1. Often mathematical functions are used to express the runtime of algorithm. You are being given five different algorithms, whose runtimes are expressed by the following functions. Each function varies with N, where N is data size.

T1(N) = N2.5, T2(N) = NlgN (lgN = log2N = log(N)/log(2) ), T3(N) = (1.25)N, T4(N) = N4 and T5(N) = NN

Arrange the algorithms from best to worst (assume N values should be sufficiently large so that you can compare different runtimes).

2. Write a C++ program to implement each of those functions, and generate a table by varying N from N = 10 to N = 100 in steps of 10 (i.e.) N = 10, 20, 30, 40 etc.

The program should output the following:

N T1(N) T2(N) T3(N) T4(N) T5(N)

10 .. .. ..

20 .. .. .. .. ..

Etc.

.. are computed values from the code.

Make sure to have the return type for each function is float and input N is integer.