#### Random Pivot Quick Sort

```/**
* @file
* @brief Implementation of the [Random Pivot Quick
* Sort](https://www.sanfoundry.com/cpp-program-implement-quick-sort-using-randomisation)
* algorithm.
* @details
*          * A random pivot quick sort algorithm is pretty much same as quick
* sort with a difference of having a logic of selecting next pivot element from
* the input array.
*          * Where in quick sort is fast, but still can give you the time
* complexity of O(n^2) in worst case.
*          * To avoid hitting the time complexity of O(n^2), we use the logic
* of randomize the selection process of pivot element.
*
*          ### Logic
*              * The logic is pretty simple, the only change is in the
* partitioning algorithm, which is selecting the pivot element.
*              * Instead of selecting the last or the first element from array
* for pivot we use a random index to select pivot element.
*              * This avoids hitting the O(n^2) time complexity in practical
* use cases.
*
*       ### Partition Logic
*           * Partitions are done such as numbers lower than the "pivot"
* element is arranged on the left side of the "pivot", and number larger than
* the "pivot" element are arranged on the right part of the array.
*
*       ### Algorithm
*           * Select the pivot element randomly using getRandomIndex() function
* from this namespace.
*           * Initialize the pInd (partition index) from the start of the
* array.
*           * Loop through the array from start to less than end. (from start
* to < end). (Inside the loop) :-
*                   * Check if the current element (arr[i]) is less than the
* pivot element in each iteration.
*                   * If current element in the iteration is less than the
* pivot element, then swap the elements at current index (i) and partition
* index (pInd) and increment the partition index by one.
*           * At the end of the loop, swap the pivot element with partition
* index element.
*           * Return the partition index from the function.
*
* @author [Nitin Sharma](https://github.com/foo290)
*/

#include <algorithm>  /// for std::is_sorted(), std::swap()
#include <array>      /// for std::array
#include <cassert>    /// for assert
#include <ctime>      /// for initializing random number generator
#include <iostream>   /// for IO operations
#include <tuple>      /// for returning multiple values form a function at once

/**
* @namespace sorting
* @brief Sorting algorithms
*/
namespace sorting {
/**
* @brief Functions for the [Random Pivot Quick
* Sort](https://www.sanfoundry.com/cpp-program-implement-quick-sort-using-randomisation)
* implementation
* @namespace random_pivot_quick_sort
*/
namespace random_pivot_quick_sort {
/**
* @brief Utility function to print the array
* @tparam T size of the array
* @param arr array used to print its content
* @returns void
* */
template <size_t T>
void showArray(std::array<int64_t, T> arr) {
for (int64_t i = 0; i < arr.size(); i++) {
std::cout << arr[i] << " ";
}
std::cout << std::endl;
}

/**
* @brief Takes the start and end indices of an array and returns a random
* int64_teger between the range of those two for selecting pivot element.
*
* @param start The starting index.
* @param end The ending index.
* @returns int64_t A random number between start and end index.
* */
int64_t getRandomIndex(int64_t start, int64_t end) {
srand(time(nullptr));  // Initialize random number generator.
int64_t randomPivotIndex = start + rand() % (end - start + 1);
return randomPivotIndex;
}

/**
* @brief A partition function which handles the partition logic of quick sort.
* @tparam size size of the array to be passed as argument.
* @param start The start index of the passed array
* @param end The ending index of the passed array
* @returns std::tuple<int64_t , std::array<int64_t , size>> A tuple of pivot
* index and pivot sorted array.
*/
template <size_t size>
std::tuple<int64_t, std::array<int64_t, size>> partition(
std::array<int64_t, size> arr, int64_t start, int64_t end) {
int64_t pivot = arr[end];  // Randomly selected element will be here from
// caller function (quickSortRP()).
int64_t pInd = start;

for (int64_t i = start; i < end; i++) {
if (arr[i] <= pivot) {
std::swap(arr[i], arr[pInd]);  // swapping the elements from current
// index to pInd.
pInd++;
}
}
std::swap(arr[pInd],
arr[end]);  // swapping the pivot element to its sorted position
return std::make_tuple(pInd, arr);
}

/**
* @brief Random pivot quick sort function. This function is the starting point
* of the algorithm.
* @tparam size size of the array to be passed as argument.
* @param start The start index of the passed array
* @param end The ending index of the passed array
* @returns std::array<int64_t , size> A fully sorted array in ascending order.
*/
template <size_t size>
std::array<int64_t, size> quickSortRP(std::array<int64_t, size> arr,
int64_t start, int64_t end) {
if (start < end) {
int64_t randomIndex = getRandomIndex(start, end);

// switching the pivot with right most bound.
std::swap(arr[end], arr[randomIndex]);

int64_t pivotIndex = 0;
// getting pivot index and pivot sorted array.
std::tie(pivotIndex, arr) = partition(arr, start, end);

// Recursively calling
std::array<int64_t, arr.size()> rightSortingLeft =
quickSortRP(arr, start, pivotIndex - 1);
std::array<int64_t, arr.size()> full_sorted =
quickSortRP(rightSortingLeft, pivotIndex + 1, end);
arr = full_sorted;
}
return arr;
}

/**
* @brief A function utility to generate unsorted array of given size and range.
