--%>
Assignment Help - homework help

What is Big-O hierarchy

The big-O hierarchy: A few basic facts about the big-O behaviour of some familiar functions are very important. Let p(n) be a polynomial in n (of any degree). Then

logbn is O(p(n)) and p(n) is O(an);

for any base b and any a. In words: logs are big-O of polynomials and polynomials are big-O of exponentials.

Note that since logbn = logcn/ logcb, we have

logbn is O(logcn);

for any fixed b and c, since logcb is a constant.

   Related Questions in Mathematics

  • Q : Define Big-O notation Big-O notation :

    Big-O notation: If f(n) and g(n) are functions of a natural number n, we write f(n) is O(g(n)) and we say f is big-O of g if there is a constant C (independent of n) such that f

    		•
  • Q : Budgeted cash disbursements The ABC

    The ABC Company, a merchandising firm, has budgeted its action for December according to the following information: • Sales at $560,000, all for cash. • The invoice cost for goods purc

    		•
  • Q : Where would we be without stochastic

    Where would we be without stochastic or Ito^ calculus?

    		•
  • Q : Pig Game Using the PairOfDice class

    Using the PairOfDice class design and implement a class to play a game called Pig. In this game the user competes against the computer. On each turn the player rolls a pair of dice and adds up his or her points. Whoever reaches 100 points first, wins. If a player rolls a 1, he or she loses all point

    		•
  • Q : Calculus I need it within 4 hours. Due

    I need it within 4 hours. Due time March 15, 2014. 3PM Pacific Time. (Los Angeles, CA)

    		•
  • Q : Problem on Datalog for defining

    The focus is on  the use of Datalog for defining properties  and queries on graphs. (a) Assume that P is some property of graphs  definable in the Datalog. Show that P is preserved beneath extensions  and homomo

    		•
  • Q : Probability assignments 1. Smith keeps

    1. Smith keeps track of poor work. Often on afternoon it is 5%. If he checks 300 of 7500 instruments what is probability he will find less than 20substandard? 2. Realtors estimate that 23% of homes purchased in 2004 were considered investment properties. If a sample of 800 homes sold in 2

    		•
  • Q : Problem on Prime theory Suppose that p

    Suppose that p and q are different primes and n = pq. (i) Express p + q in terms of Ø(n) and n. (ii) Express p - q in terms of p + q and n. (iii) Expl

    		•
  • Q : Who firstly discovered mathematical

    Who firstly discovered mathematical theory for random walks, that rediscovered later by Einstein?

    		•
  • Q : Econ For every value of real GDP,

    For every value of real GDP, actual investment equals

    		•