feat: Added Recursive Bubble Sort (#1487)

* feat: Added recursive bubble sort

* updating DIRECTORY.md

* fixed clang-tidy warnings

* fixed swap function

* improved documentation

* Reworked documentation

* reworked documentation

* fixed ubuntu compile errors

* Enhanced documentation

* Apply suggestions from code review

Co-authored-by: David Leal <halfpacho@gmail.com>

* Added explanation link and fixed documentation

* Added explanation link and fixed documentation

* Update settings.json

Removed `"cmake.configureOnOpen": false`

* Apply suggestions from code review

Co-authored-by: David Leal <halfpacho@gmail.com>

* Apply suggestions from code review

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update recursive_bubble_sort.cpp

Removed the `swap` function

* Apply suggestions from code review

Co-authored-by: David Leal <halfpacho@gmail.com>

* Apply suggestions from code review

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update recursive_bubble_sort.cpp

Replaced `int` with `uint64_t`

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: David Leal <halfpacho@gmail.com>

DIRECTORY.md

@@ -296,6 +296,7 @@
   * [Quick Sort 3](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/quick_sort_3.cpp)
   * [Radix Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/radix_sort.cpp)
   * [Radix Sort2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/radix_sort2.cpp)
+  * [Recursive Bubble Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/recursive_bubble_sort.cpp)
   * [Selection Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/selection_sort.cpp)
   * [Shell Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/shell_sort.cpp)
   * [Shell Sort2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/shell_sort2.cpp)

sorting/recursive_bubble_sort.cpp

@@ -0,0 +1,149 @@
+/**
+ * @file
+ * @author [Aditya Prakash](https://adityaprakash.tech)
+ * @brief This is an implementation of a recursive version of the [Bubble sort algorithm](https://www.geeksforgeeks.org/recursive-bubble-sort/)
+ *
+ * @details
+ * The working principle of the Bubble sort algorithm.
+
+ * Bubble sort is a simple sorting algorithm used to rearrange a set of ascending or descending order elements.
+ * Bubble sort gets its name from the fact that data "bubbles" to the top of the dataset.
+ 
+ * ### Algorithm
+
+ * What is Swap?
+
+ * Swapping two numbers means that we interchange their values.
+ * Often, an additional variable is required for this operation. 
+ * This is further illustrated in the following:
+
+ * void swap(int x, int y){
+ *     int z = x;
+ *     x = y;
+ *     y = z;
+ * }
+
+ * The above process is a typical displacement process.
+ * When we assign a value to x, the old value of x is lost.
+ * That's why we create a temporary variable z to store the initial value of x.
+ * z is further used to assign the initial value of x to y, to complete swapping.
+
+ * Recursion
+
+ * While the recursive method does not necessarily have advantages over iterative
+ * versions, but it is useful to enhance the understanding of the algorithm and
+ * recursion itself. In Recursive Bubble sort algorithm, we firstly call the
+ * function on the entire array, and for every subsequent function call, we exclude
+ * the last element. This fixes the last element for that sub-array.Formally, for
+ * `ith` iteration, we consider elements up to n-i, where n is the number of
+ * elements in the array. Exit condition: n==1; i.e. the sub-array contains only
+ * one element.
+
+ * Complexity
+ * Time complexity: O(n) best case; O(n²) average case; O(n²) worst case
+ * Space complexity: O(n)
+
+ * We need to traverse the array `n * (n-1)` times. However, if the entire array is
+ * already sorted, then we need to traverse it only once. Hence, O(n) is the best case
+ * complexity
+*/
+
+#include <cassert>   /// for assert
+#include <iostream>  /// for IO operations
+#include <vector>    /// for std::vector
+#include <array>     /// for std::array
+#include <algorithm> /// for std::is_sorted
+
+/**
+ * @namespace sorting
+ * @brief Sorting algorithms
+ */
+namespace sorting {
+
+/**
+ * @brief This is an implementation of the recursive_bubble_sort. A vector is passed
+ * to the function which is then dereferenced, so that the changes are
+ * reflected in the original vector. It also accepts a second parameter of
+ * type `int` and name `n`, which is the size of the array.
+ * 
+ * @tparam T type of data variables in the array
+ * @param nums our array of elements.
+ * @param n size of the array
+ */
+template <typename T>
+void recursive_bubble_sort(std::vector<T> *nums, uint64_t n) {
+    if (n == 1) {  //!< base case; when size of the array is 1
+        return;
+    }
+
+    for (uint64_t i = 0; i < n - 1; i++) {  //!< iterating over the entire array
+        //!< if a larger number appears before the smaller one, swap them.
+        if ((*nums)[i] > (*nums)[i + 1]) {
+            std::swap((*nums)[i], (*nums)[i + 1]);
+        }
+    }
+
+    //!< calling the function after we have fixed the last element
+    recursive_bubble_sort(nums, n - 1);
+}
+}  // namespace sorting
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+    // 1st example. Creating an array of type `int`.
+    std::cout << "1st test using `int`\n";
+    const uint64_t size = 6;
+    std::vector<int64_t> arr;
+    // populating the array
+    arr.push_back(22);
+    arr.push_back(46);
+    arr.push_back(94);
+    arr.push_back(12);
+    arr.push_back(37);
+    arr.push_back(63);
+    // array populating ends
+
+    sorting::recursive_bubble_sort(&arr, size);
+    assert(std::is_sorted(std::begin(arr), std::end(arr)));
+    std::cout << " 1st test passed!\n";
+    // printing the array
+    for (uint64_t i = 0; i < size; i++) {
+        std::cout << arr[i] << ", ";
+    }
+    std::cout << std::endl;
+
+    // 2nd example. Creating an array of type `double`.
+    std::cout << "2nd test using doubles\n";
+    std::vector<double> double_arr;
+
+    // populating the array
+    double_arr.push_back(20.4);
+    double_arr.push_back(62.7);
+    double_arr.push_back(12.2);
+    double_arr.push_back(43.6);
+    double_arr.push_back(74.1);
+    double_arr.push_back(57.9);
+    // array populating ends
+
+    sorting::recursive_bubble_sort(&double_arr, size);
+    assert(std::is_sorted(std::begin(double_arr), std::end(double_arr)));
+    std::cout << " 2nd test passed!\n";
+    // printing the array
+    for (uint64_t i = 0; i < size; i++) {
+        std::cout << double_arr[i] << ", ";
+    }
+    std::cout << std::endl;
+
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() { 
+    test();  // run self-test implementations
+    return 0;
+}