Added Iterative Quick Sort (#2684)

* feat: Added iterative quick sort using stack

* fix: Forgot to add @param for sort function

* Update sorting/quick_sort_iterative.cpp

* Update sorting/quick_sort_iterative.cpp

* Update sorting/quick_sort_iterative.cpp

* style: space b/w for and comment

* Update sorting/quick_sort_iterative.cpp

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

* Update sorting/quick_sort_iterative.cpp

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

* fixed namespace error

---------

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

sorting/quick_sort_iterative.cpp

@@ -0,0 +1,132 @@
+/**
+ * @file
+ * @brief Quick Sort without recursion. This method uses the stack instead.
+ * Both recursive and iterative implementations have O(n log n) best case
+ * and O(n^2) worst case.
+ * @details
+ * https://stackoverflow.com/questions/12553238/quicksort-iterative-or-recursive
+ * https://en.wikipedia.org/wiki/Quicksort
+ * https://www.geeksforgeeks.org/iterative-quick-sort/
+ * @author [Sebe324](https://github.com/sebe324)
+ */
+
+#include <iostream> /// for std::cout
+#include <vector> /// for std::vector
+#include <stack> /// for std::stack
+#include <algorithm> /// for std::is_sorted
+#include <cassert> /// for assert
+
+
+/**
+ * @namespace sorting
+ * @brief Sorting algorithms
+ */
+namespace sorting {
+/**
+ * @brief The partition function sorts the array from
+ * start to end and uses the last element as the pivot.
+ * @param arr the array to be sorted
+ * @param start starting index
+ * @param end ending index
+ * @return int next index of the pivot
+ */
+int partition(std::vector<int> &arr, int start, int end)
+{
+    int pivot = arr[end];
+    int index = start - 1;
+
+    for (int j = start; j < end; j++) {
+        if (arr[j] <= pivot) {
+            std::swap(arr[++index], arr[j]);
+        }
+    }
+
+    std::swap(arr[index + 1], arr[end]);
+    return index + 1;
+}
+
+/**
+ * @brief The main sorting function
+ * @details The iterative quick sort uses
+ * the stack instead of recursion for saving
+ * and restoring the environment between calls.
+ * It does not need the end and start params, because
+ * it is not recursive.
+ * @param arr array to be sorted
+ * @return void
+ */
+void iterativeQuickSort(std::vector<int> &arr)
+{
+    std::stack<int> stack;
+    int start = 0;
+    int end = arr.size()-1;
+    stack.push(start);
+    stack.push(end);
+
+    while(!stack.empty())
+    {
+        end = stack.top();
+        stack.pop();
+        start = stack.top();
+        stack.pop();
+
+        int pivotIndex = partition(arr,start,end);
+
+        if(pivotIndex -1 > start)
+        {
+            stack.push(start);
+            stack.push(pivotIndex-1);
+        }
+
+        if(pivotIndex+1<end)
+        {
+            stack.push(pivotIndex+1);
+            stack.push(end);
+        }
+    }
+}
+
+} // namespace sorting
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+void tests()
+{
+    //TEST 1 - Positive numbers
+    std::vector<int> case1={100,534,1000000,553,10,61,2000,238,2756,9,12,56,30};
+    std::cout<<"TEST 1\n";
+    std::cout<<"Before: \n";
+    for(auto x : case1) std::cout<<x<<",";
+    std::cout<<"\n";
+    sorting::iterativeQuickSort(case1);
+    assert(std::is_sorted(std::begin(case1),std::end(case1)));
+    std::cout<<"Test 1 succesful!\n";
+    std::cout<<"After: \n";
+    for(auto x : case1) std::cout<<x<<",";
+    std::cout<<"\n";
+
+    //TEST 2 - Negative numbers
+    std::vector<int> case2={-10,-2,-5,-2,-3746,-785,-123, -452, -32456};
+    std::cout<<"TEST 2\n";
+    std::cout<<"Before: \n";
+    for(auto x : case2) std::cout<<x<<",";
+    std::cout<<"\n";
+    sorting::iterativeQuickSort(case2);
+    assert(std::is_sorted(std::begin(case2),std::end(case2)));
+    std::cout<<"Test 2 succesful!\n";
+    std::cout<<"After: \n";
+    for(auto x : case2) std::cout<<x<<",";
+    std::cout<<"\n";
+}
+
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main()
+{
+    tests(); // run self test implementation
+    return 0;
+}