A stack is a linear data structure that follows the LIFO (last-in, first-out) principle for adding and removing items. It allows push and pop operations at one end called the top. Common stack operations include push to add an item to the top, pop to remove the top item, peek to view the top item without removing it, and functions to check if the stack is empty or full. Stacks have applications in expression evaluation, backtracking, recursion, undo/redo operations, and graph searches like depth-first search. Recursive functions work by calling themselves during execution and are useful for implementing stacks.

1. Stack ADT

2. • A stack is a data structure that stores a linear collection of items
with access limited to a last-in first-out (LIFO) order.
• Adding and removing items is restricted to one end known as
the top of the stack.
Stack

3. • Putting an item on top of the stack is called push.
• Removing an item is called pop.
LIFO Principle of Stack

4. • Int stk[10], top=-1
Void Push( stk[10], int n)
Int pop(stk[10])
Int peep(stk[10])
Bool isFull() // overflow
If(top>=n-1) //overflow
Bool isEmpty() //underflow
If(top<=-1) //underflow

5. • Push (item): Add an given item to the top of a stack.
• Pop(): Removes and returns the top item of the stack, if the
stack is not empty. The next item on the stack becomes the
new top item.
• Stack(): Creates a new empty stack.
• IsEmpty(): Check if the stack is empty or not. Return a
boolean value.
• IsFull(): Check if the stack is full. Return a boolean value.
• Peek(): Get the value of the top element without removing
it.
• Length(): Returns the number of items in the stack.
Stack: Basic Operations

6. 1. A pointer called TOP is used to keep track of the top element in the stack.
2. When initializing the stack, we set its value to -1 so that we can check if the stack is
empty by comparing TOP == -1.
3. On pushing an element, we increase the value of TOP and place the new element in
the position pointed to by TOP.
4. On popping an element, we return the element pointed to by TOP and reduce its
value.
5. Before pushing, we check if the stack is already full
6. Before popping, we check if the stack is already empty
Working of Stack Data Structure

7. Example: Stack Operations

8. Implementing the Stack: Using Array in C

9. Implementing the Stack: Using Single Linked List

10. • String reversal.
• Expression evaluation/conversion.
• Recursion.
• DFS(Depth First Search).
• UNDO/REDO.
• Backtracking.
Applications of Stack

11. • The process in which a function calls itself directly or indirectly
is called recursion.
• A recursive function is a function that calls itself during its
execution.
• Best example of a recursive function – factorial.
• n! = n * (n-1)!
Working of Recursive Function
Recursion and Recursive Function

12. Sum of Natural Numbers Using Recursion
Example of a Recursive Function
Output

13. Working of a Recursive Sum Function