Data structure.pdf
- 2. INTRODUCTION TO DATA STRUCTURE A data structure is a systematic way of organizing and storing data in a computer's memory or storage, designed to facilitate efficient manipulation, retrieval, and management of information for various computational tasks and algorithms.
- 3. WHAT IS STACK? LIFO (Last-In, First-Out) •Recent First: LIFO means the last item added is the first to be removed. •Stack-Like: Resembles stacking items; new items go on top, and the top one is accessed first. •Priority Handling: Useful when focusing on recent data or tasks. •Examples: Stack data structures, browser history, undo functionality. •Opposite of FIFO: Contrasts with FIFO (First-In, First-Out) principle. •Ordered Collection: A stack is an ordered collection of items with a specific arrangement. •LIFO Principle: Follows the Last-In, First-Out principle—last item added is the first removed. •Two Main Operations: Supports two primary operations: "push" to add items and "pop" to remove the top item. •Top Element: Only the top element is accessible and can be manipulated. •Usage: Widely used for managing function calls, undo operations, and tracking history. •Analogous to Real Stacks: Conceptually similar to a stack of items, like plates or books.
- 4. CORE OPERATION ON A STACK 1.Push: 1. Description: The "push" operation involves adding an element onto the top of the stack. 2. Process: When you push an element onto the stack, it becomes the new top element, and the previous top element is shifted down. 3. Use Case: Push is commonly used when you want to insert new data into the stack, such as adding items to a list of pending tasks. 2.Pop: 1. Description: The "pop" operation entails removing and retrieving the top element from the stack. 2. Process: When you pop an element from the stack, the top element is removed, and the element just below it becomes the new top element. 3. Use Case: Pop is frequently used when you want to access and process the most recent item in the stack. For example, when managing function calls, the most recent function call is the one that gets executed and removed from the call stack.
- 5. EXPLANATION OF THE PUSH OPERATION ▪ The "push" operation in a stack involves adding a new element to the top of the stack. Here's how it works: 1. Initial State: Imagine you have a stack that is initially empty. There are no elements in the stack. 2. Pushing an Element: When you perform a push operation, you're placing a new element onto the stack. This new element becomes the top element of the stack. 3. New Top Element: As a result of the push, the newly added element becomes the top of the stack. Any existing elements that were previously on top are pushed down one position. 4. Stack Growth: With each push operation, the stack grows vertically as new elements are added to the top. 5. Order Preservation: The order of the elements is preserved. The most recently pushed element is now the first one that will be removed when a pop operation is performed. ▪ Diagram depicting how elements are added to the stack
- 6. EXPLANATION OF THE POP OPERATION The "pop" operation in a stack involves removing the top element from the stack. Here's how it works: 1.Initial State: Consider a stack with several elements. The top element is the one that was most recently added. 2.Popping an Element: When you perform a pop operation, the top element is removed from the stack. 3.New Top Element: After the pop, the element just below the removed element becomes the new top element of the stack. 4.Stack Shrinking: With each pop operation, the stack becomes one element shorter as the top element is removed. 5.Order Preservation: The order of the remaining elements is preserved. The second-to-top element becomes the new top element, and the order below it remains unchanged. • Diagram illustrating how elements are removed from the stack
- 7. IMPLEMENTING A STACK INTRODUCTION •Common Approach: Implementing a stack using a list (array) is a widely used practice in programming. •Convenient Utilization: Lists offer a built-in and convenient way to create a basic stack structure. •End as Top: The end of the list is used as the top of the stack in this approach. •Addition and Removal: Elements are added and removed using list methods. •Push Operation: Use append() to push elements onto the stack (at the end). •Pop Operation: Utilize pop() to remove elements from the stack (from the end). •Simplicity: The built-in functions simplify implementing basic stack functionality. •Effective Time Complexity: Both append() and pop() operations generally have O(1) time complexity. •Versatility: Lists support other operations beyond stacks, enhancing flexibility. •Trade-offs: While efficient, resizing of lists can occasionally lead to performance considerations.
- 8. BENEFITS AND LIMITATIONS OF USING A LIST FOR STACK IMPLEMENTATION. Benefits: •Simplicity: Lists provide a straightforward way to create and manage stacks. •Efficient Push and Pop: Push and pop operations are usually O(1) time complexity. •Memory Management: Lists handle memory allocation and resizing automatically. •Versatility: Lists support various operations beyond stacks. •Familiarity: Utilizes a widely understood data structure. Limitations: •Fixed Capacity: Lists have a fixed size that can lead to resizing. •Resizing Overhead: Resizing can occasionally cause performance overhead. •Inefficient Memory Use: Lists might allocate more memory than needed. •Complexity for Stacks: Lists provide more features than necessary for simple stacks. •Not Optimized for All Scenarios: Might not be ideal for very large stacks.
- 9. PYTHON CODE: STACK IMPLEMENTATION In this code: •The stack is represented by a list named stack. •The push function adds an element to the end of the list, simulating a stack push. •The pop function removes and returns the last element of the list, simulating a stack pop. •The is_empty function checks if the list is empty, indicating an empty stack.
- 10. APPLICATIONS OF STACK Function Calls: Managing function calls and their context in programming languages. Expression Evaluation: Evaluating mathematical and logical expressions. Undo/Redo: Implementing undo and redo features in software. Backtracking Algorithms: Solving problems by exploring different paths. Browser History: Tracking visited web pages for navigation. Memory Management: Allocating and deallocating memory in programs.
- 11. Text Editors: Supporting undo and redo functionality. Task Scheduling: Managing tasks in operating systems. Syntax Parsing: Parsing and compiling programming languages. Recursive Algorithms: Handling recursive problem-solving Call Stack in Assembly: Managing function calls in assembly language. Algorithm Implementations: Storing state during algorithm execution. Expression Conversion: Converting infix to postfix expressions. Depth-First Search: Implementing graph traversal algorithms. Expression Parsing: Breaking down complex expressions
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