Why the executing time of functions not constant?

Question

I read my university class theoretically the order of growth of functions and tried implementing it practically at home. Although the order of growth turned out to be exact the same as in textbooks but their executing time changes with every single time I execute the program. Why is that?

Source Code

import time
import math
from tabulate import tabulate
n=eval(input("Enter the value of n: "));
t1=time.time()
a=12
t2=time.time()
A=t2-t1
t3=time.time()
b=n
t4=time.time()
B=t4-t3
t5=time.time()
c=math.log10(n);
t6=time.time()
C=t6-t5
t7=time.time()
d=n*math.log10(n);
t8=time.time()
D=t8-t7
t9=time.time()
e=n**2
t10=time.time()
E=t10-t9
t11=time.time()
f=2**n
t12=time.time()
F=t12-t11

print(tabulate([['constant',a,A], ['n',b,B], ['logn',c,C], ['nlogn',d,D], ['n**2',e,E], ['2**n',f,F]], headers=['Function', 'Value', 'Time']))
templist= [A,B,C,D,E,F]
print("The time order in acsending order is: ", sorted(templist,key=int)) 

First Execution

naufil@naufil-Inspiron-7559:~/Desktop/python$ python3 time_order.py
Enter the value of n: 100
Function              Value         Time
----------  ---------------  -----------
constant       12            2.14577e-06
n             100            1.43051e-06
logn            2            4.1008e-05
nlogn         200            3.57628e-06
n**2        10000            3.33786e-06
2**n            1.26765e+30  3.8147e-06
The time order in acsending order is:  [2.1457672119140625e-06, 1.430511474609375e-06, 4.100799560546875e-05, 3.5762786865234375e-06, 3.337860107421875e-06, 3.814697265625e-06]

Second Execution

naufil@naufil-Inspiron-7559:~/Desktop/python$ python3 time_order.py
Enter the value of n: 100
Function              Value         Time
----------  ---------------  -----------
constant       12            2.14577e-06
n             100            1.19209e-06
logn            2            4.64916e-05
nlogn         200            4.05312e-06
n**2        10000            3.33786e-06
2**n            1.26765e+30  3.57628e-06
The time order in acsending order is:  [2.1457672119140625e-06, 1.1920928955078125e-06, 4.649162292480469e-05, 4.0531158447265625e-06, 3.337860107421875e-06, 3.5762786865234375e-06]

Answer 1

As other comments and answers have rightly pointed out, the reason for the difference in execution times that you observe come from the way operating systems work. But doing rigorous measures is a complicated matter, so let me elaborate a bit more though and give you pointers to where you should maybe direct your experimentation.

What your OS does behind your back

You can see the OS as a conductor and programs as instrument players, and imagine there are only so many instruments that can play at the same time. The conductor must therefore choose at each time who should play, also making sure nobody is frustrated in the end! Same-wise, the OS is therefore constantly in charge of choosing what programs to execute, meaning what program to dedicate CPU time. The number of programs (or rather processes) that can be executed at the same time is usually limited by the number of cores in your processor.

In practice, the way that OS chooses what to execute is a very complex and fascinating subject, which relies on experimentation-backed heuristics. (Read more here). What you have to understand, is that there is hardly any way for you to alter this behavior, and none to guarantee the same execution time between two calls.

Using linux's time command

Calling python's time like you do measures the physical time elapsed between two calls, so because of what we have said, you don't only measure time spent on your program's execution. If you want to have a better a sense of what time the OS actually dedicated to your program, you can use the linux command time. The user time, will give you the actual CPU time dedicated to the execution of your program. Check out this thread for more info. But understand that this time as well is subject to oscillations!

What wisdom are you trying to draw from your measurements?

Finally, you should ask yourself if the exact time is really what you want. Do you care about the value? or do you want to exhibit behaviors?

Usually what is done to measure performances, is averaging the execution times of repeated calls. This way, the effects that pertain to the OS's business should be averaged out. (You can see that as building an unbiased estimator for a random process). From what I understand, you are trying to show difference in execution times for algorithms with different complexity. So the actual execution time is not so relevant, what is, is the relative order. That is why averaging multiple calls will reduce the variance of the observation and you will be able to make stronger statements as to the relative execution times.

Answer 2

You should address this question to your operating system. What else runs on your computer? List the various processes and see how many there are; all it takes is a process or even a context swap to alter your execution time. Among other things, calling time.time can invoke such a switch, as this is a call to a system process.

It also depends on what system support routines are already loaded when you call them -- many of those calls being implicit or secondary. If you need to allocate more memory for a particular instruction because another process took the last of your RAM and then swapped out ... well, you get the idea, I hope.