Create Quick_Sort.md

java/Quick_Sort.md

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+---
+id: quick-sort
+sidebar_position: 3
+title: Quick Sort
+sidebar_label: Quick-Sort
+description: Quick sorting algorithm implementation in Java.
+tags: [java, sorting, quick sort]
+---
+
+## *Description*
+
+QuickSort is a highly efficient sorting algorithm that uses the "divide and conquer" approach. It works by selecting a "pivot" element, partitioning the array around the pivot, and recursively sorting the partitions.
+
+Steps in QuickSort:
+- Choose a Pivot: Select a pivot element (commonly the last element, but other methods exist).
+- Partition: Rearrange the array so elements smaller than the pivot are on the left, and elements larger are on the right.
+- Recursively Sort: Apply the same process to the left and right subarrays.
+- Combine: Since each subarray is sorted in place, no additional combination step is needed.
+
+## *Java implementation*
+
+```
+public class QuickSort {
+
+    public static void quickSort(int[] array, int low, int high) {
+        if (low < high) {
+            // Partition the array and get the pivot index
+            int pivotIndex = partition(array, low, high);
+
+            // Recursively sort elements before and after the partition
+            quickSort(array, low, pivotIndex - 1);
+            quickSort(array, pivotIndex + 1, high);
+        }
+    }
+
+    // Helper method to partition the array around a pivot
+    private static int partition(int[] array, int low, int high) {
+        // Choose the last element as the pivot
+        int pivot = array[high];
+        int i = low - 1; // Index of the smaller element
+
+        for (int j = low; j < high; j++) {
+            // If current element is smaller than or equal to pivot
+            if (array[j] <= pivot) {
+                i++;
+                // Swap array[i] and array[j]
+                int temp = array[i];
+                array[i] = array[j];
+                array[j] = temp;
+            }
+        }
+
+        // Place the pivot element at the correct position
+        int temp = array[i + 1];
+        array[i + 1] = array[high];
+        array[high] = temp;
+
+        return i + 1; // Return the pivot index
+    }
+
+    // Main method for testing QuickSort
+    public static void main(String[] args) {
+        int[] array = {10, 7, 8, 9, 1, 5};
+        System.out.println("Original Array: " + java.util.Arrays.toString(array));
+
+        quickSort(array, 0, array.length - 1);
+        System.out.println("Sorted Array: " + java.util.Arrays.toString(array));
+    }
+}
+
+```
+
+# *Explanation of Code:*
+- Recursive quickSort Method: This method partitions the array, then recursively sorts the subarrays on either side of the pivot.
+- partition Method: This method arranges elements around a chosen pivot. Elements less than or equal to the pivot move to the left, and greater elements move to the right. The pivot is placed at its correct sorted position.
+- Swapping: In both partitioning and sorting, elements are swapped in place, reducing the need for extra memory.
+
+# *Time Complexity*
+
+- Average Case: 
+𝑂(𝑛log𝑛), when the pivot divides the array into balanced halves.
+
+- Worst Case: 
+𝑂(𝑛^2), if the pivot divides the array poorly (e.g., when the array is already sorted, and the pivot is always the smallest or largest element).
+
+To avoid the worst-case performance, Randomized QuickSort is often used, where the pivot is chosen randomly, reducing the likelihood of poor splits.
+
+# *Space Complexity*
+Space Complexity: 
+𝑂(log𝑛) due to the recursion stack in the average case.
+
+# *Advantages of QuickSort*
+- In-Place Sorting: Uses minimal additional memory.
+- Efficient: Generally faster than other 𝑂(𝑛log𝑛) algorithms (like Merge Sort) for large datasets.
+
+QuickSort is commonly used in many real-world applications due to its efficiency and relatively low memory usage compared to algorithms like Merge Sort.