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
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 )

(i)  Consider a system using flooding with hop counter. Suppose that the hop counter is originally set to the "diameter" (number of hops in the longest path without traversing any

write an algorithm for multiplication of two sparse matrices using Linked Lists

When there is requirement to access records sequentially by some key value and also to access records directly by the similar key value, the collection of records may be organized

Q. State the difference between a grounded header link list and a circular header link list?     Ans: A header linked list is a linked list which all the time c

Polynomials like  5x 4    +  2x 3    +  7x 2     +  10x  -  8  can  be  represented by using arrays. Arithmetic operations such as addition & multiplication of polynomials are com

Q. Write down an algorithm to insert a node in between any two nodes in a linked list         Ans. Insertion of a the node after the given element of the listis as follows

differences between direct and indirect recursion

P os t - o r d e r T r av er sal :  This can be done by both iteratively and recursively. The iterative solution would require a modification or alteration of the in-

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