adding new sorting Algoritm (dual_pivot_quicksort)

Sorting Algorithms/dual_pivot_quicksort.py

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+def dual_pivot_quicksort(arr, low, high):
+    """
+    Performs Dual-Pivot QuickSort on the input array.
+
+    Dual-Pivot QuickSort is an optimized version of QuickSort that uses 
+    two pivot elements to partition the array into three segments in each 
+    recursive call. This improves performance by reducing the number of 
+    recursive calls, making it faster on average than the single-pivot 
+    QuickSort.
+
+    Parameters:
+    arr (list): The list to be sorted.
+    low (int): The starting index of the segment to sort.
+    high (int): The ending index of the segment to sort.
+
+    Returns:
+    None: Sorts the array in place.
+    """
+    if low < high:
+        # Partition the array and get the two pivot indices
+        lp, rp = partition(arr, low, high)
+        # Recursively sort elements less than pivot1
+        dual_pivot_quicksort(arr, low, lp - 1)
+        # Recursively sort elements between pivot1 and pivot2
+        dual_pivot_quicksort(arr, lp + 1, rp - 1)
+        # Recursively sort elements greater than pivot2
+        dual_pivot_quicksort(arr, rp + 1, high)
+
+def partition(arr, low, high):
+    """
+    Partitions the array segment defined by low and high using two pivots.
+
+    This function arranges elements into three sections:
+    - Elements less than pivot1
+    - Elements between pivot1 and pivot2
+    - Elements greater than pivot2
+
+    Parameters:
+    arr (list): The list to partition.
+    low (int): The starting index of the segment to partition.
+    high (int): The ending index of the segment to partition.
+
+    Returns:
+    tuple: Indices of the two pivots in sorted positions (lp, rp).
+    """
+    # Ensure the left pivot is less than or equal to the right pivot
+    if arr[low] > arr[high]:
+        arr[low], arr[high] = arr[high], arr[low]
+    pivot1 = arr[low]  # left pivot
+    pivot2 = arr[high]  # right pivot
+
+    # Initialize pointers
+    i = low + 1       # Pointer to traverse the array
+    lt = low + 1      # Boundary for elements less than pivot1
+    gt = high - 1     # Boundary for elements greater than pivot2
+
+    # Traverse and partition the array based on the two pivots
+    while i <= gt:
+        if arr[i] < pivot1:
+            arr[i], arr[lt] = arr[lt], arr[i]  # Swap to move smaller elements to the left
+            lt += 1
+        elif arr[i] > pivot2:
+            arr[i], arr[gt] = arr[gt], arr[i]  # Swap to move larger elements to the right
+            gt -= 1
+            i -= 1  # Decrement i to re-evaluate the swapped element
+        i += 1
+
+    # Place the pivots in their correct sorted positions
+    lt -= 1
+    gt += 1
+    arr[low], arr[lt] = arr[lt], arr[low]     # Place pivot1 at its correct position
+    arr[high], arr[gt] = arr[gt], arr[high]   # Place pivot2 at its correct position
+
+    return lt, gt  # Return the indices of the two pivots
+
+# Example usage
+# Sample Test Case
+arr = [24, 8, 42, 75, 29, 77, 38, 57]
+dual_pivot_quicksort(arr, 0, len(arr) - 1)
+print("Sorted array:", arr)