Determination of time complexity, Data Structure & Algorithms

Assignment Help:

Determination of Time Complexity

The RAM Model

The random access model (RAM) of computation was devised through John von Neumann to study algorithms. In computer science, Algorithms are studied since they are independent of machine & language.

We will do all our design & analysis of algorithms depend on RAM model of computation:

  • Each "simple" operation (+, -, =, if, call) takes 1 step exactly.
  • Loops & subroutine calls are not easy operations, but based upon the size of the data and the contents of a subroutine.
  • Each of the memory access takes 1 step exactly.

The complexity of algorithms by using big-O notation can be described in the following way for a problem of size n:

  • Constant-time method is "order 1" : O(1). The time that needed is constant independent of the input size.
  • Linear-time method is "order n": O(n). The time needed is proportional to the input size. If input size doubles, then, the time to run the algorithm also will be doubles.
  • Quadratic-time method is "order N squared": O(n2). The time that needed is proportional to the square of input size. If the input size doubles, then, the time needed will enhance by four times.

The procedure of analysis of algorithm (program) involves analyzing each of the step of the algorithm. It based on the kinds of statements utilized in the program.


Related Discussions:- Determination of time complexity

What is algorithms optimality, What is algorithm's Optimality? Optimali...

What is algorithm's Optimality? Optimality  is  about  the  complexity  of  the  problem  that  algorithm  solves.  What  is  the  minimum amount  of  effort  any  algorithm  w

Push and pop operations, Q. Explain that how do we implement two stacks in ...

Q. Explain that how do we implement two stacks in one array A[1..n] in such a way that neither the stack overflows unless the total number of elements in both stacks together is n.

Define prims algorithm, Define Prim's Algorithm Prim's  algorithm  is  ...

Define Prim's Algorithm Prim's  algorithm  is  a  greedy  algorithm  for  constructing  a  minimum  spanning  tree  of  a  weighted linked graph. It works by attaching to a bef

Name the five popular hashing functions, Five popular hashing functions are...

Five popular hashing functions are as follows: 1) Division Method 2) Midsquare Method 3) Folding Method 4) Multiplicative method 5) Digit Analysis

Asymptotic notation.., important points on asymptotic notation to remember

important points on asymptotic notation to remember

Applications of shortest path algorithms, The minimum cost spanning tree ha...

The minimum cost spanning tree has broad applications in distinct fields. It represents several complicated real world problems such as: 1. Minimum distance for travelling all o

Multilist file organisation, what is multilist length file organisation? ex...

what is multilist length file organisation? explain with an example

How conquer technique can be applied to binary trees, How divide and conque...

How divide and conquer technique can be applied to binary trees?  As the binary tree definition itself separates a binary tree into two smaller structures of the similar type,

Draw a flowchart to input start time and end time of vehicle, Speed cameras...

Speed cameras read the time a vehicle passes a point (A) on road and then reads time it passes a second point (B) on the same road (points A and B are 100 metres apart). Speed of t

Explain the representations of graph, Explain the representations of graph....

Explain the representations of graph. The different ways of representing a graph is: Adjacency list representation : This representation of graph having of an array Adj of

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd