e investigations we determined that the program input size can be varied in a wide range and for N-bit input the program result is also always N – Bit long. Additionally we found that the program working time depends significantly on input length N, especially when N is greather than 10- 15 . Our test also revealed, that the program working time depends only on input length ,not the input itself.
During our tests, we fixed the following working times (with an accuracy of one hundredth of a second)
N = 2 – 16.38 seconds
N = 5 – 16.38 seconds
N = 10 – 16.44 seconds
N = 15 – 18.39 seconds
N = 20 – 1 minute 4.22 seconds
We also planned to test the program for N = 25 and N = 30, but for both cases the program didn’t finish within half and hour was forced to terminate it. Finally, we decided for N = 30 to not terminate the program,but to wait a little bit longer.The result was 18 hours 16 minutes 14.62 seconds . We repeated the test for N = 30 and it gave us exactly the same result, more than 18 hours.
a) Find the program working times for the following three cases N = 25, N = 40 and N = 50.
b) Explain your result and solution process.