Algorithms | Analysis of Algorithms | Question 2

What is the time complexity of fun()? 

C

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

(A)

Theta (n)

(B)

Theta (n²)

(C)

Theta (n*log(n))

(D)

Theta (n*(log(n*log(n))))

Answer: (B)
Explanation:

The time complexity can be calculated by counting the number of times the expression “count = count + 1;” is executed. The expression is executed 0 + 1 + 2 + 3 + 4 + …. + (n-1) times.

Time complexity = Theta(0 + 1 + 2 + 3 + .. + n-1) = Theta (n*(n-1)/2) = Theta(n²)

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