Algorithms | Analysis of Algorithms | Question 1

What is time complexity of fun()? 

C

int fun(int n)
{
    int count = 0;
    for (int i = n; i > 0; i /= 2)
        for (int j = 0; j < i; j++)
            count += 1;
    return count;
}

(A)

O(n²)

(B)

O(n*log(n))

(C)

O(n)

(D)

O(n*log(n*Log(n)))

Answer: (C)

Explanation:

For an input integer n, the innermost statement of fun() is executed following times. 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) 

The value of count is also n + n/2 + n/4 + .. + 1

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