feat: add recursive inserstion sort

sorting/insertion_sort.cpp

@@ -1,101 +1,90 @@
 /**
- *
  * \file
- * \brief [Insertion Sort Algorithm
+ * \brief [Recursive Insertion Sort Algorithm
  * (Insertion Sort)](https://en.wikipedia.org/wiki/Insertion_sort)
  *
  * \details
  * Insertion sort is a simple sorting algorithm that builds the final
- * sorted array one at a time. It is much less efficient compared to
- * other sorting algorithms like heap sort, merge sort or quick sort.
- * However it has several advantages such as
- * 1. Easy to implement
- * 2. For small set of data it is quite efficient
- * 3. More efficient that other Quadratic complexity algorithms like
- *    Selection sort or bubble sort.
- * 4. It's stable that is it does not change the relative order of
- *    elements with equal keys
- * 5. Works on hand means it can sort the array or list as it receives.
- *
- * It is based on the same idea that people use to sort the playing cards in
- * their hands.
- * the algorithms goes in the manner that we start iterating over the array
- * of elements as soon as we find a unsorted element that is a misplaced
- * element we place it at a sorted position.
- *
- * Example execution steps:
- * 1. Suppose initially we have
- * \f{bmatrix}{4 &3 &2 &5 &1\f}
- * 2. We start traversing from 4 till we reach 1
- * when we reach at 3 we find that it is misplaced so we take 3 and place
- * it at a correct position thus the array will become
- * \f{bmatrix}{3 &4 &2 &5 &1\f}
- * 3. In the next iteration we are at 2 we find that this is also misplaced so
- * we place it at the correct sorted position thus the array in this iteration
- * becomes
- * \f{bmatrix}{2 &3 &4 &5 &1\f}
- * 4. We do not do anything with 5 and move on to the next iteration and
- * select 1 which is misplaced and place it at correct position. Thus, we have
- * \f{bmatrix}{1 &2 &3 &4 &5\f}
+ * sorted array one at a time. The recursive version applies the same
+ * logic but sorts the sub-array recursively before inserting the current
+ * element in its correct position.
  */
 
-#include <algorithm>
-#include <cassert>
-#include <iostream>
-#include <vector>
+#include <algorithm>  // for std::is_sorted and std::swap
+#include <cassert>    // for assert
+#include <iostream>   // for std::cout and std::endl
+#include <vector>     // for std::vector
 
 /** \namespace sorting
  * \brief Sorting algorithms
  */
 namespace sorting {
-/** \brief
- * Insertion Sort Function
+/** 
+ * \brief Recursive Insertion Sort Function for an array
  *
- * @tparam T type of array
- * @param [in,out] arr Array to be sorted
- * @param n Size of Array
+ * @tparam T Type of the elements in the array
+ * @param[in,out] arr Pointer to the array to be sorted
+ * @param[in] n Size of the array
  */
 template <typename T>
-void insertionSort(T *arr, int n) {
-    for (int i = 1; i < n; i++) {
-        T temp = arr[i];
-        int j = i - 1;
-        while (j >= 0 && temp < arr[j]) {
-            arr[j + 1] = arr[j];
-            j--;
-        }
-        arr[j + 1] = temp;
+void recursiveInsertionSort(T *arr, int n) {
+    // Base case: Array of size 1 is already sorted
+    if (n <= 1) {
+        return;
+    }
+
+    // Sort the first n-1 elements recursively
+    recursiveInsertionSort(arr, n - 1);
+
+    // Insert the nth element at its correct position in the sorted array
+    T last = arr[n - 1];
+    int j = n - 2;
+
+    // Move elements of arr[0..n-1] that are greater than last to one
+    // position ahead of their current position
+    while (j >= 0 && arr[j] > last) {
+        arr[j + 1] = arr[j];
+        j--;
     }
+    arr[j + 1] = last;
 }
 
