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

Binary search, Explain binary search with an example

Explain binary search with an example

Create a binary tree , Create a class "box" that will contain a random inte...

Create a class "box" that will contain a random integer value v such that O

Darw a flowchart to input 3 numbers, This algorithm inputs 3 numbers, every...

This algorithm inputs 3 numbers, every number goes through successive division by 10 until its value is less than 1. An output is produced which comprise the number input and a val

Avl tree rotations, AVL trees and the nodes it contains must meet strict ba...

AVL trees and the nodes it contains must meet strict balance requirements to maintain O(log n) search time. These balance restrictions are kept maintained via various rotation func

Need help with working out. I dont really get it, Suppose there are exactly...

Suppose there are exactly five packet switches (Figure 4) between a sending host and a receiving host connected by a virtual circuit line (shown as dotted line in figure 4). The tr

Total impedent of the circuit, an electrical student designed a circuit in...

an electrical student designed a circuit in which the impedence in one part of a series circuit is 2+j8 ohms and the impedent is another part of the circuit is 4-j60 ohm mm program

Whether the infix expression has balanced parenthesis or not, Using stacks,...

Using stacks, write an algorithm to determine whether the infix expression has balanced parenthesis or not Algorithm parseparens This algorithm reads a source program and

Explain the prim''s minimum spanning tree algorithm, Question 1. Explai...

Question 1. Explain the different types of traversal on binary tree 2. Explain the Prim's minimum spanning tree algorithm 3. Differentiate fixed and variable storage allo

Program on radix sort., Write a program that uses the radix sort to sort 10...

Write a program that uses the radix sort to sort 1000 random digits. Print the data before and after the sort. Each sort bucket should be a linked list. At the end of the sort, the

The time and space complexities of an algorihm, Relation between the time a...

Relation between the time and space complexities of an algorithm The examining of algorithm focuses on time complexity and space complexity. As compared to time analysis, the 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