merge variety

Author: Sai Rahul Guggilam

sorts/3_way_Merge_Sort.py

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+'''
+In traditional Merge Sort, the array is recursively divided into halves until we reach subarrays of size 1. In 3-way Merge Sort, the array is recursively divided into three parts, reducing the depth of recursion and potentially improving efficiency.
+'''
+def merge(arr, left, mid1, mid2, right):
+    
+    # Sizes of three subarrays
+    size1 = mid1 - left + 1
+    size2 = mid2 - mid1
+    size3 = right - mid2
+    
+    # Temporary arrays for three parts
+    left_arr = arr[left:left + size1]
+    mid_arr = arr[mid1 + 1:mid1 + 1 + size2]
+    right_arr = arr[mid2 + 1:mid2 + 1 + size3]
+    
+    # Merge three sorted subarrays
+    i = j = k = 0
+    index = left
+    
+    while i < size1 or j < size2 or k < size3:
+        min_value = float('inf')
+        min_idx = -1
+        
+        # Find the smallest among the three current elements
+        if i < size1 and left_arr[i] < min_value:
+            min_value = left_arr[i]
+            min_idx = 0
+        if j < size2 and mid_arr[j] < min_value:
+            min_value = mid_arr[j]
+            min_idx = 1
+        if k < size3 and right_arr[k] < min_value:
+            min_value = right_arr[k]
+            min_idx = 2
+        
+        # Place the smallest element in the merged array
+        if min_idx == 0:
+            arr[index] = left_arr[i]
+            i += 1
+        elif min_idx == 1:
+            arr[index] = mid_arr[j]
+            j += 1
+        else:
+            arr[index] = right_arr[k]
+            k += 1
+        
+        index += 1
+
+def three_way_merge_sort(arr, left, right):
+    
+    # Base case: If single element, return
+    if left >= right:
+        return
+    
+    # Finding two midpoints for 3-way split
+    mid1 = left + (right - left) // 3
+    mid2 = left + 2 * (right - left) // 3
+    
+    # Recursively sort first third
+    three_way_merge_sort(arr, left, mid1)
+    
+    # Recursively sort second third
+    three_way_merge_sort(arr, mid1 + 1, mid2)
+    
+    # Recursively sort last third
+    three_way_merge_sort(arr, mid2 + 1, right)
+    
+    # Merge the sorted parts
+    merge(arr, left, mid1, mid2, right)
+
+if __name__ == "__main__":
+    
+    # Input array
+    arr = [5, 2, 9, 1, 6, 3, 8, 4, 7]
+    
+    # Calling 3-way merge sort function
+    three_way_merge_sort(arr, 0, len(arr) - 1)
+    
+    # Printing the sorted array
+    print(*arr)