Improve documentation and inline comments for QuickSort algorithm (#7182)

* Improve QuickSort documentation with detailed comments and explanations

* Format QuickSort documentation and fix JavaDoc layout

src/main/java/com/thealgorithms/sorts/QuickSort.java

@@ -1,24 +1,36 @@
 package com.thealgorithms.sorts;
 
 /**
- * @author Varun Upadhyay (https://github.com/varunu28)
- * @author Podshivalov Nikita (https://github.com/nikitap492)
+ * QuickSort is a divide-and-conquer sorting algorithm.
+ *
+ * <p>The algorithm selects a pivot element and partitions the array into two
+ * subarrays such that:
+ * <ul>
+ *   <li>Elements smaller than the pivot are placed on the left</li>
+ *   <li>Elements greater than the pivot are placed on the right</li>
+ * </ul>
+ *
+ * <p>The subarrays are then recursively sorted until the entire array is ordered.
+ *
+ * <p>This implementation uses randomization to reduce the probability of
+ * encountering worst-case performance on already sorted inputs.
+ *
+ * <p>Time Complexity:
+ * <ul>
+ *   <li>Best Case: O(n log n)</li>
+ *   <li>Average Case: O(n log n)</li>
+ *   <li>Worst Case: O(n^2)</li>
+ * </ul>
+ *
+ * <p>Space Complexity: O(log n) due to recursion stack (in-place sorting).
+ *
+ * @author Varun Upadhyay
+ * @author Podshivalov Nikita
  * @see SortAlgorithm
  */
+
 class QuickSort implements SortAlgorithm {
 
-    /**
-     * Generic Quick Sort algorithm.
-     *
-     * Time Complexity:
-     * - Best case: O(n log n) – pivot splits array roughly in half each time.
-     * - Average case: O(n log n)
-     * - Worst case: O(n^2) – occurs when pivot consistently produces unbalanced splits.
-     *
-     * Space Complexity: O(log n) – recursion stack, in-place sorting.
-     *
-     * @see SortAlgorithm
-     */
     @Override
     public <T extends Comparable<T>> T[] sort(T[] array) {
         doSort(array, 0, array.length - 1);
@@ -28,27 +40,33 @@ class QuickSort implements SortAlgorithm {
     /**
      * The sorting process
      *
-     * @param left The first index of an array
-     * @param right The last index of an array
      * @param array The array to be sorted
+     * @param left  The first index of an array
+     * @param right The last index of an array
      */
     private static <T extends Comparable<T>> void doSort(T[] array, final int left, final int right) {
+        // Continue sorting only if the subarray has more than one element
         if (left < right) {
+            // Randomly choose a pivot and partition the array
             final int pivot = randomPartition(array, left, right);
+            // Recursively sort elements before the pivot
             doSort(array, left, pivot - 1);
+            // Recursively sort elements after the pivot
             doSort(array, pivot, right);
         }
     }
 
     /**
-     * Randomize the array to avoid the basically ordered sequences
+     * Randomizes the array to avoid already ordered or nearly ordered sequences
      *
      * @param array The array to be sorted
-     * @param left The first index of an array
+     * @param left  The first index of an array
      * @param right The last index of an array
      * @return the partition index of the array
      */
     private static <T extends Comparable<T>> int randomPartition(T[] array, final int left, final int right) {
+        // Randomizing the pivot helps avoid worst-case performance
+        // for already sorted or nearly sorted arrays
         final int randomIndex = left + (int) (Math.random() * (right - left + 1));
         SortUtils.swap(array, randomIndex, right);
         return partition(array, left, right);
@@ -58,21 +76,26 @@ class QuickSort implements SortAlgorithm {
      * This method finds the partition index for an array
      *
      * @param array The array to be sorted
-     * @param left The first index of an array
-     * @param right The last index of an array Finds the partition index of an
-     * array
+     * @param left  The first index of an array
+     * @param right The last index of an array
      */
     private static <T extends Comparable<T>> int partition(T[] array, int left, int right) {
         final int mid = (left + right) >>> 1;
+        // Choose the middle element as the pivot
         final T pivot = array[mid];
-
+        // Move the left and right pointers towards each other
         while (left <= right) {
+            // Move left pointer until an element >= pivot is found
             while (SortUtils.less(array[left], pivot)) {
                 ++left;
             }
+
+            // Move right pointer until an element <= pivot is found
             while (SortUtils.less(pivot, array[right])) {
                 --right;
             }
+
+            // Swap elements that are on the wrong side of the pivot
             if (left <= right) {
                 SortUtils.swap(array, left, right);
                 ++left;