Question

If f(n) = 1000n² and each bit operation is carried out in 10⁻¹¹ seconds, what is the time complexity of f(n)?

1) O(n)
2) O(n²)
3) O(n³)
4) O(2ⁿ)

Answer 1

The function f(n) = 1000n² has a time complexity of O(n²), where each bit operation time is a constant factor and does not change the time complexity class. So, the correct answer is option 2.

Step-by-step explanation:

The time complexity of a function, in this case, f(n) = 1000n², describes how the number of operations in an algorithm scales with the size of the input. Since the function scales with the square of the input size n, its time complexity is O(n²).

Each bit operation takes 10⁻¹¹ seconds, but this is a constant factor that doesn't affect the overall time complexity class, which remains O(n²). Therefore, the answer is 2) O(n²).