Question

I am using this algorithm in my program :

for( i=0 ; i<N ; i++ )

  for( j=i+1 ; j<N+1 ; j++ )

     for( k=0 ; k<i ; k++ )

          doWork();

Can anyone help me find the time complexity of this snippet ?
I guess for the first two loops it is

N*(N+1)/2 

right ? what about the three loops all together?

Answer 1

Thanks to @Tim Meyer to correct me:

Simple equation gives for (N= 0,1,2,3,4,5,6, 7, 8 …) following series: 0, 0, 1, 4, 10, 20, 35, 56, 84 … , which is resolved with following formula:

u(n) = (n - 1)n(n + 1)/6 

So it will have O((N – 1)N(N + 1)/6) time complexity, which can be simplified to O(N^3)