Time Complexity of Loop with Powers
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 } }} |
chevron_right
filter_none
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)
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
