Question

PYTHON

List the following Big-O notations in order from fastest (1) to slowest (6) for large values of \( n \). In other words, the fastest one is assigned number 1 and the slowest one is assigned number 6 \

Answer 1

Here is the list of common Big-O notations in order from fastest (1) to slowest (6) for large values of \( n \):

1. \( O(1) \) - Constant time complexity. The algorithm's runtime remains constant regardless of the input size.

2. \( O(\log n) \) - Logarithmic time complexity. The algorithm's runtime grows logarithmically with the input size.

3. \( O(n) \) - Linear time complexity. The algorithm's runtime grows linearly with the input size.

4. \( O(n \log n) \) - Linearithmic time complexity. The algorithm's runtime grows in between linear and quadratic time.

5. \( O(n^2) \) - Quadratic time complexity. The algorithm's runtime grows quadratically with the input size.

6. \( O(2^n) \) - Exponential time complexity. The algorithm's runtime grows exponentially with the input size.

Please note that this ordering is generally applicable for standard algorithms and their time complexities, but there may be specific cases where different algorithms or optimizations can affect the actual runtime for a given problem.