Space time complexity Quiz Q1

#1

Quiz question 1:

Find the time complexity of the given code.

int count = 0;
for (int i = N; i > 0; i /= 2)
for (int j = 0; j < i; j++)
count++;

The soln itself says that the innermost loop will take n + n/2 + n/4 +…1

So how is the ans O(N) ?

#2 
 n + n/2 + n/4 + n/8 + ... + 1  
= n * (1 + 1/2 + 1/4 + 1/8 + ...) 
 = 2n

n + n/2 + n/4 + … 1

So time complexity T(n) can be written as

T(n) = O(n + n/2 + n/4 + … 1) = O(n)

i hope this helps
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if you have more doubts regarding this feel free to ask

#3

please mark doubt as resolved

#4

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