简单两种情况的算法分析

Question

Well I am studying algorithms for an upcoming exam and I am having hard time verifying if the practices below are answered right.

 i=1
 while(i<=n)
      j=1
      while(j<i)
            j=j+1
      i=i*2

The answer of mine for this one is O(n.log n)

i=1
 while(i<=n)
      j=1
      while(j<i)
            j=j*2
      i=i+1

Again I have answered it as O(n.log n)

Can someone verify that I am answering correct or not ? Also any tips regarding analysis for future practices are welcome.

Answer 1

Yes, each of these is O(n log n) . You have one loop that is a linear iteration, ie O(n) . You have another loop that is exponential; the inverse is log, so that loop is O(log n) . As they are nested, you multiple the complexities, and get O(n log n) .