docs: add algorithms section and update array examples in README

Author: AzizAlievDevelopment

README.md

@@ -42,19 +42,17 @@ ms.get_min()  # 3
 from data_structures.array.static_array import StaticArray
 from data_structures.array.dynamic_array import DynamicArray
 
-sa = StaticArray(3)
-sa.append(1)
-sa.append(2)
+sa = StaticArray([1, 2, 3])   # or StaticArray(3) for empty
+list(sa)       # [1, 2, 3]
+sa.pop()       # 3
 sa.insert(0, 0)
-list(sa)       # [0, 1, 2]
-sa.pop()       # 2
-sa.remove(0)   # 0
+sa.remove(1)   # 1
 
-da = DynamicArray()
-for i in range(10):
+da = DynamicArray([1, 2, 3])  # or DynamicArray() for empty
+for i in range(4, 11):
     da.append(i)
 len(da)        # 10
-da.pop()       # 9
+da.pop()       # 10
 da.capacity    # 16
 ```
 
@@ -84,6 +82,30 @@ dll.pop_back()    # 3
 list(dll)         # [1, 2]
 ```
 
+## Algorithms
+
+### Searching
+
+| Algorithm | Time | Space | Description |
+|---|---|---|---|
+| `binary_search` | O(log n) | O(1) | Find element index in sorted sequence, or -1. |
+| `lower_bound` | O(log n) | O(1) | Index of first element >= target. |
+| `upper_bound` | O(log n) | O(1) | Index of first element > target. |
+
+```python
+from algorithms.searching.binary_search import binary_search, lower_bound, upper_bound
+
+binary_search([1, 3, 5, 7, 9], 5)  # 2
+binary_search([1, 3, 5, 7, 9], 4)  # -1
+
+lower_bound([1, 3, 3, 3, 5], 3)    # 1  (first >= 3)
+upper_bound([1, 3, 3, 3, 5], 3)    # 4  (first > 3)
+
+# Works with StaticArray and DynamicArray too
+binary_search(StaticArray([1, 2, 3]), 2)   # 1
+binary_search(DynamicArray([1, 2, 3]), 2)  # 1
+```
+
 ## Requirements
 
 - Python >= 3.13
@@ -129,10 +151,14 @@ data_structures/
     base.py            # ISinglyLinkedList & IDoublyLinkedList ABCs
     singly_linked_list.py  # SinglyLinkedList
     doubly_linked_list.py  # DoublyLinkedList
+algorithms/
+  searching/
+    binary_search.py   # binary_search, lower_bound, upper_bound
 tests/
   test_arrays.py           # pytest suite for array implementations
   test_stacks.py           # pytest suite for stack implementations
   test_linked_lists.py     # pytest suite for linked list implementations
+  test_binary_search.py    # pytest suite for binary search
 .pre-commit-config.yaml    # pre-commit hooks (ruff, ty)
 pyproject.toml             # project config, tools settings
 ```