Merge branch 'TheAlgorithms:master' into master

math/fibonacci.cpp

@@ -1,68 +1,65 @@
 /**
  * @file
- * @brief Generate fibonacci sequence
+ * @brief n-th [Fibonacci
+ * number](https://en.wikipedia.org/wiki/Fibonacci_sequence).
  *
- * Calculate the the value on Fibonacci's sequence given an
- * integer as input.
+ * @details
+ * Naive recursive implementation to calculate the n-th Fibonacci number.
  * \f[\text{fib}(n) = \text{fib}(n-1) + \text{fib}(n-2)\f]
  *
  * @see fibonacci_large.cpp, fibonacci_fast.cpp, string_fibonacci.cpp
  */
-#include <cassert>
-#include <iostream>
+#include <cassert>   /// for assert
+#include <iostream>  /// for IO operations
 
 /**
- * Recursively compute sequences
- * @param n input
- * @returns n-th element of the Fbinacci's sequence
+ * @namespace math
+ * @brief Math algorithms
+ */
+namespace math {
+/**
+ * @namespace fibonacci
+ * @brief Functions for Fibonacci sequence
+ */
+namespace fibonacci {
+/**
+ * @brief Function to compute the n-th Fibonacci number
+ * @param n the index of the Fibonacci number
+ * @returns n-th element of the Fibonacci's sequence
  */
 uint64_t fibonacci(uint64_t n) {
-    /* If the input is 0 or 1 just return the same
-       This will set the first 2 values of the sequence */
+    // If the input is 0 or 1 just return the same (Base Case)
+    // This will set the first 2 values of the sequence
     if (n <= 1) {
         return n;
     }
 
-    /* Add the last 2 values of the sequence to get next */
+    // Add the preceding 2 values of the sequence to get next
     return fibonacci(n - 1) + fibonacci(n - 2);
 }
+}  // namespace fibonacci
+}  // namespace math
+
+/**
+ * @brief Self-test implementation
+ * @returns `void`
+ */
+static void test() {
+    assert(math::fibonacci::fibonacci(0) == 0);
+    assert(math::fibonacci::fibonacci(1) == 1);
+    assert(math::fibonacci::fibonacci(2) == 1);
+    assert(math::fibonacci::fibonacci(3) == 2);
+    assert(math::fibonacci::fibonacci(4) == 3);
+    assert(math::fibonacci::fibonacci(15) == 610);
+    assert(math::fibonacci::fibonacci(20) == 6765);
+    std::cout << "All tests have passed successfully!\n";
+}
 
 /**
- * Function for testing the fibonacci() function with a few
- * test cases and assert statement.
- * @returns `void`
-*/
-static void test() {
-    uint64_t test_case_1 = fibonacci(0);
-    assert(test_case_1 == 0);
-    std::cout << "Passed Test 1!" << std::endl;
-
-    uint64_t test_case_2 = fibonacci(1);
-    assert(test_case_2 == 1);
-    std::cout << "Passed Test 2!" << std::endl;
-
-    uint64_t test_case_3 = fibonacci(2);
-    assert(test_case_3 == 1);
-    std::cout << "Passed Test 3!" << std::endl;
-
-    uint64_t test_case_4 = fibonacci(3);
-    assert(test_case_4 == 2);
-    std::cout << "Passed Test 4!" << std::endl;
-
-    uint64_t test_case_5 = fibonacci(4);
-    assert(test_case_5 == 3);
-    std::cout << "Passed Test 5!" << std::endl;
-
-    uint64_t test_case_6 = fibonacci(15);
-    assert(test_case_6 == 610);
-    std::cout << "Passed Test 6!" << std::endl << std::endl;
-}
-
-/// Main function
+ * @brief Main function
+ * @returns 0 on exit
+ */
 int main() {
-    test();
-    int n = 0;
-    std::cin >> n;
-    assert(n >= 0);
-    std::cout << "F(" << n << ")= " << fibonacci(n) << std::endl;
+    test();  // run self-test implementations
+    return 0;
 }

sorting/insertion_sort_recursive.cpp

@@ -0,0 +1,152 @@
+/**
+ * @file
+ * @brief Insertion Sort Algorithm
+ * @author [Dhanush S](https://github.com/Fandroid745)
+ * 
+ * @details
+ * Insertion sort is a simple sorting algorithm that builds the final
+ * sorted array one element 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:
+ * - Easy to implement.
+ * - Efficient for small data sets.
+ * - More efficient than other O(n²) algorithms like selection sort or bubble sort.
+ * - Stable: it does not change the relative order of elements with equal keys.
+ * 
+ * Insertion sort works similarly to how people sort playing cards in their hands.
+ * The algorithm iterates through the list and inserts each element into its correct 
+ * position in the sorted portion of the array.
+ * 
+ * The time complexity of the algorithm is \f$O(n^2)\f$, and in some cases, it
+ * can be \f$O(n)\f$.
+ * 
+ * Example execution:
+ * 1. Start with the array [4, 3, 2, 5, 1].
+ * 2. Insert 3 in its correct position: [3, 4, 2, 5, 1].
+ * 3. Insert 2: [2, 3, 4, 5, 1].
+ * 4. Continue this until the array is sorted: [1, 2, 3, 4, 5].
+ */
+
+
+#include <algorithm>   /// for std::is_sorted
+#include <cassert>     /// for assert function in testing
+#include <iostream>    /// for std::cout and std::endl
+#include <vector>      /// for using std::vector
+
+/** 
+ * @namespace sorting
+ * @brief Contains sorting algorithms
+ */
+namespace sorting {
+
+/**
+ * @brief Insertion Sort Function
+ * 
+ * @tparam T Type of the array elements
+ * @param[in,out] arr Array to be sorted
+ * @param 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;
+    }
+}
+
+/**
+ * @brief Insertion Sort for a vector
+ * 
+ * @tparam T Type of the vector elements
+ * @param [in,out] arr Pointer to the vector to be sorted
+ */
+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->at(i);
+        int32_t j = i - 1;
+        while (j >= 0 && temp < arr->at(j)) {
+            arr->at(j + 1) = arr->at(j);
+            j--;
+        }
+        arr->at(j + 1) = temp;
+    }
+}
+
+}  // namespace sorting
+
+/**
+ * @brief Helper function to create a random array
+ * 
+ * @tparam T Type of the array elements
+ * @param arr Array to fill (must be pre-allocated)
+ * @param N Number of elements in the array
+ */
+template <typename T>
+static void create_random_array(T *arr, int N) {
+    while (N--) {
+        double r = (std::rand() % 10000 - 5000) / 100.f;
+        arr[N] = static_cast<T>(r);
+    }
+}
+
+/** 
+ * @brief self test implementation
+ * @return void
+ */
+static void tests() {
+    int arr1[10] = {78, 34, 35, 6, 34, 56, 3, 56, 2, 4};
+    std::cout << "Test 1... ";
+    sorting::insertionSort(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);
+    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);
+    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);
+    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);
+    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);
+    assert(std::is_sorted(arr6, arr6 + 50));
+    std::cout << "passed" << std::endl;
+}
+
+/** 
+ * @brief Main function
+ * @return 0 on successful exit.
+ */
+int main() {
+    tests(); /// run self test implementations
+    return 0;
+}