Use of asymptotic notation in the study of algorithm, Data Structure & Algorithms

Q. What is the need of using asymptotic notation in the study of algorithm? Describe the commonly used asymptotic notations and also give their significance.                                        

Ans:

The running time of the algorithm depends upon the number of characteristics and slight variation in the characteristics varies and affects the running time. The algorithm performance in comparison to alternate algorithm is best described by the order of growth of the running time of the algorithm. Let one algorithm for a problem has time complexity of c3n2 and another algorithm has c1n3 +c2n2 then it can be simply observed that the algorithm with complexity c3n2 will be faster compared to the one with complexity c1n3 +c2n2 for sufficiently larger values of n. Whatever be the value of c1, c2   and c3 there will be an 'n' past which the algorithm with the complexity c3n2 is quite faster than algorithm with complexity c1n3 +c2n2, we refer this n as the breakeven point. It is difficult to determine the correct breakeven point analytically, so asymptotic notation is introduced that describe the algorithm performance in a meaningful and impressive way. These notations describe the behaviour of time or space complexity for large characteristics. Some commonly used asymptotic notations are as follows:

1)      Big oh notation (O): The upper bound for a function 'f' is given by the big oh notation (O). Taking into consideration that 'g' is a function from the non-negative integers to the positive real numbers, we define O(g) as the set of function f such that for a number of real constant c>0 and some of the non negative integers constant n0  , f(n)≤cg(n) for all n≥n0. Mathematically, O(g(n))={f(n): hear exists positive constants such that 0≤f f(n)≤cg(n) for all n, n≥n0} , we say "f is oh of g".

2)      Big Omega notation (O): The lower bound for a function 'f' is given by the big omega notation (O). Considering 'g' is the function from the non-negative integers to the positive real numbers, hear we define O(g) as the set of function f  such that  for a number of real constant c>0 and a number of non negative integers constant n0  , f(n)≥cg(n) for all n≥n0. Mathematically, O(g(n))={f(n): here exists positive constants such that 0≤cg(n) ≤f(n) for all n, n≥n0}.

3)      Big Theta notation (θ):  The upper and lower bound for the function 'f' is given by the big oh notation (θ). Taking 'g' to be the function from the non-negative integers to the positive real numbers, here we define θ(g) as the set of function f  such that  for a number of real constant c1 and c2 >0 and a number of non negative integers constant n0  , c1g(n)≤f f(n)≤c2g(n) for all n≥n0. Mathematically, θ(g(n))={f(n): here exists positive constants c1 and c2 such that c1g(n)≤f f(n)≤c2g(n) for all n, n≥n0} , hence we say "f is oh of g"

Posted Date: 7/10/2012 6:17:26 AM | Location : United States







Related Discussions:- Use of asymptotic notation in the study of algorithm, Assignment Help, Ask Question on Use of asymptotic notation in the study of algorithm, Get Answer, Expert's Help, Use of asymptotic notation in the study of algorithm Discussions

Write discussion on Use of asymptotic notation in the study of algorithm
Your posts are moderated
Related Questions
Containers Introduction Simple abstract data types are useful for manipulating simple sets of values, such as integers or real numbers however more complex abstract data t

Question a) Describe how the endogenous model is an improvement to the neo-classical model in explaining the long-run effect of investment on economic growth of a country.

an electrical student designed a circuit in which the impedence in one part of a series circuit is 2+j8 ohms and the impedent is another part of the circuit is 4-j60 ohm mm program

Q. Write down a non recursive algorithm to traverse a binary tree in order.                    Ans: N on - recursive algorithm to traverse a binary tree in inorder is as

Determine about the Post conditions assertion A  post condition is an assertion which should be true at completion of an operation. For instance, a post condition of the squ

Initially Nodes are inserted in an AVL tree in the same manner as an ordinary binary search tree. Though, the insertion algorithm for any AVL tree travels back along with the pa

Q. Explain the insertion sort with a proper algorithm. What is the complication of insertion sort in the worst case?

Worst Fit method:- In this method the system always allocate a portion of the largest free block in memory. The philosophy behind this method is that by using small number of a ve

As we have seen, as the traversal mechanisms were intrinsically recursive, the implementation was also easy through a recursive procedure. Though, in the case of a non-recursive me

Column Major Representation In memory the second method of representing two-dimensional array is the column major representation. Under this illustration, the first column of