Merge remote-tracking branch 'origin/master'

# Conflicts:
#	graphs/edmonds_blossom_algorithm.py

Author: TarunVishwakarma1

graphs/edmonds_blossom_algorithm.py

@@ -1,11 +1,15 @@
 from collections import deque, defaultdict
+from typing import List, Tuple, Dict
+
 
 UNMATCHED = -1  # Constant to represent unmatched vertices
 
 
 class EdmondsBlossomAlgorithm:
     @staticmethod
-    def maximum_matching(edges: list[tuple[int, int]], vertex_count: int) -> list[tuple[int, int]]:
+    def maximum_matching(
+        edges: List[Tuple[int, int]], vertex_count: int
+    ) -> List[Tuple[int, int]]:
         """
         Finds the maximum matching in a general graph using Edmonds' Blossom Algorithm.
 
@@ -16,7 +20,7 @@ def maximum_matching(edges: list[tuple[int, int]], vertex_count: int) -> list[tu
         >>> EdmondsBlossomAlgorithm.maximum_matching([(0, 1), (1, 2), (2, 3)], 4)
         [(0, 1), (2, 3)]
         """
-        graph: dict[int, list[int]] = defaultdict(list)
+        graph: Dict[int, List[int]] = defaultdict(list)
 
         # Populate the graph with the edges
         for vertex_u, vertex_v in edges:
@@ -80,10 +84,16 @@ def maximum_matching(edges: list[tuple[int, int]], vertex_count: int) -> list[tu
                                 EdmondsBlossomAlgorithm.contract_blossom(
                                     BlossomData(
                                         BlossomAuxData(
-                                            queue, parent, base, in_blossom,
-                                            match, in_queue
+                                            queue,
+                                            parent,
+                                            base,
+                                            in_blossom,
+                                            match,
+                                            in_queue,
                                         ),
-                                        current_vertex, neighbor, base_vertex
+                                        current_vertex,
+                                        neighbor,
+                                        base_vertex,
                                     )
                                 )
 
@@ -96,7 +106,9 @@ def maximum_matching(edges: list[tuple[int, int]], vertex_count: int) -> list[tu
         return matching_result
 
     @staticmethod
-    def update_matching(match: list[int], parent: list[int], current_vertex: int) -> None:
+    def update_matching(
+        match: List[int], parent: List[int], current_vertex: int
+    ) -> None:
         """
         Updates the matching along the augmenting path found.
 
@@ -119,7 +131,7 @@ def update_matching(match: list[int], parent: list[int], current_vertex: int) ->
 
     @staticmethod
     def find_base(
-        base: list[int], parent: list[int], vertex_u: int, vertex_v: int
+        base: List[int], parent: List[int], vertex_u: int, vertex_v: int
     ) -> int:
         """
         Finds the base of a node in the blossom.
@@ -155,7 +167,7 @@ def find_base(
             current_vertex_v = parent[current_vertex_v]
 
     @staticmethod
-    def contract_blossom(blossom_data: 'BlossomData') -> None:
+    def contract_blossom(blossom_data: "BlossomData") -> None:
         """
         Contracts a blossom in the graph, modifying the base array
         and marking the vertices involved.
@@ -171,7 +183,9 @@ def contract_blossom(blossom_data: 'BlossomData') -> None:
         current_vertex_u = blossom_data.u
         while blossom_data.aux_data.base[current_vertex_u] != blossom_data.lca:
             base_u = blossom_data.aux_data.base[current_vertex_u]
-            match_base_u = blossom_data.aux_data.base[blossom_data.aux_data.match[current_vertex_u]]
+            match_base_u = blossom_data.aux_data.base[
+                blossom_data.aux_data.match[current_vertex_u]
+            ]
             blossom_data.aux_data.in_blossom[base_u] = True
             blossom_data.aux_data.in_blossom[match_base_u] = True
             current_vertex_u = blossom_data.aux_data.parent[
@@ -181,7 +195,9 @@ def contract_blossom(blossom_data: 'BlossomData') -> None:
         current_vertex_v = blossom_data.v
         while blossom_data.aux_data.base[current_vertex_v] != blossom_data.lca:
             base_v = blossom_data.aux_data.base[current_vertex_v]
-            match_base_v = blossom_data.aux_data.base[blossom_data.aux_data.match[current_vertex_v]]
+            match_base_v = blossom_data.aux_data.base[
+                blossom_data.aux_data.match[current_vertex_v]
+            ]
             blossom_data.aux_data.in_blossom[base_v] = True
             blossom_data.aux_data.in_blossom[match_base_v] = True
             current_vertex_v = blossom_data.aux_data.parent[
@@ -203,8 +219,13 @@ class BlossomAuxData:
     """
 
     def __init__(
-        self, queue: deque, parent: list[int], base: list[int], in_blossom: list[bool],
-        match: list[int], in_queue: list[bool]
+        self,
+        queue: deque,
+        parent: List[int],
+        base: List[int],
+        in_blossom: List[bool],
+        match: List[int],
+        in_queue: List[bool],
     ) -> None:
         self.queue = queue
         self.parent = parent