-/** Insertion Sort Function
+/** 
+ * \brief Recursive Insertion Sort Function for a vector
  *
- * @tparam T type of array
- * @param [in,out] arr pointer to array to be sorted
+ * @tparam T Type of the elements in the vector
+ * @param[in,out] arr Pointer to the vector to be sorted
+ * @param[in] n Size of the vector
  */
 template <typename T>
-void insertionSort(std::vector<T> *arr) {
-    size_t n = arr->size();
-
-    for (size_t i = 1; i < n; i++) {
-        T temp = arr[0][i];
-        int32_t j = i - 1;
-        while (j >= 0 && temp < arr[0][j]) {
-            arr[0][j + 1] = arr[0][j];
-            j--;
-        }
-        arr[0][j + 1] = temp;
+void recursiveInsertionSort(std::vector<T> *arr, size_t n) {
+    // Base case: If the vector has one or fewer elements, it's already sorted
+    if (n <= 1) {
+        return;
+    }
+
+    // Sort the first n-1 elements recursively
+    recursiveInsertionSort(arr, n - 1);
+
+    // Insert the nth element at its correct position in the sorted vector
+    T last = arr->at(n - 1);
+    int j = n - 2;
+
+    while (j >= 0 && arr->at(j) > last) {
+        arr->at(j + 1) = arr->at(j);
+        j--;
     }
+    arr->at(j + 1) = last;
 }
 
 }  // namespace sorting
 
-/**
- * @brief Create a random array objecthelper function to create a random array
+/** 
+ * \brief Helper function to create a random array
  *
- * @tparam T type of array
- * @param arr array to fill (must be pre-allocated)
- * @param N number of array elements
+ * @tparam T Type of array elements
+ * @param[out] arr Pointer to the array to be filled
+ * @param[in] N Size of the array
  */
 template <typename T>
 static void create_random_array(T *arr, int N) {
@@ -105,75 +94,57 @@ static void create_random_array(T *arr, int N) {
     }
 }
 
-/** Test Cases to test algorithm */
+/** 
+ * \brief Test cases to validate the recursive insertion sort algorithm 
+ */
 void tests() {
     int arr1[10] = {78, 34, 35, 6, 34, 56, 3, 56, 2, 4};
     std::cout << "Test 1... ";
-    sorting::insertionSort(arr1, 10);
+    sorting::recursiveInsertionSort(arr1, 10);
     assert(std::is_sorted(arr1, arr1 + 10));
     std::cout << "passed" << std::endl;
 
     int arr2[5] = {5, -3, 7, -2, 1};
     std::cout << "Test 2... ";
-    sorting::insertionSort(arr2, 5);
+    sorting::recursiveInsertionSort(arr2, 5);
     assert(std::is_sorted(arr2, arr2 + 5));
     std::cout << "passed" << std::endl;
 
     float arr3[5] = {5.6, -3.1, -3.0, -2.1, 1.8};
     std::cout << "Test 3... ";
-    sorting::insertionSort(arr3, 5);
+    sorting::recursiveInsertionSort(arr3, 5);
     assert(std::is_sorted(arr3, arr3 + 5));
     std::cout << "passed" << std::endl;
 
     std::vector<float> arr4({5.6, -3.1, -3.0, -2.1, 1.8});
     std::cout << "Test 4... ";
-    sorting::insertionSort(&arr4);
+    sorting::recursiveInsertionSort(&arr4, arr4.size());
     assert(std::is_sorted(std::begin(arr4), std::end(arr4)));
     std::cout << "passed" << std::endl;
 
     int arr5[50];
     std::cout << "Test 5... ";
     create_random_array(arr5, 50);
-    sorting::insertionSort(arr5, 50);
+    sorting::recursiveInsertionSort(arr5, 50);
     assert(std::is_sorted(arr5, arr5 + 50));
     std::cout << "passed" << std::endl;
 
     float arr6[50];
     std::cout << "Test 6... ";
     create_random_array(arr6, 50);
-    sorting::insertionSort(arr6, 50);
+    sorting::recursiveInsertionSort(arr6, 50);
     assert(std::is_sorted(arr6, arr6 + 50));
     std::cout << "passed" << std::endl;
 }
 
-/** Main Function */
+/** 
+ * \brief Main function
+ * 
+ * Empty except for the call to `tests()`.
+ * 
+ * @return 0 Always returns 0.
+ */
 int main() {
-    /// Running predefined tests to test algorithm
     tests();
-
-    /// For user insteraction
-    size_t n;
-    std::cout << "Enter the length of your array (0 to exit): ";
-    std::cin >> n;
-    if (n == 0) {
-        return 0;
-    }
-
-    int *arr = new int[n];
-    std::cout << "Enter any " << n << " Numbers for Unsorted Array : ";
-
-    for (int i = 0; i < n; i++) {
-        std::cin >> arr[i];
-    }
-
-    sorting::insertionSort(arr, n);
-
-    std::cout << "\nSorted Array : ";
-    for (int i = 0; i < n; i++) {
-        std::cout << arr[i] << " ";
-    }
-
-    std::cout << std::endl;
-    delete[] arr;
     return 0;
 }