# Leetcode 133 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 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.

```
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).
```

```
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.
```

Using breadth first search, we need to pay attention to the problem of undirected edges. Here, the hash table is also used to store the nodes that have been accessed and the corresponding clone nodes. The following is the specific algorithm:

Hash table is used to store the nodes that have been accessed and the corresponding clone nodes; Clone the given node and store it in the hash table. At the same time, with the help of auxiliary queue, the given node is put into the queue first. Out of the queue, access all the adjacent points of the node. If the node is not in the hash table, the adjacent points of the cloned current node are stored in the hash table. At the same time, the adjacent node is queued and placed in the adjacent table of the corresponding node in the clone graph. Repeat until the queue is empty, indicating the end of graph traversal.

```
class Solution:
def cloneGraph(self, node: 'Node') -> 'Node':
oldToNew = {}
def dfs(node):
if node in oldToNew:
return oldToNew[node]
copy = Node(node.val)
oldToNew[node] = copy
for nei in node.neighbors:
copy.neighbors.append(dfs(nei))
return copy
return dfs(node) if node else None
```