'''
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, t
he 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.
Example 4:


Input: adjList = [[2],[1]]
Output: [[2],[1]]
'''


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


class Solution:
    def cloneGraph(self, node: 'Node') -> 'Node':
        old_to_new = {}

        # clone
        def dfs(node):
            # have we already made a clone?
            if node in old_to_new:
                # if yes then just return that clone
                return old_to_new[node]

            # if not then we make a copy of the original node
            copy = Node(node.val)
            # take the copy and add to the hashmap new node is copy
            old_to_new[node] = copy

            # now we want to make copies of every single neighbor of the original node
            for neighbor in node.neighbors:
                # this return a copy and with that copy we append it to the list of neighbors
                copy.neighbors.append(dfs(neighbor))
            # once all the copies of neighbors are made we return the copy we made in the current function call
            return copy

        # the original could be 0 too
        return dfs(node) if node else None

'''
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, t
he 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.
Example 4:


Input: adjList = [[2],[1]]
Output: [[2],[1]]
'''


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


class Solution:
    def cloneGraph(self, node: 'Node') -> 'Node':
        old_to_new = {}

        # clone
        def dfs(node):
            # have we already made a clone?
            if node in old_to_new:
                # if yes then just return that clone
                return old_to_new[node]

            # if not then we make a copy of the original node
            copy = Node(node.val)
            # take the copy and add to the hashmap new node is copy
            old_to_new[node] = copy

            # now we want to make copies of every single neighbor of the original node
            for neighbor in node.neighbors:
                # this return a copy and with that copy we append it to the list of neighbors
                copy.neighbors.append(dfs(neighbor))
            # once all the copies of neighbors are made we return the copy we made in the current function call
            return copy

        # the original could be 0 too
        return dfs(node) if node else None

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, t he 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. Example 4:   Input: adjList = [[2],[1]] Output: [[2],[1]] # Definition for a Node. # clone # have we already made a clone? # if yes then just return that clone # if not then we make a copy of the original node # take the copy and add to the hashmap new node is copy # now we want to make copies of every single neighbor of the original node # this return a copy and with that copy we append it to the list of neighbors # once all the copies of neighbors are made we return the copy we made in the current function call # the original could be 0 too