docs, test: Fit bubble_sort into guidelines and enhance bubble sort algorithm (#2800)

* Update bubble_sort.cpp

* Update bubble_sort.cpp

* Update bubble_sort.cpp

Add latex notation

* Update sorting/bubble_sort.cpp

Co-authored-by: realstealthninja <[email protected]>

* Update sorting/bubble_sort.cpp

Co-authored-by: realstealthninja <[email protected]>

* Update bubble_sort.cpp

---------

Co-authored-by: realstealthninja <[email protected]>

Author: hollowcrust

sorting/bubble_sort.cpp

@@ -2,82 +2,133 @@
  * @file
  * @brief Bubble sort algorithm
  *
- * The working principle of the Bubble sort algorithm:
+ * @details
+ * Bubble sort algorithm is the bubble sorting algorithm. The most important reason
+ * for calling the bubble is that the largest number is thrown at the end of this
+ * algorithm. This is all about the logic. In each iteration, the largest number is
+ * expired and when iterations are completed, the sorting takes place.
+ * 
+ * What is Swap?
+ * 
+ * Swap in the software means that two variables are displaced.
+ * An additional variable is required for this operation. x = 5, y = 10.
+ * We want x = 10, y = 5. Here we create the most variable to do it.
+ * 
+ * ```cpp
+ * int z;
+ * z = x;
+ * x = y;
+ * y = z;
+ * ```
+ * 
+ * The above process is a typical displacement process.
+ * When x assigns the value to x, the old value of x is lost.
+ * That's why we created a variable z to create the first value of the value of x,
+ * and finally, we have assigned to y.
+ * 
+ * ## Bubble Sort Algorithm Analysis (Best Case - Worst Case - Average Case)
+ * 
+ * ### Best Case
+ * Bubble Sort Best Case Performance. \f$O(n)\f$. However, you
+ * can't get the best status in the code we shared above. This happens on the
+ * optimized bubble sort algorithm. It's right down there.
+ * 
+ * ### Worst Case
+ * Bubble Sort Worst Case Performance is \f$O(n^{2})\f$. Why is that? Because if you
+ * remember Big O Notation, we were calculating the complexity of the algorithms in
+ * the nested loops. The \f$n * (n - 1)\f$ product gives us \f$O(n^{2})\f$ performance. In the
+ * worst case all the steps of the cycle will occur.
+ * 
+ * ### Average Case
+ * Bubble Sort is not an optimal algorithm. In average, \f$O(n^{2})\f$ performance is taken. 
+ * 
+ * @author [Deepak](https://github.com/Deepak-j-p)
+ * @author [Nguyen Phuc Chuong](https://github.com/hollowcrust)
+ */
 
-Bubble sort algorithm is the bubble sorting algorithm. The most important reason
-for calling the bubble is that the largest number is thrown at the end of this
-algorithm. This is all about the logic. In each iteration, the largest number is
-expired and when iterations are completed, the sorting takes place.
+#include <algorithm> /// for std::is_sorted
+#include <cassert>   /// for assert
+#include <iostream>  /// for IO implementations
+#include <string>    /// for std::string
+#include <utility>   /// for std::pair, std::swap
+#include <vector>    /// for std::vector, std::vector::push_back, std::vector::size
 
-What is Swap?
+/**
+ * @namespace sorting
+ * @brief Sorting algorithms
+ */
+namespace sorting {
+/**
+ * @namespace bubble_sort
+ * @brief Bubble sort algorithm
+ */
+namespace bubble_sort {
+/**
+ * @brief Bubble sort algorithm
+ * @param array An array to be sorted
+ * @return The array sorted in ascending order
+ */
+template <typename T> 
+std::vector<T> bubble_sort(std::vector<T>& array) {
+  // swap_check flag to terminate the function early
+  // if there is no swap occurs in one iteration.
+  bool swap_check = true;
+  int size = array.size();
+  for (int i = 0; (i < size) && (swap_check); i++) {
+    swap_check = false;
+    for (int j = 0; j < size - 1 - i; j++) {
+      if (array[j] > array[j + 1]) {
+        swap_check = true;
+        std::swap(array[j], array[j + 1]);
+      }
+    }
+  }
 
-Swap in the software means that two variables are displaced.
-An additional variable is required for this operation. x = 5, y = 10.
-We want x = 10, y = 5. Here we create the most variable to do it.
+  return array;
+}
+} // namespace bubble_sort
+} // namespace sorting
 
