Clone Graph

Problem

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.

class Node {
    public int val;
    public List<Node> neighbors;
}

Test case format:

For simplicity, each node’s value is the same as the node’s index (1-indexed). For example, the first node with val == 1, the second node with val == 2, and so on. The graph is represented in the test case using an adjacency list.

An adjacency list is a collection of unordered lists used to represent a finite graph. Each list describes the set of neighbors of a node in the graph.

The given node will always be the first node with val = 1. You must return the copy of the given node as a reference to the cloned graph.

Example 1:

Input: adjList = [[2,4],[1,3],[2,4],[1,3]]
Output: [[2,4],[1,3],[2,4],[1,3]]
Explanation: There are 4 nodes in the graph.
1st node (val = 1)'s neighbors are 2nd node (val = 2) and 4th node (val = 4).
2nd node (val = 2)'s neighbors are 1st node (val = 1) and 3rd node (val = 3).
3rd node (val = 3)'s neighbors are 2nd node (val = 2) and 4th node (val = 4).
4th node (val = 4)'s neighbors are 1st node (val = 1) and 3rd node (val = 3).

Example 2:

Input: adjList = [[]]
Output: [[]]
Explanation: Note that the input contains one empty list. The graph consists of only one node with val = 1 and it does not have any neighbors.

Example 3:

Input: adjList = []
Output: []
Explanation: This an empty graph, it does not have any nodes.

Constraints:

• The number of nodes in the graph is in the range [0, 100].

• 1 <= Node.val <= 100

• Node.val is unique for each node.

• There are no repeated edges and no self-loops in the graph.

• The Graph is connected and all nodes can be visited starting from the given node.

Pattern

Hash Table, Depth-First Search, Breadth-First Search, Graph Theory

Approaches

BFS

Code

from __future__ import annotations

from collections import defaultdict, deque


class Node:
    """Node in a graph with adjacency list."""

    def __init__(self, val: int = 0, neighbors: list | None = None):
        self.val = val
        self.neighbors = neighbors if neighbors is not None else []


"""
class Node:
    def __init__(val = 0, neighbors = None):
        self.val = val
        self.neighbors = neighbors if neighbors is not None else []
"""


def cloneGraph(node: "Node" | None) -> "Node" | None:
    if node is None:
        return None

    stack = deque()
    stack.append(node)

    old2new = defaultdict(Node)
    visited = set()
    while stack:
        old_node = stack.pop()

        if old_node in visited:
            continue

        visited.add(old_node)

        new_node = old2new[old_node]
        new_node.val = old_node.val
        new_node.neighbors = [
            old2new[neighbor] for neighbor in old_node.neighbors
        ]

        stack.extend(old_node.neighbors)

    return old2new[node]

Test

>>> from clone_graph__bfs import cloneGraph, Node
>>> node1 = Node(1); node2 = Node(2); node3 = Node(3); node4 = Node(4)
>>> node1.neighbors = [node2, node4]; node2.neighbors = [node1, node3]
>>> node3.neighbors = [node2, node4]; node4.neighbors = [node1, node3]
>>> clone = cloneGraph(node1)
>>> clone is not node1 and clone.val == 1
True
>>> cloneGraph(None) is None
True

class clone_graph__bfs.Node(val: int = 0, neighbors: list | None = None)

Bases: object

Node in a graph with adjacency list.

clone_graph__bfs.cloneGraph(node: 'Node' | None) → 'Node' | None