and n = 1.
Sample Algorithms
- Algorithms for PUSH and POP operations in both array and linked list implementations are structured guides to manipulating the stack efficiently.
- Recursive algorithms for calculating factorial and Fibonacci values offer clear methods for solving these problems.
Precedence of Operators
- Operator precedence varies, affecting the outcome of expressions, which is critical in evaluating infix expressions correctly.
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Description
Explore the fundamentals of stacks, a vital linear data structure characterized by its LIFO (Last In First Out) property. Learn about the insertion and deletion processes, known as 'PUSH' and 'POP', and understand why stacks are considered restricted data structures. This quiz will test your knowledge of stack operations and their applications.
