Notes on Stacks
Introduction:
Stacks are an important data structure in computer science that follow the Last-In-First-Out
(LIFO) principle. They provide a simple and efficient way to manage data by allowing operations
like push (insertion) and pop (removal) to be performed on the top of the stack. This set of notes
will provide an overview of stacks, their operations, implementation, and common applications.
1. Definition:
- A stack is an ordered collection of elements where insertion and deletion occur at only one
end, known as the top of the stack.
- The last element inserted is the first one to be removed, hence the Last-In-First-Out (LIFO)
property.
2. Stack Operations:
- Push: Adds an element to the top of the stack.
- Pop: Removes and returns the topmost element from the stack.
- Peek (or Top): Returns the value of the topmost element without removing it.
- IsEmpty: Checks if the stack is empty.
- Size: Returns the number of elements in the stack.
3. Stack Implementation:
- Array-based implementation: In this approach, a fixed-size array is used to store the stack
elements. The top of the stack is tracked using an index variable.
- Linked list-based implementation: Here, a linked list data structure is used, where each
element (node) contains the value and a reference to the next node.
4. Time Complexity:
- Push, Pop, Peek, IsEmpty, and Size operations have a time complexity of O(1) in both array-
based and linked list-based implementations.
5. Applications of Stacks:
- Function call stack: Stacks are used by programming languages to manage function calls and
their local variables.
- Expression evaluation: Stacks can be used to evaluate arithmetic expressions by converting
them into postfix notation and using a stack to store intermediate results.
- Undo/Redo functionality: Stacks can be employed to implement undo and redo operations in
various applications.
- Backtracking: Stacks are useful in backtracking algorithms, where the state of the search is
stored and restored as needed.
- Parsing and syntax analysis: Stacks are used in compilers and interpreters to check the
correctness and structure of programming language syntax.
6. Stack Overflow and Underflow:
Introduction:
Stacks are an important data structure in computer science that follow the Last-In-First-Out
(LIFO) principle. They provide a simple and efficient way to manage data by allowing operations
like push (insertion) and pop (removal) to be performed on the top of the stack. This set of notes
will provide an overview of stacks, their operations, implementation, and common applications.
1. Definition:
- A stack is an ordered collection of elements where insertion and deletion occur at only one
end, known as the top of the stack.
- The last element inserted is the first one to be removed, hence the Last-In-First-Out (LIFO)
property.
2. Stack Operations:
- Push: Adds an element to the top of the stack.
- Pop: Removes and returns the topmost element from the stack.
- Peek (or Top): Returns the value of the topmost element without removing it.
- IsEmpty: Checks if the stack is empty.
- Size: Returns the number of elements in the stack.
3. Stack Implementation:
- Array-based implementation: In this approach, a fixed-size array is used to store the stack
elements. The top of the stack is tracked using an index variable.
- Linked list-based implementation: Here, a linked list data structure is used, where each
element (node) contains the value and a reference to the next node.
4. Time Complexity:
- Push, Pop, Peek, IsEmpty, and Size operations have a time complexity of O(1) in both array-
based and linked list-based implementations.
5. Applications of Stacks:
- Function call stack: Stacks are used by programming languages to manage function calls and
their local variables.
- Expression evaluation: Stacks can be used to evaluate arithmetic expressions by converting
them into postfix notation and using a stack to store intermediate results.
- Undo/Redo functionality: Stacks can be employed to implement undo and redo operations in
various applications.
- Backtracking: Stacks are useful in backtracking algorithms, where the state of the search is
stored and restored as needed.
- Parsing and syntax analysis: Stacks are used in compilers and interpreters to check the
correctness and structure of programming language syntax.
6. Stack Overflow and Underflow:
