Merge pull request #359 from Vijayaa21/main

Create mergeSort.py

Author: Pradeepsingh61

Python/algorithms/sorting/mergeSort.py

@@ -0,0 +1,72 @@
+"""
+Algorithm: Merge Sort
+
+Description:
+    Merge Sort is a Divide and Conquer sorting algorithm. It divides the input 
+    array into two halves, recursively sorts them, and then merges the sorted halves 
+    to produce a fully sorted array.
+
+Steps:
+    1. Divide the array into two halves until each subarray has one element.
+    2. Recursively sort both halves.
+    3. Merge the sorted halves to form a larger sorted array.
+
+Use Case:
+    Merge Sort is useful when stable sorting is required or when working with 
+    linked lists, external sorting (large data that doesn’t fit into memory), 
+    and scenarios where worst-case performance guarantees are important.
+
+Time Complexity:
+    - Best Case: O(N log N)
+    - Average Case: O(N log N)
+    - Worst Case: O(N log N)
+    
+Space Complexity:
+    O(N) auxiliary space (due to temporary arrays during merging).
+
+Stability:
+    Merge Sort is a **stable sorting algorithm**, meaning it maintains the 
+    relative order of equal elements.
+"""
+def merge_sort(arr):
+    if len(arr) > 1:
+        mid = len(arr) // 2  
+        L = arr[:mid]        
+        R = arr[mid:]
+
+        # Recursive calls to sort both halves
+        merge_sort(L)
+        merge_sort(R)
+
+        i = j = k = 0
+
+        # Merge the two halves
+        while i < len(L) and j < len(R):
+            if L[i] <= R[j]:   
+                arr[k] = L[i]
+                i += 1
+            else:
+                arr[k] = R[j]
+                j += 1
+            k += 1
+
+        # Copy any remaining elements of L
+        while i < len(L):
+            arr[k] = L[i]
+            i += 1
+            k += 1
+
+        # Copy any remaining elements of R
+        while j < len(R):
+            arr[k] = R[j]
+            j += 1
+            k += 1
+
+
+
+if __name__ == "__main__":
+    arr = [38, 27, 43, 3, 9, 82, 10]
+    print("Original array:", arr)
+    merge_sort(arr)
+    print("Sorted array:", arr)
+# Sorted array: [3, 9, 10, 27, 38, 43, 82]