Question

Given that f(n) = n³ 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(log n)

Answer 1

The time complexity of f(n) = n³ is O(n³).

Step-by-step explanation:

The time complexity of a function is a measure of how the running time of the function grows as the input size increases. In this case, the function f(n) = n³, where n represents the size of the input.

Since each bit operation is carried out in 10–11 seconds, we can assume that each multiplication operation in the function takes the same amount of time. Therefore, the time complexity of f(n) can be determined by counting the number of multiplication operations that need to be performed.

For each value of n, there are n multiplications needed to calculate f(n). So, the time complexity of f(n) is O(n³).