I want to find the Time Complexity of the following code

Question

Here Nested loops are used, the time complexity of outer loop will be O(n) but how to calculate the complexity of inner loop as it depends on the value of i

Answer 1

Both inner and outer loop are $O(n)$, and the total time complexity is $O(n^2)$. This is because the inner loop will make at most $2*n$ steps which is clearly $O(n)$.

The loop will make $$2\cdot1 + 2\cdot 2 + 2\cdot 3 + 2\cdot 4 + \dots + 2 \cdot n = \\ 2(1 + 2 + \dots + n) = \\ 2(\frac{n\cdot(n+1)}{2}) = \\n \cdot (n+1) = O(n^2)$$