Big-O for different sized loops

Question

Hi,
When calculating the big-O complexity of a piece of code, I understand how the principle works with the following example where the loops all use N as a number (from http://forum.java.sun.com/thread.jspa?forumID=31&threadID=580958):
for (int i=0; i<N; i++)
   for (int j=0; j><N; j++)
      for (int k=0; k><N; k++)
         for (int l=0; l><N; l++)
             // N*N*N*N iterationsyet I am not so sure of how to calculate big-O for an example like this:
for(int w = 0; w < A; w ++) {
  for (int d = 0; d < B; d ++){
    for (int e = 0; e < C; e++) {
  for (int i = 0; i < E; i ++){
  for (int f = 0; f < B; f ++){
    for (int g = 0; g < C; g ++) {
  for (int h = 0; h < F; h ++){
  for (int i = 0; i < B; i ++){
    for (int j = 0; j < C; j ++) {
}where some loops use the same variables but most do not.
Any help would be appreciated
Cheers
N

Answer 1

an algorithm like "while x<n do y" is O(n)*O(y) = O(n*O(y))
an algorithm like "x ; y" is O(x) + O(y) = O(max{x, y})
so your example which isn't really that complicated is
O(A)*(O(B)*O(C) + O(E) + O(B)*O(C) + O(F) + O(B)*O(C)) =
O(A)*(O(BC) + O(E) + O(BC) + O(F) + O(BC)) =
O(A)*O(max{BC, E, F}) =
O(max{ABC, AE, AF})