Stack.docx

# Stacks ## Definition of Stacks - A stack is a linear data structure that follows the LIFO (Last In, First Out) principle. - This means that the last element added to the stack is the first one to be removed. ## Key Characteristics: - **LIFO**: Last element in is the first element out. - **Top of...

# Stacks ## Definition of Stacks - A stack is a linear data structure that follows the LIFO (Last In, First Out) principle. - This means that the last element added to the stack is the first one to be removed. ## Key Characteristics: - **LIFO**: Last element in is the first element out. - **Top of the Stack**: The point of interaction where insertion (push) and deletion (pop) operations take place. ## Applications of Stacks - A stack can be visualized as a collection of elements arranged one on top of the other, similar to a stack of coins where only the top plate is accessible. ## Applications of Stack Data Structures - Recursion - Expression Evaluation and Parsing - Depth-First Search (DFS) - Undo/Redo Operations - Browser History - Function Calls ## Applications of Stacks: ### Function Call Management (Recursion) - When a function calls another function, the current function is suspended, and the new function is executed. - The suspended function is stored on a stack, allowing control to return to it later. ### Expression Evaluation: - Stacks are used in evaluating arithmetic expressions, particularly in postfix (Reverse Polish Notation) and prefix notation. ### Undo Mechanism in Text Editors: - Each modification to the document is pushed onto a stack, and when the user undoes an action, the last operation is popped off the stack. ### Backtracking: - Stacks help in exploring possibilities in algorithms such as Depth-First Search (DFS), solving mazes, etc. ### Parenthesis Matching: - Stacks are used to ensure the correct matching of parentheses in mathematical expressions. ## Key Operations on Stack Data Structures - **Push**: Adds an element to the top of the stack. - **Pop**: Removes the top element from the stack. - **Peek**: Returns the top element without removing it. - **IsEmpty**: Checks if the stack is empty. - **IsFull**: Checks if the stack is full (in case of fixed-size arrays). ## Stack Operations - The following operations are fundamental to working with stacks: - **Push (Insert an Element onto the Stack):** - This operation adds an element to the top of the stack. - If the stack has limited capacity and is already full, a stack overflow condition may occur. - **Pop (Remove the Top Element from the Stack):** - This operation removes the top element from the stack. - If the stack is empty, a stack underflow condition occurs - **Peek (View the Top Element without Removing It):** - This operation returns the top element of the stack without removing it. ## Recursion - Recursion is a powerful tool for solving problems, especially when working with data structures like stacks. - A stack follows the LIFO (Last In, First Out) principle, meaning the last element added is the first one to be removed. - Recursion itself follows a similar process where function calls are pushed onto the call stack, and when the base case is reached, they are resolved in reverse order. ## Examples: Recursive Operations on a Stack - **Recursive Push Operation**: Recursion can be used to insert elements into the stack based on certain conditions, although the typical push operation is iterative. - For example, you can recursively add an element to the bottom of a stack.