--%>
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 : 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 : Global And Regional Economic Development

    The Pharmatec Group, a supplier of pharmaceutical equipment, systems and services, has its head office in London and primary production facilities in the US. The company also has a successful subsidiary in South Africa, which was established in 1990. Pharmatec South A

    		•
  • Q : Numerical Analysis Hi, I was wondering

    Hi, I was wondering if there is anyone who can perform numerical analysis and write a code when required. Thanks

    		•
  • Q : Area Functions & Theorem Area Functions

    Area Functions 1. (a) Draw the line y = 2t + 1 and use geometry to find the area under this line, above the t - axis, and between the vertical lines t = 1 and t = 3. (b) If x > 1, let A(x) be the area of the region that lies under the line y = 2t + 1 between t

    		•
  • Q : Explain Factorisation by Fermats method

    Factorisation by Fermat's method: This method, dating from 1643, depends on a simple and standard algebraic identity. Fermat's observation is that if we wish to nd two factors of n, it is enough if we can express n as the di fference of two squares.

    		•
  • 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 : Define terms Terms : Terms are defined

    Terms: Terms are defined inductively by the following clauses.               (i) Every individual variable and every individual constant is a term. (Such a term is called atom

    		•
  • Q : Problem on Fermats method A public key

    A public key for RSA is published as n = 17947 and a = 3. (i) Use Fermat’s method to factor n. (ii) Check that this defines a valid system and find the private key X.

    Q : Problem on mass balance law Using the

    Using the mass balance law approach, write down a set of word equations to model the transport of lead concentration. A) Draw a compartmental model to represent  the diffusion of lead through the lungs and the bloodstream.

    		•
  • Q : Solve each equation by factoring A

    A college student invested part of a $25,000 inheritance at 7% interest and the rest at 6%.  If his annual interest is $1,670 how much did he invest at 6%?  If I told you the answer is $8,000, in your own words, using complete sentences, explain how you

    		•