> ## Documentation Index
> Fetch the complete documentation index at: https://leetcode-py.wisl.dev/llms.txt
> Use this file to discover all available pages before exploring further.

> ## Agent Instructions
> leetcode-py is a Python LeetCode practice environment generator with one CLI: lcpy. It is not a service or platform.
> Each problem is a directory under leetcode/ with README.md, solution.py, test_solution.py, helpers.py, and playground.ipynb. lcpy gen creates them from JSON templates bundled with the package.
> Examples are backed by tests; copy them verbatim.

# Clone Graph Python Solution with Tests

> Tested Python solution for LeetCode 133 with 63 pytest cases. Generate a practice environment with lcpy.

LeetCode 133, Medium. Topics: Hash Table, Depth-First Search, Breadth-First Search, Graph. [View on LeetCode](https://leetcode.com/problems/clone-graph/description/).

Generate this problem as a practice environment: tested reference solution, 63 [parametrized pytest cases](/practice/testing), and a playground notebook:

```bash theme={"theme":{"light":"github-light","dark":"github-dark"}}
lcpy gen -n 133   # by problem number
lcpy gen -s clone_graph   # by problem name
```

## Problem

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.

### Examples

![Example 1](https://assets.leetcode.com/uploads/2019/11/04/133_clone_graph_question.png)

```
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](https://assets.leetcode.com/uploads/2020/01/07/graph.png)

```
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.

```
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.

## Solution

Reference implementation from [solution.py on GitHub](https://github.com/wislertt/leetcode-py/blob/main/leetcode/clone_graph/solution.py), full suite in [test\_solution.py](https://github.com/wislertt/leetcode-py/blob/main/leetcode/clone_graph/test_solution.py):

```python theme={"theme":{"light":"github-light","dark":"github-dark"}}
from collections import deque

from leetcode_py import GraphNode


class Solution:
    # Time: O(V + E)
    # Space: O(V)
    def clone_graph(self, node: GraphNode | None) -> GraphNode | None:
        if node is None:
            return None

        def dfs(node: GraphNode, visited: dict[int, GraphNode]):
            if node.val in visited:
                return visited[node.val]

            clone = GraphNode(node.val)
            visited[node.val] = clone

            for neighbor in node.neighbors:
                clone.neighbors.append(dfs(neighbor, visited))

            return clone

        return dfs(node, visited={})


class SolutionDFS:
    # DFS Iterative
    # Time: O(V + E)
    # Space: O(V)
    def clone_graph(self, node: GraphNode | None) -> GraphNode | None:
        if node is None:
            return None

        stack = [node]
        visited = {node.val: GraphNode(node.val)}

        while stack:
            current = stack.pop()
            clone = visited[current.val]

            for neighbor in current.neighbors:
                if neighbor.val not in visited:
                    visited[neighbor.val] = GraphNode(neighbor.val)
                    stack.append(neighbor)
                clone.neighbors.append(visited[neighbor.val])

        return visited[node.val]


class SolutionBFS:
    # BFS
    # Time: O(V + E)
    # Space: O(V)
    def clone_graph(self, node: GraphNode | None) -> GraphNode | None:
        if node is None:
            return None

        queue = deque([node])
        visited = {node.val: GraphNode(node.val)}

        while queue:
            current = queue.popleft()
            clone = visited[current.val]

            for neighbor in current.neighbors:
                if neighbor.val not in visited:
                    visited[neighbor.val] = GraphNode(neighbor.val)
                    queue.append(neighbor)
                clone.neighbors.append(visited[neighbor.val])

        return visited[node.val]
```

## Complexity

| Time     | Space |
| -------- | ----- |
| O(V + E) | O(V)  |

## Tags

[Grind 75](/catalog/grind-75), [Grind](/catalog/grind), [Blind 75](/catalog/blind-75), [NeetCode 150](/catalog/neetcode-150), [NeetCode 250](/catalog/neetcode-250), [NeetCode All](/catalog/neetcode), [AlgoMaster 75](/catalog/algo-master-75).