Added algorithm to deeply clone a graph (#9765)

* Added algorithm to deeply clone a graph

* Fixed file name and removed a function call

* Removed nested function and fixed class parameter types

* Fixed doctests

* bug fix

* Added class decorator

* Updated doctests and fixed precommit errors

* Cleaned up code

* Simplified doctest

* Added doctests

* Code simplification

graphs/deep_clone_graph.py

@@ -0,0 +1,77 @@
+"""
+LeetCode 133. Clone Graph
+https://leetcode.com/problems/clone-graph/
+
+Given a reference of a node in a connected undirected graph.
+
+Return a deep copy (clone) of the graph.
+
+Each node in the graph contains a value (int) and a list (List[Node]) of its
+neighbors.
+"""
+from dataclasses import dataclass
+
+
+@dataclass
+class Node:
+    value: int = 0
+    neighbors: list["Node"] | None = None
+
+    def __post_init__(self) -> None:
+        """
+        >>> Node(3).neighbors
+        []
+        """
+        self.neighbors = self.neighbors or []
+
+    def __hash__(self) -> int:
+        """
+        >>> hash(Node(3)) != 0
+        True
+        """
+        return id(self)
+
+
+def clone_graph(node: Node | None) -> Node | None:
+    """
+    This function returns a clone of a connected undirected graph.
+    >>> clone_graph(Node(1))
+    Node(value=1, neighbors=[])
+    >>> clone_graph(Node(1, [Node(2)]))
+    Node(value=1, neighbors=[Node(value=2, neighbors=[])])
+    >>> clone_graph(None) is None
+    True
+    """
+    if not node:
+        return None
+
+    originals_to_clones = {}  # map nodes to clones
+
+    stack = [node]
+
+    while stack:
+        original = stack.pop()
+
+        if original in originals_to_clones:
+            continue
+
+        originals_to_clones[original] = Node(original.value)
+
+        stack.extend(original.neighbors or [])
+
+    for original, clone in originals_to_clones.items():
+        for neighbor in original.neighbors or []:
+            cloned_neighbor = originals_to_clones[neighbor]
+
+            if not clone.neighbors:
+                clone.neighbors = []
+
+            clone.neighbors.append(cloned_neighbor)
+
+    return originals_to_clones[node]
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()