Relation of time and space complexities of an algorithm, Data Structure & Algorithms

Assignment Help:

What is complexity of an algorithm? What is the basic relation between the time and space complexities of an algorithm? Justify your answer by giving an example.                         

Complexity of an algorithm is the measure of analysis of the algorithm. Analyzing an Algorithm means predicting the resources that the algorithm needs such as memory, communication bandwidth, time and logic gates. Most often it is computational or calculation time that is measured for finding a more suitable algorithm. This is called as time complexity of the algorithm.  The running time of a program is described or defined as a function of the size of its  input. On a specific input, it is traditionally measured as the number of primitive operations or steps executed.

The analysis of algorithm focuses on time complexity and space complexity both. As compared to time analysis, the analysis of space requirement for an algorithm is generally easier and faster, but wherever necessary, both the techniques can be used. The space is referred to as storage needed in addition to the space required storing the input data.  The amount of memory needed by the program to run to completion is referred to as space complexity. For an algorithm, time complexity depends only upon the size of the input, thus, it is a function of input size 'n'. So the amount of time required by an algorithm to run to its completion is referred as time complexity.

The best algorithm to solve a given problem is the one that requires less memory and takes less time to complete its execution of the algorithm. But in practice it is not always likely to achieve both of these objectives. There may be number of approaches to solve a same problem. One such approach may require more space but takes less time to complete its execution while on other hand the other approach requires less space but

more time to complete its execution. Thus we may have to compromise one thing to improve the other. That is, we may be able to reduce space requirement by increasing running time or we can reduce running time by allocating more memory space. This situation where we compromise one to improve the other is known as Time-space trade off.

 


Related Discussions:- Relation of time and space complexities of an algorithm

Designed to manage the booking, Beauty Salon is a system to be designed to...

Beauty Salon is a system to be designed to manage the booking and the payment of a single beauty parlour. Beauty Therapists: A beauty parlour has a number of staff members mo

Problem logicall, Given a list containing Province, CustomerName and SalesV...

Given a list containing Province, CustomerName and SalesValue (sorted by Province and CustomerName), describe an algorithm you could use that would output each CustomerName and Sal

Pseudo code, since the gregorian calendar was introduced in 1752,a leap yea...

since the gregorian calendar was introduced in 1752,a leap year occurs every 4 years.you are to write a pseudo code to find out whether a year is a leap year.your progrm should dis

State in detail about the integer, State in detail about the Integer ...

State in detail about the Integer Carrier set of the Integer ADT is the set {..., -2, -1, 0, 1, 2, ...}, and  operations on these values are addition, multiplication, subtrac

Threads in main method, Create main method or a test class that creates 2 E...

Create main method or a test class that creates 2 Element objects that are neighbours of each other, the first element temperature set at 100, the 2nd at 0 and use an appropriate h

Illustrate the visual realism applications, Illustrate the Visual realism a...

Illustrate the Visual realism applications a)   Robot Simulations : Visualization of movement of their links and joints  and end effector movement etc. b)  CNC programs ver

Chaining Method as Method of Collision Resolution , Q. The given values are...

Q. The given values are to be stored in a hash table 25, 42, 96, 101, 102, 162, 197 Explain how the values are hashed by using division technique of hashing with a table

Write a procedure that produces independent stack, Write a procedure (make-...

Write a procedure (make-stack) that produces independent stack objects, using a message-passing style, e.g. (define stack1 (make-stack))  (define stack2 (make-stack)) W

Construct a minimum spanning tree, Construct G for α, n, and W given as com...

Construct G for α, n, and W given as command line parameters. Throw away edges that have an asymmetric relation between nodes. That is, if A is connected to B, but B is not connect

What is a binary search tree (bst), What is a Binary Search Tree (BST)? ...

What is a Binary Search Tree (BST)? A binary search tree B is a binary tree every node of which satisfies the three conditions: 1.  The value of the left-subtree of 'x' is le

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