Question

How much time does an algorithm take to solve a problem of size n if this algorithm uses 2n^2 + 2^n operations, each requiring 10^-9 seconds, with these values of n?

a. 10 b. 20 c. 50 d. 100

Answer 1

The algorithm takes approximately 1.224 microseconds to solve a problem of size 10.

Step-by-step explanation:

An algorithm that uses 2n^2 + 2^n operations will take a certain amount of time to solve a problem of size n. Each operation requires 10^-9 seconds.

To find the total time taken, we need to substitute the given values of n into the expression for the number of operations and then multiply by the time taken for each operation.

Let's substitute the given values into the expression:
For n = 10, the expression becomes 2*(10^2) + 2^10 = 200+1024 = 1224.

Now, let's calculate the total time taken:
Time taken = 1224 * 10^-9 seconds = 1.224 * 10^-6 seconds.

Therefore, the algorithm takes approximately 1.224 microseconds to solve a problem of size 10.