Algorithmic Analysis (Analyze Algorithm) Means To Check And Analyze An Algorithm’s Efficiency.
Because algorithms are designed to solve problems, one of the main criteria for their comparison is their efficiency and execution speed. Algorithmic analysis examines the resources used by the algorithm (such as time and memory). It can help calculate the execution time of the algorithm according to the size of the input data.
Algorithmic analysis can help design algorithms with better performance. For example, by analyzing the efficiency of two different algorithms to solve a problem, the best algorithm can be selected according to the needs of the problem.
Also, algorithmic analysis can help better understand the algorithm’s behavior in different conditions and make it possible to optimize the existing algorithms.
What is the algorithm?
An algorithm is a step-by-step instruction set to solve a specific problem. Each algorithm can include several steps, and in each step, a series of operations are performed, with the help of which the solution to the problem can be obtained.
Algorithms are used in many fields, including computer science, mathematics, physics, accounting, etc. In computer science, algorithms are written to solve problems such as searching, sorting, image processing, machine learning, etc.
Also, algorithms are usually written mathematically and using special symbols. For example, the simple linear search algorithm is written as follows:
- In array I for each element
- If i is equal to the desired number
- show the position of I and leave the algorithm
- We failed to find the number of any component, so we returned a return value of -1.
In this algorithm, each operation is written in a separate line, and starting from the first line, we proceed to the end of the algorithm.
An example of a widely used algorithm in computer science
Algorithms are used in many fields of computer science. The sorting algorithm is one of the most used algorithms in computer science. Sorting algorithms are designed to sort data (such as arrays). One of the most used sorting algorithms is the Bubble Sort algorithm. This algorithm works as follows:
- Starting from the beginning of the collection and comparing the first two.
- If the second value is smaller than the initial value, replace them and go to the next step.
- Otherwise, go to the next two comparisons.
- Repeat this until the end of the array and start again from the beginning.
- Repeat until no changes are made.
If we want to run this algorithm to sort an array with n elements, its execution time will be O(n^2). In other words, if the number of array elements reaches one million, the execution time of the algorithm may become very long. To solve this problem, sorting algorithms with better execution times (such as Quick Sort and Merge Sort) have been designed.
Are all algorithms written mathematically?
No, algorithms can be written and presented mathematically, but this is not required. Algorithms, in pseudocode, flow charts, etc., can be written graphically to solve various problems. For example, sorting algorithms can be represented using flow charts, and the sorting process can be displayed graphically.
On the other hand, the algorithms that are written in programming languages are presented in the form of code that includes special commands and structures. These commands can be pseudocode or the desired language (C, Java, Python, etc.). Therefore, algorithms can be written in different ways, and how they are written depends on the type of problem and the tools used.
Is algorithmic analysis useful in all problems?
Yes, algorithmic analysis is one of the most important topics in computer science and is used in many problems. Algorithmic analysis helps us mathematically estimate the time and space consumed by an algorithm. With this, we can choose the best algorithm to solve a problem by comparing and selecting different algorithms.
In many computer problems, algorithm execution time is significant, and we may be able to improve algorithm execution time by algorithmic analysis. For example, different sorting algorithms are presented with additional execution times, and with algorithmic analysis, we can choose a more optimal method for sorting.
Also, algorithmic analysis helps us to get a better understanding of the behavior of algorithms and their performance in different situations. This skill can be useful in solving more complex problems and designing optimal algorithms. In general, algorithmic analysis is one of the most important tools available to programmers and researchers in computer science.
Technical explanation of the algorithmic analysis
Algorithmic analysis is a process in which, using mathematical calculations, the time and space consumed by an algorithm to solve a problem are accurately estimated. In this process, the number of operations the algorithm performs and the amount of memory required for its execution is calculated. This information helps programmers and researchers choose the best algorithm to solve problems.
For example, in algorithmic analysis, for a sorting algorithm, the execution time of the algorithm depends on the number of array elements. For example, the bubble sort algorithm takes O(n^2) time given the number of array elements. This means that if we double the number of array elements, the execution time of the algorithm will be quadrupled.
Algorithmic analysis examines the algorithm execution process and analyzes its costs. For example, in the binary search algorithm, the search interval is halved in each step, which makes the execution time of the algorithm logarithmically dependent on the number of input elements. Therefore, as the number of input elements increases, the execution time of the algorithm will not grow but will remain relatively constant.
In short, in algorithmic analysis, the best algorithm to solve a problem is selected by examining and carefully the algorithms, including the number of operations and the amount of memory required to execute them.
How to write an algorithm?
Writing an algorithm may seem difficult to some people. But writing an algorithm to solve a problem can be done differently. Next, we describe several steps to write an algorithm:
- Understanding the problem and its inputs: To write an algorithm, you must carefully examine it. For example, if the problem is to calculate the sum of the numbers of an array, you must first understand the length of the collection and its numbers.
- Design a solution: Once you understand the problem, you can design a solution. You may need creative thinking and experience for this. At this point, you need to find an algorithm that solves the problem correctly.
- Writing the algorithm: after designing the solution, the algorithm should be written formally and accurately. It includes defining the different steps of the algorithm, its inputs, and outputs.
