feat: add dnf sort (#1558)

* add dnf sort

* refactored code

* remove extra empty lines

* add tests

* update date type for non-negative values

* Update sorting/dnf_sort.cpp

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

* Update sorting/dnf_sort.cpp

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

* Update sorting/dnf_sort.cpp

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

* Update sorting/dnf_sort.cpp

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

* Update sorting/dnf_sort.cpp

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

* Update sorting/dnf_sort.cpp

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

* Update sorting/dnf_sort.cpp

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

* Update sorting/dnf_sort.cpp

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

* Update sorting/dnf_sort.cpp

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

* updating DIRECTORY.md

* Update sorting/dnf_sort.cpp

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

* update data type for variables

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

sorting/dnf_sort.cpp

@@ -0,0 +1,109 @@
+/**
+ * @file
+ * @brief Implementation of the [DNF
+ * sort](https://www.geeksforgeeks.org/sort-an-array-of-0s-1s-and-2s/) implementation
+ * @details
+ * C++ program to sort an array with 0, 1 and 2 in a single pass(DNF sort).
+ * Since one traversal of the array is there hence it works in O(n) time
+ * complexity.
+ * @author [Sujal Gupta](https://github.com/heysujal)
+ */
+
+#include <algorithm>  /// for std::is_sorted
+#include <cassert>    /// for assert
+#include <iostream>   /// for std::swap and io operations
+#include <vector>     /// for std::vector
+
+/**
+ * @namespace sorting
+ * @breif Sorting algorithms
+ */
+namespace sorting {
+/**
+ * @namespace dnf_sort
+ * @brief Functions for the [DNF
+ * sort](https://en.wikipedia.org/wiki/Dutch_national_flag_problem) implementation
+ */
+namespace dnf_sort {
+/**
+ * @brief The main function implements DNF sort
+ * @tparam T type of array
+ * @param a array to be sorted,
+ * @param arr_size size of array
+ * @returns void
+ */
+template <typename T>
+std::vector<T> dnfSort(const std::vector<T> &in_arr) {
+    std::vector<T> arr(in_arr);
+    uint64_t lo = 0;
+    uint64_t hi = arr.size() - 1;
+    uint64_t mid = 0;
+
+    // Iterate till all the elements
+    // are sorted
+    while (mid <= hi) {
+        switch (arr[mid]) {
+            // If the element is 0
+            case 0:
+                std::swap(arr[lo++], arr[mid++]);
+                break;
+
+            // If the element is 1 .
+            case 1:
+                mid++;
+                break;
+
+            // If the element is 2
+            case 2:
+                std::swap(arr[mid], arr[hi--]);
+                break;
+        }
+    }
+    return arr;
+}
+}  // namespace dnf_sort
+}  // namespace sorting
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+    // 1st test
+    // [1, 0, 2, 1] return [0, 1, 1, 2]
+    std::vector<uint64_t> array1 = {0, 1, 1, 2};
+    std::cout << "Test 1... ";
+    std::vector<uint64_t> arr1 = sorting::dnf_sort::dnfSort(array1);
+    assert(std::is_sorted(std::begin(arr1), std::end(arr1)));
+    std::cout << "passed" << std::endl;
+    // 2nd test
+    // [1, 0, 0, 1, 1, 0, 2, 1] return [0, 0, 0, 1, 1, 1, 1, 2]
+    std::vector<uint64_t> array2 = {1, 0, 0, 1, 1, 0, 2, 1};
+    std::cout << "Test 2... ";
+    std::vector<uint64_t> arr2 = sorting::dnf_sort::dnfSort(array2);
+    assert(std::is_sorted(std::begin(arr2), std::end(arr2)));
+    std::cout << "passed" << std::endl;
+    // 3rd test
+    // [1, 1, 0, 0, 1, 2, 2, 0, 2, 1] return [0, 0, 0, 1, 1, 1, 1, 2, 2, 2]
+    std::vector<uint64_t> array3 = {1, 1, 0, 0, 1, 2, 2, 0, 2, 1};
+    std::cout << "Test 3... ";
+    std::vector<uint64_t> arr3 = sorting::dnf_sort::dnfSort(array3);
+    assert(std::is_sorted(std::begin(arr3), std::end(arr3)));
+    std::cout << "passed" << std::endl;
+    // 4th test
+    // [2, 2, 2, 0, 0, 1, 1] return [0, 0, 1, 1, 2, 2, 2]
+    std::vector<uint64_t> array4 = {2, 2, 2, 0, 0, 1, 1};
+    std::cout << "Test 4... ";
+    std::vector<uint64_t> arr4 = sorting::dnf_sort::dnfSort(array4);
+    assert(std::is_sorted(std::begin(arr4), std::end(arr4)));
+    std::cout << "passed" << std::endl;
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // execute the test
+    return 0;
+}