# Nhut Nguyen # 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.

## 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 is 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: Cloning with marking

The most important thing when cloning a node is knowing if it was already cloned to avoid recreation.

One way of doing that is by storing the nodes that have been cloned.

## Code

``````#include <vector>
#include <iostream>
#include <unordered_map>
using namespace std;
class Node {
public:
int val;
vector<Node*> neighbors;
Node() {
val = 0;
neighbors = vector<Node*>();
}
Node(int _val) {
val = _val;
neighbors = vector<Node*>();
}
Node(int _val, vector<Node*> _neighbors) {
val = _val;
neighbors = _neighbors;
}
};

Node* clone(Node* node, unordered_map<int, Node*>& created) {
if (node == nullptr) {
return nullptr;
}
auto it = created.find(node->val);
if (it != created.end()) {
return it->second;
}
Node* newNode = new Node(node->val);
created[node->val] = newNode;
for (Node* n : node->neighbors) {
newNode->neighbors.push_back(clone(n, created));
}
return newNode;
}

Node* cloneGraph(Node* node) {
unordered_map<int, Node*> created;
return clone(node, created);
}

void print(Node* node, unordered_map<int, int>& printed) {
if (node == nullptr || printed[node->val] > 0) {
return;
}
cout << "[";
for (Node* n : node->neighbors) {
cout << n->val << ",";
}
cout << "]";
printed[node->val]++;;
for (Node* n : node->neighbors) {
print(n, printed);
}
}

void printGraph(Node* node) {
unordered_map<int, int> printed;
cout << "[";
print(node, printed);
cout << "]\n";
}

int main() {
{
Node one(1);
Node two(2);
Node three(3);
Node four(4);
one.neighbors.push_back(&two);
one.neighbors.push_back(&four);
two.neighbors.push_back(&one);
two.neighbors.push_back(&three);
three.neighbors.push_back(&two);
three.neighbors.push_back(&four);
four.neighbors.push_back(&one);
four.neighbors.push_back(&three);
printGraph(cloneGraph(&one));
}
{
Node anotherOne(1);
printGraph(cloneGraph(&anotherOne));
}
{
printGraph(cloneGraph(nullptr));
}
}
``````
``````Output:
[[2,4,][1,3,][2,4,][1,3,]]
[[]]
[]
``````

## Complexity

• Runtime: `O(2*M)`, where `M` is the number of graph edges. Each edge represents the neighborhood between two nodes, which is called twice, `a neighbors b` and `b neighbors a`.

• Extra space: `O(N)`, where `N` is the number of graph vertices of the graph. It is for the map that stores the created nodes during the cloning.