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

Sparse matrix, Q. Define a sparse matrix. Explain different types of sparse...

Q. Define a sparse matrix. Explain different types of sparse matrices? Show how a triangular array is stored in memory. Evaluate the method to calculate address of any element ajk

Collision resolution techniques, complete information about collision resol...

complete information about collision resolution techniques

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

Implement an algorithm to simulate car re-organizing, Design  and implement...

Design  and implement  an algorithm  to simulate car  re-organizing of the train at the railway switching junction. You can only use stacks as the data structure to represent the t

Insertion sort, It is a naturally occurring sorting method exemplified thro...

It is a naturally occurring sorting method exemplified through a card player arranging the cards dealt to him. He picks up the cards like they are dealt & added them into the neede

The best average behaviour, The best average behaviour is shown by  Qui...

The best average behaviour is shown by  Quick Sort

Comp. sci algorithms, 1. develop an algorithm which reads two decimal numbe...

1. develop an algorithm which reads two decimal numbers x and y and determines and prints out wether x>y or y>x. the input values, x and y, are whole number > or equal to 0, which

Sort list of distinct numbers in ascending order - quicksort, (1) Sort a li...

(1) Sort a list of distinct numbers in ascending order, using the following divide- and-conquer strategy (Quicksort): divide the list of numbers into two lists: one that contains a

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