Question

Analyze the following code and provide a "Big-O" estimate of its running time in terms of n. Explain your analysis. Assume k is a constant given by the problem.

for (i=1; i<=n; i++)

     p = pow(i,k); // p = i to the power of k

     for (j=1; j<=p; j++)

          Some O(1) work

     end for

  end for

Answer 1

for i=1, j loop runs 1^k times

for i=2, j loop runs 2^k times

for i=3, j loop runs 3^k​​​​​​​ times

for i=4 j loop runs 4^k​​​​​​​ times

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for i=n, j loop runs n^k​​​​​​​ times

sum is 1^k+2^k+3^k+-------+ n^k

=O(n^k+1)