Add missing type hints to hill_climbing.py (#14260)

* Add missing type hints to hill_climbing.py

This commit adds the missing type annotations to searches/hill_climbing.py.

- Added type annotation for function_to_optimize using Callable [[int, int], int]
- Added return type hints to get_neighbors, __hash__, __eq__, and __str__
- Added missing type hint for search_prob in hill_climbing()
- Improved type clarity while preserving existing logic
- Used modern Python type hints (PEP 585)

This improves readability and typing consistency across the repository.

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Fix unnecessary empty iterable in deque initialization (RUF037)

* Update type hint for objective function to allow float return values

* Update score() return type to support int | float

Mypy reported an incompatible return type because function_to_optimize may return float values. 
Updated score() return type from int to int | float for full compatibility.

* Initialize deque with empty list for None values

* updating DIRECTORY.md

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: cclauss <cclauss@users.noreply.github.com>

Author: 3 people

DIRECTORY.md

@@ -1351,6 +1351,7 @@
   * [Capitalize](strings/capitalize.py)
   * [Check Anagrams](strings/check_anagrams.py)
   * [Count Vowels](strings/count_vowels.py)
+  * [Count Vowels Consonants](strings/count_vowels_consonants.py)
   * [Credit Card Validator](strings/credit_card_validator.py)
   * [Damerau Levenshtein Distance](strings/damerau_levenshtein_distance.py)
   * [Detecting English Programmatically](strings/detecting_english_programmatically.py)

searches/hill_climbing.py

@@ -1,5 +1,6 @@
 # https://en.wikipedia.org/wiki/Hill_climbing
 import math
+from collections.abc import Callable
 
 
 class SearchProblem:
@@ -8,7 +9,13 @@ class SearchProblem:
     The interface will be illustrated using the example of mathematical function.
     """
 
-    def __init__(self, x: int, y: int, step_size: int, function_to_optimize):
+    def __init__(
+        self,
+        x: int,
+        y: int,
+        step_size: int,
+        function_to_optimize: Callable[[int, int], int | float],
+    ) -> None:
         """
         The constructor of the search problem.
 
@@ -22,7 +29,7 @@ def __init__(self, x: int, y: int, step_size: int, function_to_optimize):
         self.step_size = step_size
         self.function = function_to_optimize
 
-    def score(self) -> int:
+    def score(self) -> int | float:
         """
         Returns the output of the function called with current x and y coordinates.
         >>> def test_function(x, y):
@@ -34,7 +41,7 @@ def score(self) -> int:
         """
         return self.function(self.x, self.y)
 
-    def get_neighbors(self):
+    def get_neighbors(self) -> list["SearchProblem"]:
         """
         Returns a list of coordinates of neighbors adjacent to the current coordinates.
 
@@ -58,21 +65,21 @@ def get_neighbors(self):
             )
         ]
 
-    def __hash__(self):
+    def __hash__(self) -> int:
         """
         hash the string representation of the current search state.
         """
         return hash(str(self))
 
-    def __eq__(self, obj):
+    def __eq__(self, obj: object) -> bool:
         """
         Check if the 2 objects are equal.
         """
         if isinstance(obj, SearchProblem):
             return hash(str(self)) == hash(str(obj))
         return False
 
-    def __str__(self):
+    def __str__(self) -> str:
         """
         string representation of the current search state.
         >>> str(SearchProblem(0, 0, 1, None))
@@ -84,7 +91,7 @@ def __str__(self):
 
 
 def hill_climbing(
-    search_prob,
+    search_prob: SearchProblem,
     find_max: bool = True,
     max_x: float = math.inf,
     min_x: float = -math.inf,