I have problem with calculate complexity

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Hello ....I have problem with calculate complexity for second loop

C++

f=1;
x=3;
for (int i = 1; i <= n; i*=2) 
   for (int j = 1; j <= i * i; j++) 
      if (i % j == 0) 
      for (int k = 1; k <= j; k++) 
         f=f*x;

What I have tried:

I calculate the third loop complexitiy
the result is O(j)

Posted 6-Jun-18 4:54am

Member 13849940

Updated 6-Jun-18 9:38am

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OriginalGriff 6-Jun-18 10:59am

And?
What's the problem?
What have you tried?
Where are you stuck?
What help do you need?

Member 13849940 6-Jun-18 11:02am

I stuck with this condition
for (int j = 1; j <= i * i; j++)
if (i % j == 0)

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CPallini · Answer 1 · 2018-06-06T09:40:00

I suggest you an experimental approach, run the folllowing program and have a look at the output. It gives some insight and could make you able to understand the actual algorithm asymptotic behaviour.

C++

using namespace std;

int main()
{
  const int MAXN = 1000; // try different values

  for (int  n=1; n<MAXN; ++n)
  {
    int count = 0;
    cout << "********************************\nn=" << n << "\n";
    for (int i = 1; i <= n; i*=2)
      for (int j = 1; j <= i * i; j++)
        if (i % j == 0)
          for (int k = 1; k <= j; k++)
          {
            cout << i << " " <<  j  << " " << k  << "\n";
            ++count;
          }
    cout << count <<  endl;
  }
}