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# ft\_recursive\_factorial

**Objective:**

Create a **recursive function** that calculates the factorial of a given number. The function should return **0** if the input is invalid (i.e., negative numbers).

**Turn-in Directory:**

ex01/

**Files to Turn In:**

ft\_recursive\_factorial.c

**Allowed Functions:**

None

**Prototype:**

```c
int ft_recursive_factorial(int nb);
```

***

#### **Detailed Explanation**

The **ft\_recursive\_factorial** function calculates the factorial of a given number `nb` using recursion. The factorial of a number `n` is defined as the product of all positive integers less than or equal to `n`. For example:

* Factorial of 5: `5! = 5 * 4 * 3 * 2 * 1 = 120`
* Factorial of 0: `0! = 1`

The function returns:

* The factorial of `nb` if `nb` is a non-negative integer.
* **0** if `nb` is negative (invalid input).

***

#### **Code Implementation**

```c
int ft_recursive_factorial(int nb)
{
    if (nb < 0)  // Handle invalid input (negative numbers)
        return (0);
    if (nb <= 1)  // Base case: factorial of 0 or 1 is 1
        return (1);
    return (nb * ft_recursive_factorial(nb - 1));  // Recursive case
}
```

***

#### **Example Usage**

```c
#include <stdio.h>

int ft_recursive_factorial(int nb);

int main(void)
{
    printf("Factorial of 5: %d\n", ft_recursive_factorial(5));  // Output: 120
    printf("Factorial of 0: %d\n", ft_recursive_factorial(0));  // Output: 1
    printf("Factorial of -3: %d\n", ft_recursive_factorial(-3)); // Output: 0
    printf("Factorial of 10: %d\n", ft_recursive_factorial(10)); // Output: 3628800

    return 0;
}
```

***

#### **Edge Cases to Consider**

1. **Negative Numbers**:
   * Input: `-3` → Returns **0** (invalid input).
2. **Zero**:
   * Input: `0` → Returns **1** (by definition, `0! = 1`).
3. **Positive Numbers**:
   * Input: `5` → Returns **120** (`5! = 120`).
4. **Large Numbers**:
   * Input: `10` → Returns **3628800** (`10! = 3628800`).

***

#### **Limitations of ft\_recursive\_factorial**

1. **No Handling of Overflows**:
   * The function does not handle integer overflows. For large values of `nb`, the result may exceed the range of an `int`, leading to undefined behavior.
2. **Recursion Depth**:
   * For very large values of `nb`, the function may cause a stack overflow due to excessive recursion depth.

***

#### **How It Works**

1. **Base Case 1 (Invalid Input)**:

   * If `nb` is negative, the function immediately returns **0**.

   ```c
   if (nb < 0)
       return (0);
   ```
2. **Base Case 2 (Factorial of 0 or 1)**:

   * If `nb` is **0** or **1**, the function returns **1** because the factorial of 0 and 1 is 1.

   ```c
   if (nb <= 1)
       return (1);
   ```
3. **Recursive Case**:

   * For any positive integer greater than 1, the function calls itself with `nb - 1` and multiplies the result by `nb`.

   ```c
   return (nb * ft_recursive_factorial(nb - 1));
   ```

***

#### **Key Points to Remember**

1. **Recursion**:
   * The function uses recursion to calculate the factorial, which means it calls itself with a smaller value of `nb` until it reaches the base case.
2. **Base Cases**:
   * The base cases ensure the recursion terminates correctly and handle edge cases like `0` and negative numbers.
3. **Efficiency**:
   * The time complexity is **O(n)**, where `n` is the value of `nb`. Each recursive call reduces `nb` by 1 until it reaches the base case.

***

<br>


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