# Time Complexity of Loop with Powers

• Difficulty Level : Medium
• Last Updated : 30 Dec, 2021

What is the time complexity of the below function?

## C++

 `void` `fun(``int` `n, ``int` `k)``{``    ``for` `(``int` `i = 1; i <= n; i++)``    ``{``        ``int` `p = ``pow``(i, k);``        ``for` `(``int` `j = 1; j <= p; j++)``        ``{``            ``// Some O(1) work``        ``}``    ``}``}` `// This code is contributed by Shubham Singh`

## C

 `void` `fun(``int` `n, ``int` `k)``{``    ``for` `(``int` `i = 1; i <= n; i++)``    ``{``        ``int` `p = ``pow``(i, k);``        ``for` `(``int` `j = 1; j <= p; j++)``        ``{``            ``// Some O(1) work``        ``}``    ``}``}`

## Java

 `static` `void` `fun(``int` `n, ``int` `k)``{``    ``for` `(``int` `i = ``1``; i <= n; i++)``    ``{``        ``int` `p = Math.pow(i, k);``        ``for` `(``int` `j = ``1``; j <= p; j++)``        ``{``            ``// Some O(1) work``        ``}``    ``}``}` `// This code is contributed by umadevi9616`

## Python3

 `def` `fun(n, k):``    ` `    ``for` `i ``in` `range``(``1``, n ``+` `1``):``        ``p ``=` `pow``(i, k)``        ``for` `j ``in` `range``(``1``, p ``+` `1``):``            ``# Some O(1) work``        `  `# This code is contributed by Shubham Singh`

## C#

 `static` `void` `fun(``int` `n, ``int` `k)``{``    ``for` `(``int` `i = 1; i <= n; i++)``    ``{``        ``int` `p = Math.Pow(i, k);``        ``for` `(``int` `j = 1; j <= p; j++)``        ``{``            ``// Some O(1) work``        ``}``    ``}``}` `// This code is contributed by umadevi9616`

## Javascript

 ``

Time complexity of above function can be written as 1k + 2k + 3k + … n1k.

Let us try few examples:

```k=1
Sum = 1 + 2 + 3 ... n
= n(n+1)/2
= n2/2 + n/2

k=2
Sum = 12 + 22 + 32 + ... n12.
= n(n+1)(2n+1)/6
= n3/3 + n2/2 + n/6

k=3
Sum = 13 + 23 + 33 + ... n13.
= n2(n+1)2/4
= n4/4 + n3/2 + n2/4     ```

In general, asymptotic value can be written as (nk+1)/(k+1) + Θ(nk)
If  n>=k then the time complexity will be considered in O((nk+1)/(k+1)) and if n<k, then the time complexity will be considered as  in the O(nk)