**Recursion** in C programming is a technique where a function calls itself directly or indirectly to solve a problem. Recursive functions are typically used to break down complex problems into simpler sub-problems. This method can be particularly effective for tasks that have a repetitive nature, such as calculating factorials, navigating trees, and solving puzzles.

### Key Concepts of Recursion

**Base Case**:- Every recursive function must have a base case (or termination condition) that stops the recursion. Without a base case, the function will call itself indefinitely, leading to a stack overflow.

**Recursive Case**:- This part of the function contains the logic that breaks the problem down into smaller instances of the same problem, leading to the eventual base case.

**Stack Memory**:- Each time a function calls itself, a new instance of the function is pushed onto the call stack. This stack keeps track of each function call, its parameters, and local variables. Once the base case is reached, the functions return and are popped off the stack in the reverse order of their calls.

### Example of a Recursive Function

Let's look at a classic example of recursion: calculating the factorial of a number.

#### Factorial Example

The factorial of a non-negative integer $n$ is the product of all positive integers less than or equal to $n$. It's defined as:

- $n! = n \times (n-1)!$ for $n > 0$
- $0! = 1$ (base case)

Here’s how you can implement this in C:

```
#include <stdio.h>
// Recursive function to calculate factorial
int factorial(int n) {
// Base case
if (n == 0) {
return 1; // 0! is 1
} else {
// Recursive case
return n * factorial(n - 1); // n! = n * (n-1)!
}
}
int main() {
int number;
printf("Enter a non-negative integer: ");
scanf("%d", &number);
if (number < 0) {
printf("Factorial is not defined for negative numbers.\n");
} else {
printf("Factorial of %d is %d\n", number, factorial(number));
}
return 0;
}
```

### Explanation of the Example

**Function Definition**:- The function
`factorial`

takes an integer $n$ as input and checks for the base case where $n$ is`0`

. If so, it returns`1`

. - If $n$ is greater than
`0`

, the function calls itself with $n-1$ and multiplies the result by $n$.

- The function
**Base Case**:- The base case here is
`if (n == 0) return 1;`

. This prevents infinite recursion and stops the function from calling itself indefinitely.

- The base case here is
**Recursive Case**:- The line
`return n * factorial(n - 1);`

is where the recursion happens. It reduces the problem size until it eventually reaches the base case.

- The line
**User Input**:- In the
`main`

function, the user is prompted to enter a non-negative integer, and the factorial function is called with this value. If the input is negative, a message is displayed stating that the factorial is not defined for negative numbers.

- In the

### Advantages of Recursion

**Simplicity**: Recursive solutions can be more straightforward and easier to read than iterative solutions for problems that naturally fit a recursive approach (like tree traversals).**Reduced Code Size**: Recursion can often lead to less code compared to an equivalent iterative solution.

### Disadvantages of Recursion

**Performance**: Recursive functions can be less efficient due to the overhead of multiple function calls and the use of stack memory. Each call adds a new layer to the call stack, which can lead to stack overflow for deep recursions.**Memory Usage**: Each recursive call uses memory on the stack, which can lead to increased memory usage compared to iterative solutions.

### Conclusion

Recursion is a powerful programming concept that allows functions to solve problems by calling themselves. It’s crucial to define a clear base case to prevent infinite loops. While recursion can simplify code for certain problems, it’s essential to consider the potential performance impacts and use it judiciously. Understanding recursion is fundamental for advanced programming techniques, particularly in algorithms and data structures like trees and graphs.