--%>
Assignment Help - homework help

State Measuring complexity

Measuring complexity: Many algorithms have an integer n, or two integers m and n, as input - e.g., addition, multiplication, exponentiation, factorisation and primality testing. When we want to describe or analyse the `easiness' or `hardness' of the algorithm, we want to measure its `running time' as a function of the `size' of the input value(s).

If the input value is n, then it is usual to use the number of (decimal) digits, or bits (binary digits), required to store n as a measure of the size of n.

Given input n, the number of decimal digits in n is given by

[log10 n] +1;

where [x], pronounced `floor of x', denotes the greatest integer less than or equal to x. The number of binary digits or bits is similarly given by

[lg n] +1;

where we use the abbreviation lg x for log2 x (this notation is common, but not completely standard).

   Related Questions in Mathematics

  • Q : Who firstly discovered mathematical

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

    		•
  • Q : Explain Factorisation by trial division

    Factorisation by trial division: The essential idea of factorisation by trial division is straightforward. Let n be a positive integer. We know that n is either prime or has a prime divisor less than or equal to √n. Therefore, if we divide n in

    		•
  • Q : Set Theory & Model of a Boolean Algebra

    II. Prove that Set Theory is a Model of a Boolean Algebra The three Boolean operations of Set Theory are the three set operations of union (U), intersection (upside down U), and complement ~.  Addition is set

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

    For every value of real GDP, actual investment equals

    		•
  • Q : State Fermat algorithm The basic Fermat

    The basic Fermat algorithm is as follows: Assume that n is an odd positive integer. Set c = [√n] (`ceiling of √n '). Then we consider in turn the numbers c2 - n; (c+1)2 - n; (c+2)2 - n..... until a perfect square is found. If th

    		•
  • 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 : How do it? integral e^(-t)*e^(tz) t

    integral e^(-t)*e^(tz) t between 0 and infinity for Re(z)<1

    		•
  • Q : Mathematical and Theoretical Biology

    Mathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in the fields of biology, biotechnology, and medicine. The field may be referred to as mathematical biology or biomathematics to stress the mathematical

    		•
  • Q : Numerical solution of PDE this

    this assignment contains two parts theoretical and coding the code has to be a new. old code and modified code will appear in the university website .

    		•
  • Q : Problem on budgeted cash collections

    XYZ Company collects 20% of a month's sales in the month of sale, 70% in the month following sale, and 5% in the second month following sale. The remainder is not collectible. Budgeted sales for the subsequent four months are:     

    		•