Created Divide and Conquer Algorithm

contrib/ds-algorithms/divide-and-conquer-algorithm.md

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+# Divide and Conquer Algorithms
+
+Divide and Conquer is a paradigm for solving problems that involves breaking a problem into smaller sub-problems, solving the sub-problems recursively, and then combining their solutions to solve the original problem.
+
+## Merge Sort
+
+Merge Sort is a popular sorting algorithm that follows the divide and conquer strategy. It divides the input array into two halves, recursively sorts the halves, and then merges them.
+
+**Algorithm Overview:**
+- **Divide:** Divide the unsorted list into two sublists of about half the size.
+- **Conquer:** Recursively sort each sublist.
+- **Combine:** Merge the sorted sublists back into one sorted list.
+
+```python
+def merge_sort(arr):
+    if len(arr) > 1:
+        mid = len(arr) // 2
+        left_half = arr[:mid]
+        right_half = arr[mid:]
+
+        merge_sort(left_half)
+        merge_sort(right_half)
+
+        i = j = k = 0
+
+        while i < len(left_half) and j < len(right_half):
+            if left_half[i] < right_half[j]:
+                arr[k] = left_half[i]
+                i += 1
+            else:
+                arr[k] = right_half[j]
+                j += 1
+            k += 1
+
+        while i < len(left_half):
+            arr[k] = left_half[i]
+            i += 1
+            k += 1
+
+        while j < len(right_half):
+            arr[k] = right_half[j]
+            j += 1
+            k += 1
+
+arr = [12, 11, 13, 5, 6, 7]
+merge_sort(arr)
+print("Sorted array:", arr)
+```
+
+## Complexity Analysis
+- **Time Complexity:** O(n log n) in all cases
+- **Space Complexity:** O(n) additional space for the merge operation
+
+---