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.

Author: anandvenugopal-tech

searches/hill_climbing.py

@@ -1,14 +1,20 @@
 # https://en.wikipedia.org/wiki/Hill_climbing
 import math
-
+from collections.abc import Callable
 
 class SearchProblem:
     """
     An interface to define search problems.
     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]
+    ) -> None:
         """
         The constructor of the search problem.
 
@@ -34,7 +40,7 @@ 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 +64,21 @@ 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 +90,7 @@ 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,