Question

A method is O(Nlog₂N). It takes 10 seconds for the method to run when N = 1,000,000. What is the expected time for the method to run when N = 4,000,000? (Please label and explain steps for clarity)

Answer 1

To find the expected time for the method to run when N = 4,000,000, we can use the fact that the method has a time complexity of O(Nlog₂N). By substituting the given values into the equation and solving, we can find the expected time.

Step-by-step explanation:

To determine the expected time for the method to run when N = 4,000,000, we can use the fact that the method is O(Nlog₂N). This means that the running time of the method is proportional to N multiplied by the logarithm of N to the base 2. Let's denote the running time as T.

Given:

• N = 1,000,000
• T = 10 seconds

We can set up the equation:

T = C × Nlog₂N

where C is a constant factor.

Substituting the given values:

10 = C × 1,000,000 × log₂(1,000,000)

Solving this equation gives C ≈ 10 ÷ (1,000,000 × log₂(1,000,000)).

To find the expected time for N = 4,000,000:

T' = C × 4,000,000 × log₂(4,000,000)

Substituting C and simplifying will yield the expected time when N = 4,000,000.