Assume that an O(log2N) algorithm runs for 10 milliseconds when the input size (N) is 32. What input size makes the algorithm run for 14 milliseconds

An input size of N = 128 makes the algorithm run for 14 milliseconds

Explanation:

O(log2N)

This means that the running time for an algorithm of length N is given by:

In which C is a constant.

Runs for 10 milliseconds when the input size (N) is 32.

This means that

So

Since

Then

Thus:

What input size makes the algorithm run for 14 milliseconds

N for which . So

An input size of N = 128 makes the algorithm run for 14 milliseconds

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