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Describe the process of analyzing the running time of an algorithm using Big-O notation.

Revati S Misra42919-Apr-2023

Describe the process of analyzing the running time of an algorithm using Big-O notation. 

algorithmalgorithm Algorithm analysis 
Updated on 22-Apr-2023
Revati S Misra

Revati S Misra

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Aryan Kumar

Aryan Kumar

22-Apr-2023

Big-O notation is a way of describing the time complexity of an algorithm, which is a measure of how the runtime of an algorithm grows as the input size increases. The process of analyzing the running time of an algorithm using Big-O notation typically involves the following steps:

  1. Identify the basic operations performed by the algorithm: The first step in analyzing the running time of an algorithm is to identify the basic operations performed by the algorithm, such as assignments, comparisons, and arithmetic operations. These basic operations are the building blocks of the algorithm and will be used to estimate its running time.
  2. Count the number of times each basic operation is performed: Once the basic operations have been identified, the next step is to count the number of times each operation is performed as a function of the input size. For example, if an algorithm performs a single assignment operation for each element in an array of size n, then the number of assignments performed is n.
  3. Express the running time as a function of the input size: Once the number of times each basic operation is performed has been determined, the next step is to express the total running time of the algorithm as a function of the input size. This involves combining the number of times each basic operation is performed into a single expression that represents the overall running time of the algorithm.
  4. Simplify the expression using Big-O notation: The final step in analyzing the running time of an algorithm is to simplify the expression using Big-O notation. Big-O notation is a way of expressing the upper bound of the running time of an algorithm as a function of the input size. This involves identifying the term in the expression that grows the fastest as the input size increases, and dropping any lower-order terms or constant factors. The resulting expression is the Big-O notation for the algorithm.
Krishnapriya Rajeev

Krishnapriya Rajeev

20-Apr-2023

Big-O notation is a mathematical notation used to describe the growth rate of a function and is commonly used to describe the time complexity of an algorithm.

 

The process of analysing the running time of an algorithm using Big-O notation can be broken down into the following steps:


1. Identifying the algorithm: The first step is to identify the algorithm whose running time you want to analyse. This could be any algorithm that performs some computation, such as searching, sorting, or traversing a data structure.


2. Determining the input size: The next step is to determine the input size of the algorithm. The input size could be the number of items in a list, the number of nodes in a tree, or any other measure of the input size.


3. Identifying the basic operation: The next step is to identify the basic operation that is performed repeatedly in the algorithm. This could be a comparison, a swap, or any other operation that is performed repeatedly in the algorithm.


4. Counting the number of times the basic operation is performed: The next step is to count the number of times the basic operation is performed as a function of the input size. This can be done by examining the code and identifying how many times the basic operation is performed in terms of the input size.


5. Simplifying the expression: The next step is to simplify the expression that represents the number of times the basic operation is performed in terms of the input size. This involves ignoring constant factors and lower-order terms in the expression.


6. Determining the Big-O notation: The final step is to determine the Big-O notation of the expression. This involves identifying the highest-order term in the expression and dropping any lower-order terms. The resulting expression is the Big-O notation of the algorithm's running time.

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