# A maths algorithm question (pseudo code)

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#1
Hi all, I came to this question which I have no idea what it meant to do. It's would be great if anybody can help out here please! I need to know what this program does. It is written in pseudo code. (I'm sorry for the bad layout)
-----------
Input: an integer k >= 0
Output: ??

1) X <- 0
2) Y <- 1
3) for i <- 1 to k do
4) c <- x + y
5) x <- y
6) y <- c
7) return x
--------
Here is my working out, a short explanation of this is if k = 7, the program will loops 7 times until it worked out that x = 13.

k <- 1, 2, 3, 4, 5, 6, 7, 8...
c <- 1, 2, 3, 5, 8, 13, 21, 34...
x <- 1, 1, 2, 3, 5, 8, 13, 21...
y <- 1, 2, 3, 5, 8, 13, 21, 34...

I can see the pattern but I don't know what they represent, does anyone can explain what it is?

Thank you!
0
5 years ago
#2
it computes the first k terms of the fibonacci sequence and it has exponential complexity.
1
#3
I'll be damn, thanks very much!
0
5 years ago
#4
It loops 1 to k and does a constant amount of work each iteration.. Where did you get exponential from?
1
5 years ago
#5
I think exponential complexity would have applied had it been done recursively and without memoization, in this case it is linear.
0
5 years ago
#6
Jooooshy is correct. The complexity of the program is linear in input k.
0
5 years ago
#7
(Original post by thecsstudent)
I think exponential complexity would have applied had it been done recursively and without memoization, in this case it is linear.
(Original post by Jooooshy)
It loops 1 to k and does a constant amount of work each iteration.. Where did you get exponential from?
I think you guys are right; linear complexity for k loops makes sense. I read on stackoverflow that fibonacci has a worst-case complexity of O(2^n) http://stackoverflow.com/questions/3...nacci-sequence.
1
5 years ago
#8
That's a nice answer on SO
0
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