--%>
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 : 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 : Econ For every value of real GDP,

    For every value of real GDP, actual investment equals

    		•
  • Q : What is the probability that the film

    T.C.Fox, marketing director for Metro-Goldmine Motion Pictures, believes that the studio's upcoming release has a 60 percent chance of being a hit, a 25 percent chance of being a moderate success, and a 15 percent chance of being a flop. To test the accuracy of his op

    		•
  • Q : State Measuring complexity Measuring

    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 a

    		•
  • Q : Profit-loss based problems A leather

    A leather wholesaler supplies leather to shoe companies. The manufacturing quantity requirements of leather differ depending upon the amount of leather ordered by the shoe companies to him. Due to the volatility in orders, he is unable to precisely predict what will b

    		•
  • Q : How to calculate area of pyramid

    Calculate area of pyramid, prove equation?

    		•
  • Q : What is limit x tends to 0 log(1+x)/x

    What is limit x tends to 0  log(1+x)/x to the base a?

  • Q : Problem on inverse demand curves In

    In differentiated-goods duopoly business, with inverse demand curves: P1 = 10 – 5Q1 – 2Q2P2 = 10 – 5Q2 – 2Q1 and per unit costs for each and every firm equal to 1.<

    		•
  • Q : Elasticity of Demand For the demand

    For the demand function D(p)=410-0.2p(^2), find the maximum revenue.

    		•
  • Q : Who developed a rigorous theory for

    Who developed a rigorous theory for Brownian motion?

    		•