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Foo function

Recently I took the test for Computer Science and I got a Level 3... I couldn't figure out the Level 4 Question and I found it quite interesting and could anyone explain me how it works..?

How many '1' s are printed out when you call foo(5)?

   # python code start
   def foo(n):
        count = 1
        if n > 0:
            count += foo(n - 1) + foo(n - 1)
        print '1'
        return count

Note by Muzaffar Ahmed
2 years, 11 months ago

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the answer is exactly 28 Shivam Banka · 2 years, 4 months ago

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Have you tried doing it for \(n=1\) and \(n=2\)? Josh Silverman Staff · 2 years, 11 months ago

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@Josh Silverman Nope.. I'm not so good at programming so can you please explain me this one from the beginning..? Muzaffar Ahmed · 2 years, 11 months ago

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@Muzaffar Ahmed If you call foo(1), it is greater than zero and, so, the function passes the if statement. It the adds 2*foo(0) (which needs to be called) to count and prints 1.

When it calls foo(0), 0 is not greater than 0 and, so, the if statement is not passed. The function then runs the code that appears after the if statement, where it returns the current value of count which is 1 and prints 1. However, foo(0) was called twice (count += foo(0) + foo(0)), so it prints 1 twice.

So, for foo(1), we print 1 a total three times.

If we called foo(2), this same kind of branching process would occur. I.e., we'd print 1, then we'd call foo(1) twice, which would print 1 twice, then for each foo(1), we'd call foo(0) twice (a total of 4 foo(0)) calls, which would print 1 four times. Making a total of 7. In general, calling foo(n), we print 1 a total of \(2^{n+1}-1\) times. Josh Silverman Staff · 2 years, 11 months ago

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@Josh Silverman Ohh.. I got it.. ! Thanks bro :-) Muzaffar Ahmed · 2 years, 11 months ago

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@Muzaffar Ahmed No problem. It was foon to explain. Josh Silverman Staff · 2 years, 11 months ago

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@Josh Silverman Lol :D Muzaffar Ahmed · 2 years, 11 months ago

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:) There's a trick. Zi Song Yeoh · 2 years, 11 months ago

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@Zi Song Yeoh So tell me please :) I know we can directly execute it but I want to understand how it works.. Muzaffar Ahmed · 2 years, 11 months ago

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