# Can someone please explain this asymptotic analysis for me?

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## 1 Replies - 1266 Views - Last Post: 19 June 2016 - 03:02 AM

### #1 harro.rm

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# Can someone please explain this asymptotic analysis for me?

Posted 18 June 2016 - 09:16 PM

I was reading through some class materials and there was an example in the book:

```BottleOfBeer(n):
for i <-- n to i
sing "i bottles of beer on the wall, i bottles of beer"
sing "take one down, pass it around, i - 1 bottles of beer on the wall"
sing "no bottles of beer on the wall, no bottles of beer"
sing "go to the store, buy some more, n bottles of beer on the wall

```

The text says the word "beer" is sung three times in every verse... but I see only max of two. Or maybe each sing line is one verse.
Anyways, it says for BottleOfBeer(n) --> it uses 3n + 3 but doesn't give a clear explanation.

So is 3n the number of times "beer" is sang? Whats the other 3 from?

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## Replies To: Can someone please explain this asymptotic analysis for me?

### #2 Atli

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## Re: Can someone please explain this asymptotic analysis for me?

Posted 19 June 2016 - 03:02 AM

Quote

i bottles of beer on the wall, i bottles of beer
take one down, pass it around, i - 1 bottles of beer on the wall

I count three.

Quote

So is 3n the number of times "beer" is sang? Whats the other 3 from?

If N is the number of bottles you pass to the function, then the number of times the word "beer" is sung is:
```(N * 3) + 3

```

3 being the number of "beer" in each verse, times the number of verses that are sung, plus 3 for the obligatory end verse.

Another way to look at it would be:
```(N + 1) * 3

```

That number of main verses plus the end verse, times the number of "beer" references per verse.

This post has been edited by Atli: 19 June 2016 - 03:06 AM