Merge pull request #42 from sudipbanfse/patch-1

Added more extensive time complexities

Data Structures - Arrays/Arrays.py

@@ -39,3 +39,71 @@
 
 #to implement arrays as a stack 
 #https://docs.python.org/3/library/collections.html#collections.deque
+In Python, lists are implemented as dynamic arrays, and the time complexity for various operations can be described using Big O notation. Here are the common operations and their time complexities:
+
+# <!-- 1. **Indexing (Accessing an element)**
+#    - **Operation**: `list[i]`
+#    - **Time Complexity**: O(1)
+
+# 2. **Appending an element**
+#    - **Operation**: `list.append(x)`
+#    - **Time Complexity**: Amortized O(1)
+
+# 3. **Inserting an element at the end**
+#    - **Operation**: `list.insert(len(list), x)`
+#    - **Time Complexity**: O(1)
+
+# 4. **Inserting an element at the beginning or middle**
+#    - **Operation**: `list.insert(i, x)`
+#    - **Time Complexity**: O(n)
+
+# 5. **Deleting an element by index**
+#    - **Operation**: `del list[i]`
+#    - **Time Complexity**: O(n)
+
+# 6. **Removing an element by value**
+#    - **Operation**: `list.remove(x)`
+#    - **Time Complexity**: O(n)
+
+# 7. **Popping an element from the end**
+#    - **Operation**: `list.pop()`
+#    - **Time Complexity**: O(1)
+
+# 8. **Popping an element from the beginning or middle**
+#    - **Operation**: `list.pop(i)`
+#    - **Time Complexity**: O(n)
+
+# 9. **Concatenation**
+#    - **Operation**: `list1 + list2`
+#    - **Time Complexity**: O(n + m) where n and m are the lengths of the lists
+
+# 10. **Slicing**
+#     - **Operation**: `list[start:end]`
+#     - **Time Complexity**: O(k) where k is the length of the slice
+
+# 11. **Checking if an element exists**
+#     - **Operation**: `x in list`
+#     - **Time Complexity**: O(n)
+
+# 12. **Length of the list**
+#     - **Operation**: `len(list)`
+#     - **Time Complexity**: O(1)
+
+# 13. **Sorting the list**
+#     - **Operation**: `list.sort()`
+#     - **Time Complexity**: O(n log n)
+
+# 14. **Reversing the list**
+#     - **Operation**: `list.reverse()`
+#     - **Time Complexity**: O(n)
+
+# ### Summary
+# - **O(1)**: Indexing, appending, popping from the end, checking length.
+# - **O(n)**: Inserting/removing elements (not at the end), deleting by index, removing by value, checking if an element exists, reversing.
+# - **O(n log n)**: Sorting.
+# - **O(n + m)**: Concatenation.
+# - **O(k)**: Slicing. -->
+
+
+
+