# Problem

This function takes a number and calculates its factorial using recursion.

```python
def factorial(n):
    if n == 0:
        return 1
    else:
        return n * factorial(n-1)
```

# Solution

| Input Size | Recursions  |
| --- | --- |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |

### How does the running time increase w.r.t the input?
The number of recursions is determined by the size of the input: $N$.

### What is the time complexity?

$O(N)$

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