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

Prefix and Postfix Expressions, Q.   Draw the expression tree of the infix ...

Q.   Draw the expression tree of the infix expression written below and then  convert it intoPrefix and Postfix expressions. ((a + b) + c * (d + e) + f )* (g + h )

Example of single node with multiple elements, The class Element represents...

The class Element represents a single node that can be part of multiple elements on a hotplate and runs in its own thread. The constructor accepts the initial temperature and a hea

What are the things require to implement abstract data types, What are the ...

What are the things require to implement ADT Abstract data types are very useful for helping us understand the mathematical objects which we use in our computations but, of cou

Explain b tree (binary tree), B Tree Unlike a binary-tree, every node o...

B Tree Unlike a binary-tree, every node of a B-tree may have a variable number of keys and children. The keys are stored in non-decreasing order. Every key has an associated ch

Bayesian statistics question, Suppose that there is a Beta(2,2) prior distr...

Suppose that there is a Beta(2,2) prior distribution on the probability theta that a coin will yield a "head" when spun in a specified manner. The coin is independently spun 10 tim

Explain the interfaces in ruby, Explain the Interfaces in Ruby Recall...

Explain the Interfaces in Ruby Recall that in object-oriented programming, an interface is a collection of abstract operations that cannot be instantiated. Even though Ruby i

Files structures, The structures of files vary from operating system to ope...

The structures of files vary from operating system to operating system. In this unit, we will discuss the fundamentals of file structures with the generic file organisations. A

What is complexity, Complexity is the rate at which the needed storage or c...

Complexity is the rate at which the needed storage or consumed time rise as a function of the problem size. The absolute growth based on the machine utilized to execute the program

Define order of growth, Define order of growth The  efficiency  analysi...

Define order of growth The  efficiency  analysis  framework  concentrates   on  the  order  of  growth  of  an  algorithm's   basic operation count as the principal indicator o

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