# O- be O(N2). The below table helps to user

O- notation            To indicate the asymptotic high end is O-notation. For agiven function g(n) and indicate by O(g(n)).O(g(n)) = {f(n): thereexist positive constants t and n0 such that 0 ? f(n) ? t *g(n) forall  n ? n0 } ?-notation            To indicate the asymptotic low endis ?-notation. Fora given function g(n) and indicate  by ?(g(n)). ?(g(n)) ={f(n): there exist positive constants t and n0 such that 0 ? t *g(n)? f(n) for all  n ? n0 } ?-notation            To indicate asymptotic tight boundis ?-notation. For a given function g(n) andindicate by ?(g(n)).?(g(n))= {f(n): there exist positive constants t1,t2 and n0 such that 0 ? t1 *g(n) ? f(n) ) ? t2*g(n)  for all  n > n0 }The all above scenario shownin fig.

Fig. Time Complexity notations  During analyzing analgorithm, mostly consider O-notation because it will give us the high end of executiontime. This is the worst case of execution time.                         Tocompute O-notation lower order terms need to ignore.

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Because lower order termsare relatively insignificant for large input.Let f(N) = 2 * N2 + 3 * N +5O(f(N)) = O (2 * N2 + 3 * N +5) = O(N2) Let us consider the scenario.                        cnt =0for edges node.edges            cnt++            ifedge not in resolved                         dep_resolve(edge,resolved)resolved.append(node) Lets observe cnt++ execute count.When node length is 0, it will execute count 0. When node length is 1, it will execute count 1.

When node length is 2, it will execute count 2.Total number ofexecution count cnt++ is 0 + 1 + 2 +… + (N-1) = N*(N-1) / 2. So Time complexitywill be O(N2).The below table helpsto user understand the growth of several common time complexity. Thus help touser judge if the algorithm is fast enough to get an acceptance.

Length of Input (N) Worst Accepted Algorithm ?10..11?10..11 O(N!),O(N6)O(N!),O(N6) ?15..18?15..18 O(2N?N2)O(2N?N2) ?18..22?18..22 O(2N?N)O(2N?N) ?100?100 O(N4)O(N4) ?400?400 O(N3)O(N3) ?2K?2K O(N2?logN)O(N2?logN) ?10K?10K O(N2)O(N2) ?1M?1M O(N?logN)O(N?logN) ?100M?100M O(N),O(logN),O(1)                                     Table.Several Common Time Complexity