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

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.

 

Posted Date: 7/9/2012 9:50:02 PM | Location : United States







Related Discussions:- Relation of time and space complexities of an algorithm, Assignment Help, Ask Question on Relation of time and space complexities of an algorithm, Get Answer, Expert's Help, Relation of time and space complexities of an algorithm Discussions

Write discussion on Relation of time and space complexities of an algorithm
Your posts are moderated
Related Questions
The two famous methods for traversing are:- a) Depth first traversal b) Breadth first

Complexity of an Algorithm An algorithm is a sequence of steps to solve a problem; there may be more than one algorithm to solve a problem. The choice of a particular algorith

What is algorithm's Optimality? Optimality  is  about  the  complexity  of  the  problem  that  algorithm  solves.  What  is  the  minimum amount  of  effort  any  algorithm  w

How memory is freed using Boundary tag method in the context of Dynamic memory management? Boundary Tag Method to free Memory To delete an arbitrary block from the free li

Representation of data structure in memory is known as: Abstract data type

#2 example of recursion

Program Insertion of a node into any Circular Linked List Figure depicts a Circular linked list from which an element was deleted. ALGORITHM (Deletion of an element from a

Write an algorithm for compound interest.

Data Structure and Algorithm 1. Explain linked list and its types. How do you represent linked list in memory? 2. List and elucidate the types of binary tree. 3. Descr

Implementation of Stack :- Stacks can be executed in the 2 ways: a)  Arrays b)  Linked List