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# ft\_recursive\_power

**Objective:**

Create a **recursive function** that calculates the power of a given number `nb` raised to the exponent `power`. The function should return **0** if the exponent is negative and **1** if the exponent is **0**.

**Turn-in Directory:**

ex03/

**Files to Turn In:**

ft\_recursive\_power.c

**Allowed Functions:**

None

**Prototype:**

```c
int ft_recursive_power(int nb, int power);
```

***

#### **Detailed Explanation**

The **ft\_recursive\_power** function calculates the value of `nb` raised to the power of `power` using recursion. For example:

* `2^3 = 2 * 2 * 2 = 8`
* `5^0 = 1` (any number raised to the power of 0 is 1)
* `3^-2 = 0` (negative exponents are not handled, so the function returns 0)

The function returns:

* The result of `nb^power` if `power` is a non-negative integer.
* **1** if `power` is **0**.
* **0** if `power` is negative.

***

#### **Code Implementation**

```c
int ft_recursive_power(int nb, int power)
{
    int result;

    result = nb;
    if (power < 0)  // Negative exponents are not handled
        return (0);
    if (power == 0)  // Any number raised to the power of 0 is 1
        return (1);
    else if (power > 1)  // Recursive calculation of power
        result = result * ft_recursive_power(nb, power - 1);
    return (result);
}
```

***

#### **Example Usage**

```c
#include <stdio.h>

int ft_recursive_power(int nb, int power);

int main(void)
{
    printf("2^3: %d\n", ft_recursive_power(2, 3));  // Output: 8
    printf("5^0: %d\n", ft_recursive_power(5, 0));  // Output: 1
    printf("3^-2: %d\n", ft_recursive_power(3, -2)); // Output: 0
    printf("10^5: %d\n", ft_recursive_power(10, 5)); // Output: 100000

    return 0;
}
```

***

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

1. **Power of 0**:
   * Input: `5^0` → Returns **1** (any number raised to the power of 0 is 1).
2. **Negative Power**:
   * Input: `3^-2` → Returns **0** (negative exponents are not handled).
3. **Positive Power**:
   * Input: `2^3` → Returns **8** (`2 * 2 * 2 = 8`).
4. **Large Power**:
   * Input: `10^5` → Returns **100000** (`10 * 10 * 10 * 10 * 10 = 100000`).

***

#### **Limitations of ft\_recursive\_power**

1. **No Handling of Negative Exponents**:
   * The function does not handle negative exponents and returns **0** for such cases.
2. **No Handling of Overflows**:
   * The function does not handle integer overflows. For large values of `nb` and `power`, the result may exceed the range of an `int`, leading to undefined behavior.
3. **Recursion Depth**:
   * For very large values of `power`, the function may cause a stack overflow due to excessive recursion depth.

***

#### **How It Works**

1. **Base Case 1 (Negative Power)**:

   * If `power` is negative, the function immediately returns **0** (negative exponents are not handled).

   ```c
   if (power < 0)
       return (0);
   ```
2. **Base Case 2 (Power of 0)**:

   * If `power` is **0**, the function returns **1** (since any number raised to the power of 0 is 1).

   ```c
   if (power == 0)
       return (1);
   ```
3. **Recursive Case**:

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

   ```c
   else if (power > 1)
       result = result * ft_recursive_power(nb, power - 1);
   ```
4. **Return the Result**:

   * Once the recursion ends, the function returns the value of `result`, which is `nb^power`.

   ```c
   return (result);
   ```

***

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

1. **Recursive Approach**:
   * The function uses recursion to calculate the power, calling itself with a smaller value of `power` until it reaches the base case.
2. **Base Cases**:
   * The base cases handle edge cases like `power = 0` and `power < 0`.
3. **Efficiency**:
   * The time complexity is **O(power)**, where `power` is the exponent. Each recursive call reduces `power` by 1 until it reaches **0**.

***

#### **Best Practices**

1. **Input Validation**:
   * Always check for invalid inputs (e.g., negative exponents) to avoid unexpected behavior.
2. **Edge Cases**:
   * Test edge cases like `power = 0`, `power < 0`, and large values of `power` to ensure the function behaves as expected.
3. **Overflow Handling**:
   * Consider adding overflow handling for large inputs, though it is not required in this exercise.


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