Time Complexity of Loop with Powers
What is the time complexity of the below function?
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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)
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