Algorithm Classification and Examples

Classification of algorithms helps in selecting the most suitable algorithm for a specific task, allowing developers to optimize their code and obtain better performance. In computer science, an algorithm is a well-defined set of instructions used to solve a problem or perform a specific task. The efficiency and effectiveness of these algorithms are critical in determining the overall performance of the program.

In this article, we will discuss two common ways to classify algorithms, namely based on time complexity and based on design techniques.

grammar

The syntax of the main function is used in the code of both methods -

int main() {
   // Your code here
}

algorithm

• Determine the problem to be solved.

• Choose appropriate methods to classify algorithms.

• Write code in C using the method of choice.

• Compile and run the code.

• Analyze output.

What is the time complexity?

Time complexity is a measure of how long it takes an algorithm to run as a function of the input size. It is a way of describing the efficiency of an algorithm and its scalability as the size of the input increases.

Time complexity is usually expressed in big O notation, which gives an upper limit on the running time of the algorithm. For example, an algorithm with a time complexity of O(1) means that the running time remains constant regardless of the input size, while an algorithm with a time complexity of O(n^2) means that the running time grows quadratically with the input size. . Understanding the time complexity of an algorithm is important when choosing the right algorithm to solve a problem and when comparing different algorithms.

Method 1: Classify algorithms based on time complexity

This approach covers the classification of algorithms based on their time complexity.

This requires first interpreting the duration complexity of the algorithm, and then classifying it into one of five categories based on its elapsed time complexity: O(1) constant time complexity, O(log n) logarithm Time complexity, O(n) linear time complexity, O(n^2) quadratic time complexity, or O(2^n) exponential time complexity. This classification reveals the effectiveness of the algorithm, and the input data size and expected completion time can be taken into consideration when selecting an algorithm.

The Chinese translation of

Example-1

is:

Example-1

The code below shows a demonstration of the linear search algorithm, which has a linear time complexity of O(n). This algorithm performs a systematic check of the elements in an array to determine if any match a specified search element. Once found, the function returns the index of the element, otherwise it returns -1, indicating that the element is not in the array. The main function starts by initializing the array and searching for elements, calling the linearSearch function, and finally rendering the results.

<int>#include <iostream>
#include <vector>
#include <algorithm>
// Linear search function with linear time complexity O(n)
int linearSearch(const std::vector<int>& arr, int x) {
    for (size_t i = 0; i < arr.size(); i++) {
        if (arr[i] == x) {
            return static_cast<int>(i);
        }
    }
    return -1;
}
int main() {
    std::vector<int> arr = {1, 2, 3, 4, 5, 6, 7, 8, 9};
    int search_element = 5;
    int result = linearSearch(arr, search_element);
    if (result != -1) {
        std::cout << "Element found at index: " << result << std::endl;
    } else {
        std::cout << "Element not found in the array." << std::endl;
    }
    return 0;
}
</int>

Output

Element found at index: 4

Method 2: Classify algorithms based on design techniques.

• Design skills of analysis algorithms.

• Classify algorithms into one of the following categories −

  • Brute-force algorithm

  • Divide and Conquer Algorithm

  • Greedy algorithm

  • Dynamic programming algorithm

  • Backtracking algorithm

The Chinese translation of

Example-2

is:

Example-2

The following program shows the implementation of the binary search algorithm, which uses the divide-and-conquer strategy and has logarithmic time complexity O(log n). The algorithm repeatedly splits the array into two parts and checks the middle element. If this intermediate element is equal to the search element being sought, the index is returned immediately. If the middle element exceeds the search element, the search continues in the left half of the array, if the middle element is smaller, the search proceeds in the right half. The main function initializes the array and searches for elements, arranges the array by sorting, calls the binarySearch function, and finally presents the results.

#include <iostream>
#include <vector>
#include <algorithm>

// Binary search function using divide and conquer technique with logarithmic time complexity O(log n)
int binarySearch(const std::vector<int>& arr, int left, int right, int x) {
   if (right >= left) {
      int mid = left + (right - left) / 2;

      if (arr[mid] == x) {
         return mid;
      }

      if (arr[mid] > x) {
         return binarySearch(arr, left, mid - 1, x);
      }

      return binarySearch(arr, mid + 1, right, x);
   }
   return -1;
}

int main() {
   std::vector<int> arr = {1, 2, 3, 4, 5, 6, 7, 8, 9};
   int search_element = 5;

   // The binary search algorithm assumes that the array is sorted.
   std::sort(arr.begin(), arr.end());

   int result = binarySearch(arr, 0, static_cast<int>(arr.size()) - 1, search_element);

   if (result != -1) {
      std::cout << "Element found at index: " << result <<std::endl;
   } else {
      std::cout << "Element not found in the array." << std::endl;
   }
   return 0;
}

Output

Element found at index: 4

in conclusion

Therefore, in this article, two approaches to classification algorithms are discussed - based on their time complexity and based on their design methods. As examples, we introduce a linear search algorithm and a binary search algorithm, both implemented in C. The linear search algorithm uses a brute force method and has a linear time complexity of O(n), while the binary search algorithm uses the divide-and-conquer method and exhibits a logarithmic time complexity of O(log n). A thorough understanding of the various classifications of algorithms will help in selecting the best algorithm for a specific task and improving the code to improve performance.

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