Consider the following C function.int fun(int n) { int i, j; for(i = 1; i <= n; i++) { for(j = 1; j < n; j += i) { printf(" %d %d",i,j); } } }Time complexity of fun in terms of $\Theta$ notation is

Let us analyze the number of times the printf statement is executed:

1. The outer loop runs for $i = 1, 2, 3, \dots, n$.

2. For a fixed value of $i$, the inner loop starts at $j = 1$ and increases $j$ by $i$ at each step until $j < n$.

3. The number of iterations of the inner loop for a given $i$ is:

4. Summing the inner loop executions over all values of $i$ from $1$ to $n$:

5. The summation $\sum_{i=1}^{n} \frac{1}{i}$ is the harmonic series $H_n$, which is $\Theta(\log n)$.

Therefore, option C is correct.