I provided the solution for the question but i want to know the reason for this
ID: 3004099 • Letter: I
Question
I provided the solution for the question but i want to know the reason for this order .... here is the typical growth late in order for the function, i want you to follow it by explaining it to me
Function ..... Name
c .... constant
log N .... logarithmic
log2 N ..... log- sqauared
N ..... linear
N log N
N2 ....... Quadratic
N3 ....... Cubic
2N ...... exponential
Order the following functions by growth rate: N, N, N1.5, N2, N log N, N log log N, N log2 N, N log(N2), 2/N, 2N, 2N/2, 37, N2 logN, N3. Indicate which functions grow at the same rate.
Solution: 2/N, 37, N, N, N log log N, N log N, N log(N2), N log2 N, N1.5, N2, N2 log N, N3, 2N/2, 2N . N log N and N log(N2) grow at the same rate.
Explanation / Answer
The order of the following function is decided by checking the behavior of the program or code at high value of input when N=10,0000
At that high number of inputs, which function will be the fastest and which will be the slowest determine the benefit of using a particular algorithm
Order in the above List
2/N, 37, (N)^(0,5), N, N log log(N), N log(N), Nlog(N^2), N log^2(N), N^(1,5), N^2, N^2log(N), N^3, 2^(N/2), 2^(N)
2/N is inversely proportional to N, hence it will decay down very fast as the value of N increases
then comes the constant 37 followed by N^(0.5) and so on
N log(N) and N log(N^2)
N log(N^2) = N * 2* log(N) = 2Nlog(N), hence the growth rate of both the function is proportional to Nlog(N)
ask still in case of any doubts