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Problem 29 Project Euler Solution with python

Distinct powers

Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:

22=4, 23=8, 24=16, 25=32
32=9, 33=27, 34=81, 35=243
42=16, 43=64, 44=256, 45=1024
52=25, 53=125, 54=625, 55=3125
If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?

This problem doesn't require a lot of background work, just a bit of basics in python can solve this problem. I think you should read the following two articles before seeing the program. They are optional of course.

I think there is no need for any algorithm because we just have used a very direct and basic solution.

Program 

In this program we have used sets at the end even though sets are unordered lists because we are not actually concerned about the order in which the numbers are arranged but we are concerned about the length of the iterable. You can arrange the order if you want to. The solution will be the same even if you will arrange the order or not.
 
You might be wondering with a few questions after seeing the program. 

Why did I use lists instead I could have just used sets?
When I tried sets, instead of lists I found that there was no considerable improvement in the performance, may be because we are just looping for small range. I have sticked myself to lists so that the code is readable and easy to understand for each and everyone.

Why did I use append instead of extend?
When I tried extend instead of append I found that the execution time increased. This might be because of converting each and iterable to a list to add it. I am not sure why, but you can tell it to me if you know why. 

Why did I use '**' instead of using pow()?
Again I have seen same execution time for both of these methods and I have sticked myself to using the more familiar '**' instead of pow().

 Guys I am writing what I have seen on my computer. This might not be the case on your computer. I suggest you check these on your computer and you can comment your experience in the comment box below. Please do include the reason in the comment if you know.

Discussions are welcome.

You can download the source code from Github Gist pep29.py

Output


Summary

I am not bothered about the performance of the program because it is running under 1/50 of a second. Also it didn't take a lot of time for me to solve this problem. This may be because of using python for programming the solution, which already has a lot of in-built tools for over coming some of the common problems. 

If you have any doubt or didn't understand anything then feel free to comment in the comment box below and I will be glad to help you as soon as possible.

Please feel free to comment if you have found any typo or have a better solution or a different program or any suggestion. 

 You can also contact me.

Thank you. Have a nice day😃.
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