* @tparam size Size of the output array.
* @param from Stating of the range.
* @param to Ending of the range.
* @returns std::array<int64_t , size> Unsorted array of specified size.
* */
template <size_t size>
std::array<int64_t, size> generateUnsortedArray(int64_t from, int64_t to) {
srand(time(nullptr));
std::array<int64_t, size> unsortedArray{};
assert(from < to);
int64_t i = 0;
while (i < size) {
int64_t randomNum = from + rand() % (to - from + 1);
if (randomNum) {
unsortedArray[i] = randomNum;
i++;
}
}
return unsortedArray;
}

}  // namespace random_pivot_quick_sort
}  // namespace sorting

/**
* @brief a class containing the necessary test cases
*/
class TestCases {
private:
/**
* @brief A function to print64_t given message on console.
* @tparam T Type of the given message.
* @returns void
* */
template <typename T>
void log(T msg) {
// It's just to avoid writing cout and endl
std::cout << "[TESTS] : ---> " << msg << std::endl;
}

public:
/**
* @brief Executes test cases
* @returns void
* */
void runTests() {
log("Running Tests...");

testCase_1();
testCase_2();
testCase_3();

log("Test Cases over!");
std::cout << std::endl;
}

/**
* @brief A test case with single input
* @returns void
* */
void testCase_1() {
const int64_t inputSize = 1;
log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"
"~");
log("This is test case 1 for Random Pivot Quick Sort Algorithm : ");
log("Description:");
log("   EDGE CASE : Only contains one element");
std::array<int64_t, inputSize> unsorted_arr{2};

int64_t start = 0;
int64_t end = unsorted_arr.size() - 1;  // length - 1

log("Running algorithm of data of length 50 ...");
std::array<int64_t, unsorted_arr.size()> sorted_arr =
sorting::random_pivot_quick_sort::quickSortRP(unsorted_arr, start,
end);
log("Algorithm finished!");

log("Checking assert expression...");
assert(std::is_sorted(sorted_arr.begin(), sorted_arr.end()));
log("Assertion check passed!");

log("[PASS] : TEST CASE 1 PASS!");
log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"
"~");
}

/**
* @brief A test case with input array of length 500
* @returns void
* */
void testCase_2() {
const int64_t inputSize = 500;
log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"
"~");
log("Description:");
log("   BIG INPUT : Contains 500 elements and repeated elements");
log("This is test case 2 for Random Pivot Quick Sort Algorithm : ");
std::array<int64_t, inputSize> unsorted_arr =
sorting::random_pivot_quick_sort::generateUnsortedArray<inputSize>(
1, 10000);

int64_t start = 0;
int64_t end = unsorted_arr.size() - 1;  // length - 1

log("Running algorithm of data of length 500 ...");
std::array<int64_t, unsorted_arr.size()> sorted_arr =
sorting::random_pivot_quick_sort::quickSortRP(unsorted_arr, start,
end);
log("Algorithm finished!");

log("Checking assert expression...");
assert(std::is_sorted(sorted_arr.begin(), sorted_arr.end()));
log("Assertion check passed!");

log("[PASS] : TEST CASE 2 PASS!");
log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"
"~");
}

/**
* @brief A test case with array of length 1000.
* @returns void
* */
void testCase_3() {
const int64_t inputSize = 1000;
log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"
"~");
log("This is test case 3 for Random Pivot Quick Sort Algorithm : ");
log("Description:");
log("   LARGE INPUT : Contains 1000 elements and repeated elements");
std::array<int64_t, inputSize> unsorted_arr =
sorting::random_pivot_quick_sort::generateUnsortedArray<inputSize>(
1, 10000);

int64_t start = 0;
int64_t end = unsorted_arr.size() - 1;  // length - 1

log("Running algorithm...");
std::array<int64_t, unsorted_arr.size()> sorted_arr =
sorting::random_pivot_quick_sort::quickSortRP(unsorted_arr, start,
end);
log("Algorithm finished!");

log("Checking assert expression...");
assert(std::is_sorted(sorted_arr.begin(), sorted_arr.end()));
log("Assertion check passed!");

log("[PASS] : TEST CASE 3 PASS!");
log("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"
"~");
}
};

/**
* @brief Self-test implementations
* @returns void
*/
static void test() {
TestCases tc = TestCases();
tc.runTests();
}

/**
* @brief Main function
* @param argc commandline argument count (ignored)
* @param argv commandline array of arguments (ignored)
* @returns 0 on exit
*/
int main(int argc, char *argv[]) {
test();  // Executes various test cases.

const int64_t inputSize = 10;
std::array<int64_t, inputSize> unsorted_array =
sorting::random_pivot_quick_sort::generateUnsortedArray<inputSize>(
50, 1000);
std::cout << "Unsorted array is : " << std::endl;
sorting::random_pivot_quick_sort::showArray(unsorted_array);

std::array<int64_t, inputSize> sorted_array =
sorting::random_pivot_quick_sort::quickSortRP(
unsorted_array, 0, unsorted_array.size() - 1);
std::cout << "Sorted array is : " << std::endl;
sorting::random_pivot_quick_sort::showArray(sorted_array);
return 0;
}
```