Question

Write the following asymptotic efficiency classes in increasing order of magnitude.

O(n²), O(2ⁿ), O(1), O(n lg n), O(n), O(n!), O(n³), O(lg n), O(n^n), O(n²Ig n)

Answer 1

The asymptotic efficiency classes in increasing order are O(1), O(lg n), O(n), O(n lg n), O(n²), O(n² lg n), O(n³), O(2ⁿ), O(n!), and O(n^n), representing how the time complexity of algorithms increases with larger inputs.

Step-by-step explanation:

The question concerns ordering asymptotic efficiency classes, which are used in computer science to describe the time complexity of an algorithm as its input size tends to infinity. In increasing order of magnitude, the correct sequence is:

1. O(1) - Constant time complexity
2. O(lg n) - Logarithmic time complexity
3. O(n) - Linear time complexity
4. O(n lg n) - Linearithmic time complexity
5. O(n²) - Quadratic time complexity
6. O(n² lg n) - Quadratic times logarithmic time complexity
7. O(n³) - Cubic time complexity
8. O(2ⁿ) - Exponential time complexity
9. O(n!) - Factorial time complexity
10. O(n^n) - Exponential time complexity, where the base is the variable itself

Understanding these classes is crucial for assessing the efficiency of different algorithms and making decisions about which algorithm to use for a particular problem.