-int z;
-z = x;
-x = y;
-y = z;
+/**
+ * @brief Self-test implementation
+ * @return void
+ */
+static void test() {
+  std::vector<int> vec_1 = {3, 1, -9, 0};
+  std::vector<int> sorted_1 = sorting::bubble_sort::bubble_sort(vec_1);
 
-The above process is a typical displacement process.
-When x assigns the value to x, the old value of x is lost.
-That's why we created a variable z to create the first value of the value of x,
-and finally, we have assigned to y.
+  std::vector<int> vec_2 = {3};
+  std::vector<int> sorted_2 = sorting::bubble_sort::bubble_sort(vec_2);
 
-Bubble Sort Algorithm Analysis (Best Case - Worst Case - Average Case)
+  std::vector<int> vec_3 = {10, 10, 10, 10, 10};
+  std::vector<int> sorted_3 = sorting::bubble_sort::bubble_sort(vec_3);
 
-Bubble Sort Worst Case Performance is O (n²). Why is that? Because if you
-remember Big O Notation, we were calculating the complexity of the algorithms in
-the nested loops. The n * (n - 1) product gives us O (n²) performance. In the
-worst case all the steps of the cycle will occur. Bubble Sort (Avarage Case)
-Performance. Bubble Sort is not an optimal algorithm. in average, O (n²)
-performance is taken. Bubble Sort Best Case Performance. O (n). However, you
-can't get the best status in the code we shared above. This happens on the
-optimized bubble sort algorithm. It's right down there.
-*/
+  std::vector<float> vec_4 = {1234, -273.1, 23, 150, 1234, 1555.55, -2000};
+  std::vector<float> sorted_4 = sorting::bubble_sort::bubble_sort(vec_4);
 
-#include <iostream>
-#include <vector>
+  std::vector<char> vec_5 = {'z', 'Z', 'a', 'B', ' ', 'c', 'a'};
+  std::vector<char> sorted_5 = sorting::bubble_sort::bubble_sort(vec_5);
 
-int main() {
-    int n;
-    bool swap_check = true;
-    std::cout << "Enter the amount of numbers to sort: ";
-    std::cin >> n;
-    std::vector<int> numbers;
-    std::cout << "Enter " << n << " numbers: ";
-    int num;
+  std::vector<std::string> vec_6 = {"Hello", "hello", "Helo", "Hi", "hehe"};
+  std::vector<std::string> sorted_6 = sorting::bubble_sort::bubble_sort(vec_6);
 
-    // Input
-    for (int i = 0; i < n; i++) {
-        std::cin >> num;
-        numbers.push_back(num);
-    }
+  std::vector<std::pair<int, char>> vec_7 = {{10, 'c'}, {2, 'z'}, {10, 'a'}, {0, 'b'}, {-1, 'z'}};
+  std::vector<std::pair<int, char>> sorted_7 = sorting::bubble_sort::bubble_sort(vec_7);
 
-    // Bubble Sorting
-    for (int i = 0; (i < n) && (swap_check); i++) {
-        swap_check = false;
-        for (int j = 0; j < n - 1 - i; j++) {
-            if (numbers[j] > numbers[j + 1]) {
-                swap_check = true;
-                std::swap(numbers[j],
-                          numbers[j + 1]);  // by changing swap location.
-                                            // I mean, j. If the number is
-                                            // greater than j + 1, then it
-                                            // means the location.
-            }
-        }
-    }
+  assert(std::is_sorted(sorted_1.begin(), sorted_1.end()));
+  assert(std::is_sorted(sorted_2.begin(), sorted_2.end()));
+  assert(std::is_sorted(sorted_3.begin(), sorted_3.end()));
+  assert(std::is_sorted(sorted_4.begin(), sorted_4.end()));
+  assert(std::is_sorted(sorted_5.begin(), sorted_5.end()));
+  assert(std::is_sorted(sorted_6.begin(), sorted_6.end()));
+  assert(std::is_sorted(sorted_7.begin(), sorted_7.end()));
+}
 
-    // Output
-    std::cout << "\nSorted Array : ";
-    for (int i = 0; i < numbers.size(); i++) {
-        if (i != numbers.size() - 1) {
-            std::cout << numbers[i] << ", ";
-        } else {
-            std::cout << numbers[i] << std::endl;
-        }
-    }
-    return 0;
+/**
+ * @brief Main function
+ * @return 0 on exit
+ */
+int main() {
+  test();
+  return 0;
 }