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

Road transport booking system, what algorithms can i use for the above titl...

what algorithms can i use for the above title in my project desing and implmentation of road transport booking system

Algorithm, Example of worse case of time

Example of worse case of time

What is Oscillating Sort?, For the Oscillating sort to be applied, it is ne...

For the Oscillating sort to be applied, it is necessary for the tapes to be readable in both directions and able to be quickly reversed. The oscillating sort is superior to the po

Algorithm for multiplication of two sparse matrices using li, algorithm for...

algorithm for multiplication of two sparse matrices using linked lists..

Define big omega notation, Define Big Omega notation Big Omega notatio...

Define Big Omega notation Big Omega notation (?) : The lower bound for the function 'f' is given by the big omega notation (?). Considering 'g' to be a function from the non-n

Ruby implements range of t abstract data type, Ruby implements Range of T A...

Ruby implements Range of T Abstract data type Ruby implements Range of T ADT in its Range class. Elements of carrier set are represented in Range instances by recording interna

Depth-First Traversal, With the help of a program and a numerical example e...

With the help of a program and a numerical example explain the Depth First Traversal of a tree.

Time complexity, The  total  of  time  needed  by  an algorithm to run to i...

The  total  of  time  needed  by  an algorithm to run to its completion is termed as time complexity. The asymptotic running time of an algorithm is given in terms of functions. Th

User-specified memory location, You need to implement a function which will...

You need to implement a function which will write out a given user-specified memory location to disk in base 10. That means that you have to convert the large number data structure

Data Structure, Ask consider the file name cars.text each line in the file ...

Ask consider the file name cars.text each line in the file contains information about a car ( year,company,manufacture,model name,type) 1-read the file 2-add each car which is repr

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