- Testing the Algorithm: After writing the algorithm, you must try it to ensure it works properly. To do this, you can give different inputs to the algorithm and examine its outputs.
- Algorithm improvement: If the algorithm is not working optimally, you can change it. For example, you can use more optimal algorithms to solve the problem or apply optimizations to the algorithm.
- Documentation: Finally, you must document it accurately and in detail for future use. This topic includes describing algorithm steps, inputs, outputs, and how to use them.
Overall, writing an algorithm can be a complicated process. Still, you can design effective algorithms to solve various issues by understanding the problem and familiarizing yourself with algorithm design and testing methods.
Also, you can use the previous algorithms and modify them to your needs.
Now look at the following example to better understand the issue. In the pseudocode below, we have written a simple algorithm to calculate the sum of the numbers of an array so that you can better understand the subject. Below I mention you:
Algorithm subarray(arr):
sum = 0
for i from 0 to length(arr)-1:
sum = sum + arr[i]
return sum
This algorithm collects all the array elements using the for loop and uses the sum variable to calculate their sum.
Also, another algorithm used to calculate the maximum value inside an array is as follows:
Algorithm findMax(arr):
max = arr[0]
for i from 1 to length(arr)-1:
if arr[i] > max:
max = arr[i]
return max
Using the for loop, this algorithm checks all the array elements individually and stores the largest value in the max variable. Every time a factor greater than max is found, the max value is changed to that element.
Analysis of an algorithm
Algorithm analysis means examining the time and space that the algorithm needs to solve a problem. In this method, the algorithm’s performance is checked according to the size of its inputs.
For example, consider the algorithm for calculating the sum of the numbers of an array that I wrote in the previous answer. This algorithm adds all the array elements using a for loop. The execution time of this algorithm directly depends on the number of array elements. In other words, if the array’s length is n, the execution time of the algorithm increases linearly with the number of n.
Since each operation of adding two numbers similarly requires a constant amount of time, the execution time of the algorithm increases linearly with n. In other words, the execution time of the algorithm is equal to O(n). This means that the execution time of the algorithm is directly related to the size of its input.
Also, the space that the algorithm needs to run is important. In the algorithm for calculating the sum of the numbers of an array, the space required to store the collection and the variables needed to calculate the sum is constant and is O(1).
According to the temporal and spatial analysis of the algorithm, you can check its strengths and weaknesses and, if necessary, make changes to it.
What is the time spent by an algorithm?
The time spent by an algorithm means the amount of time the algorithm needs to solve a problem. This time is determined according to the size of the algorithm’s inputs. In other words, the time spent by an algorithm is directly related to the size of its input.
The time spent by an algorithm can be done intermittently or as a set of operations. For example, the bubble sort algorithm moves the array’s length twice using a for loop, each driving the largest element to the end of the collection. The execution time of this algorithm is linear with the number of array elements and is equal to O(n^2).
Also, there are other algorithms whose execution time potentially increases with the size of their input. For example, the algorithm for calculating the power of a number uses division and a recursion loop, which greatly increases its execution time by increasing the input value. This algorithm works using division and recursive loops, and its execution time is O(log n), where n is equal to the input value of the algorithm.
In general, to check the time spent by an algorithm, we must pay attention to the size of its inputs and estimate the execution time of the algorithm according to this size of information.
Step Count (Frequency Count)
Frequency Count is a useful way to check the number of times a certain event occurs in a set. This method is used in various algorithms and is usually used to examine the distribution of objects, especially arrays. For example, below is a simple algorithm to count the number of times each element in an array is repeated:
Algorithm frequency count(arr):
freq = {}
for i from 0 to length(arr)-1:
if arr[i] not in freq:
freq[arr[i]] = 1
Otherwise:
freq[arr[i]] = freq[arr[i]] + 1
return freq
In this algorithm, a dictionary named freq is defined. At each step of the loop, if the desired element is not already in the dictionary, it is added, and its counter is set to 1. If the component exists in the dictionary, its counter is incremented by 1. Finally, the dictionary freq contains the number of occurrences of each element in the array and is returned as the algorithm’s output.
Using step counting for a collection of objects, especially arrays, one can obtain the number of occurrences of each element and use that to find distinct values and distributions of data.
last word
Algorithmic analysis is very important for solving problems efficiently, choosing the best solution, and checking the efficiency of algorithms. Below we mention some important reasons that show that algorithmic analysis is critical.
- Improving the performance of algorithms: With algorithmic analysis, it is possible to check the improvement of algorithms and design better algorithms. Improved algorithm performance can save time, memory, and other computer resources.
- Choosing the best solution: With algorithmic analysis, you can select the best solution to solve a problem. For example, by examining the execution time of different algorithms for a specific issue, one can choose the best solution and minimize the time spent on solving the problem.
- Identifying the limitations of algorithms: With algorithmic analysis, it is possible to identify and predict the limitations of algorithms. For example, an algorithm may be highly efficient for solving a problem with a small input size but require a lot of time and memory to run for a large input size.
In general, algorithmic analysis is used to improve the performance of algorithms, choose the best solution, identify the limitations of algorithms, etc.