### Problem Statement#

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.

``````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).
``````

### DFS: Recursive#

``````"""
# 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 __init__(self):
self.mp = dict()

def cloneGraph(self, node: 'Node') -> 'Node':
# Return node if node is empty
if not node:
return node

# If the node has been cloned (added to the map),
# return the new node. This will terminate
# the recursion as the recursive calls below
# will never happen.
if node in self.mp:
return self.mp[node]

# If the node has not been cloned, clone the node
# and add it to the hash map.
self.mp[node] = Node(node.val)
# Recursively loop through the neighbours and add
# cloned nodes to the neighbors lists. The
# recursive calls will terminate when previously
# clone nodes are found in the hash map.
self.mp[node].neighbors = [self.cloneGraph(nbr) for nbr in node.neighbors]

return self.mp[node]
``````

### DFS: Iterative#

``````"""
# 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 []
"""
from collections import deque
class Solution:
def cloneGraph(self, node: 'Node') -> 'Node':
if not node:
return node

mp = {}
mp[node] = Node(node.val)

stack = deque([node])

while stack:
curr = stack.pop()
# Loop through neighbors and add cloned nodes to stack
for nbr in curr.neighbors:
if nbr not in mp:
mp[nbr] = Node(nbr.val)
stack.append(nbr)
# Append cloned neighbor nodes to clone curr node
mp[curr].neighbors.append(mp[nbr])

# Return original copy
return mp[node]

"""
stack = []; 3
mp = {
1;1*.[2*, 4*],
2:2*.[1*, 3*],
3:3*.[2*, 4*],
4:4*.[1*, 3*],
}
#1:[2,4],
#2:[1,3],
#3:[2,4],
#4:[1,3]
"""
``````

Leetcode 133 Clone Graph