Give big-O estimate for the number of operations (multiplication or addition) used in the following algorithm segment (ignore comparisons to check while conditions).
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t = 0
while i <= n
i = t+i
t = 2i
I don't understand how it grows (other than rather ripidly), let alone how quickly it approaches n.
Generally BIG'O notation is asymptotic analysis so it considers only average case.... so for above case 4,5 line both assignments are considered as one operation and since we are iterating n times the complexity is O(n).
I'm pretty sure the big O is actually O(log n)
Not really a proof but anyway.
If you write out the values before each iteration of the loop you get.
L - iteration number
L i t
1 1 0
2 1 2
3 3 6
4 9 18
5 27 54
6 81 162
So if n was 80 it would take 6 iterations
You can see i is growing like 3^(L-2)
So if n was 1000
1000 = 3^(L-2)
log(1000) [base 3] = L - 2
log(1000) [base 3] + 2 = L
8.287709822868152 = L
and if you ceil the answer you get L = 9
and just to check with the table
6 81 162
7 243 486
8 729 1458
9 2187 ...
The table isn't perfect but hopefully you get the main idea.
Hope this helps =)