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

Importance of object-oriented over java, Importance of Object-Oriented over...

Importance of Object-Oriented over java Java is basically based on OOP notions of classes and objects. Java uses a formal OOP type system that should be obeyed at compile-t

Avl trees, An AVL tree is a binary search tree that has the given propertie...

An AVL tree is a binary search tree that has the given properties: The sub-tree of each of the node differs in height through at most one. Each sub tree will be an AVL tre

Explain threaded binary tree, Threaded Binary Tree : If a node in a bin...

Threaded Binary Tree : If a node in a binary tree is not having left or right child or it is a leaf node then that absence of child node is shown by the null pointers. The spac

What is algorithm, What is Algorithm A finite sequence of steps for a...

What is Algorithm A finite sequence of steps for accomplishing some computational task. An algorithm should Have steps which are simple and definite enough to be done

What is bubble sort, What is bubble sort? Bubble Sort: The basic ide...

What is bubble sort? Bubble Sort: The basic idea in bubble sort is to scan the array to be sorted sequentially various times. Every pass puts the largest element in its corr

Linked list, How to creat ATM project by using double linked list?

How to creat ATM project by using double linked list?

FIRST function in the compiler construction, I need a recursive algorithm t...

I need a recursive algorithm to implement the FIRST function to any grammar

Determine the area subdivision method, Area Subdivision Method In this ...

Area Subdivision Method In this method, the viewport is examined for clear decisions on the polygons situated in it, in regard to their overlap and visibility to the viewer. Fo

Parallel implementation of the raytracer, You are supposed to do the follow...

You are supposed to do the following: Write a parallel implementation of the raytracer using pthreads. Measure and compare the execution times for (i) the sequential ver

What are the dynamic arrays, What are the Dynamic arrays Dynamic arrays...

What are the Dynamic arrays Dynamic arrays are convenient for programmers since they can never be too small-whenever more space is needed in a dynamic array, it can simply be e

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