# Space And Time Complexity Of An Algorithm Pdf File Name: space and time complexity of an algorithm .zip
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Published: 19.12.2020  Edit Reply. You would have come across a term called space complexity when you deal with time complexity.

## Why is Time Complexity Essential and What is Time Complexity?

For any defined problem, there can be N number of solution. This is true in general. If I have a problem and I discuss about the problem with all of my friends, they will all suggest me different solutions. And I am the one who has to decide which solution is the best based on the circumstances. Similarly for any problem which must be solved using a program, there can be infinite number of solutions. Let's take a simple example to understand this.

There are multiple ways to solve a problem using a computer program. For instance, there are several ways to sort items in an array. You can use merge sort , bubble sort , insertion sort , etc. All these algorithms have their own pros and cons. An algorithm can be thought of a procedure or formula to solve a particular problem. The question is, which algorithm to use to solve a specific problem when there exist multiple solutions to the problem? Algorithm analysis refers to the analysis of the complexity of different algorithms and finding the most efficient algorithm to solve the problem at hand.

Analysis of efficiency of an algorithm can be performed at two different stages, before implementation and after implementation, as. Efficiency of algorithm is measured by assuming that all other factors e. The chosen algorithm is implemented using programming language. Next the chosen algorithm is executed on target computer machine. In this analysis, actual statistics like running time and space needed are collected. ## Complexity Analysis

Whenever a solution to a problem is written some memory is required to complete. For any algorithm memory may be used for the following:. Space complexity is the amount of memory used by the algorithm including the input values to the algorithm to execute and produce the result. Sometime Auxiliary Space is confused with Space Complexity. But Auxiliary Space is the extra space or the temporary space used by the algorithm during it's execution. Sometimes an algorithm function may be called inside another algorithm function.

Space and Time define any physical object in the Universe. Similarly, Space and Time complexity can define the effectiveness of an algorithm. While we know there is more than one way to solve the problem in programming, knowing how the algorithm works efficiently can add value to the way we do programming. While we reserve the space to understand Space complexity for the future, let us focus on Time complexity in this post. Time is Money! Complexity of algorithm measures how fast is the algorithm. (time complexity) and what amount of memory it uses. (space complexity) - time and memory - 2 basic resources in E.g. for our example the pessimistic time complexity is given by.

## Time Complexity of Algorithms

There are three methods to solve the recurrence relation given as: Master method , Substitution Method and Recursive Tree method. Recurrence equation is substituted itself to find the final generalized form of the recurrence equation. Using recursion method, n element problem can be further divided into two or more sub problems. Every day we come across many problems and we find one or more than one solutions to that particular problem.

#### II. The relationship between asymptotic notations :

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