# Problem 

This loop keeps running until the array's length reaches 1. Calculate the time complexity.

```python
def loop_until_one(arr):
    while len(arr) > 1:
        arr = arr[:len(arr)//3] ## divides array by 3
```

# Solution

| Input Size | Steps  |
| --- | --- |
| 3 | 1 |
| 9 | 2 |
| 27 | 3 |

### How does the running time increase w.r.t the input?

The running time's rate of increase is $log_3N$. The number of steps reflects how many times the input size can be divided by 3.

### What is the time complexity?

$O(logN)$

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