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Clone Graph⚓︎

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Description⚓︎

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.

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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:

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.
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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:

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.

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⚓︎

DFS⚓︎

DFS Way 1⚓︎

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/*
// Definition for a Node.
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;
    }
};
*/

class Solution {
private:
    unordered_map<Node*, Node*> visited;
public:
    Node* cloneGraph(Node* node) {
        if (node == nullptr) return node;

        // If the node has already been accessed, the corresponding clone is returned directly from the hash table
        if (visited.count(node)) return visited[node];

        // Clone the node, noting that for deep copy we will not clone the list of its neighbors
        Node* clone = new Node(node->val);
        visited[node] = clone;

        // Iterate through the neighbors of this node and update the neighbor list of the cloned node
        for (auto& neighbor : node->neighbors) {
            clone->neighbors.emplace_back(cloneGraph(neighbor));
        }
        return clone;
    }
};
  • Time complexity: \(O(N)\), where \(N\) is the number of nodes;
  • Space complexity: \(O(N)\) for storing the hash table of the cloned and original nodes, and \(O(H)\) for the stack, where \(H\) is the height of the graph.

DFS Way 2⚓︎

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class Solution {
private:
    unordered_map<Node*, Node*> visited;

    void dfs(Node* node) {
        visited[node] = new Node(node->val);

        for (auto& neighbor : node->neighbors) {
            if (!visited.count(neighbor)) dfs(neighbor);
        }
    }

public:
    Node* cloneGraph(Node* node) {
        if (!node) return nullptr;
        dfs(node);

        for (auto& [src, dst] : visited) {
            for (auto& neighbor : src->neighbors) {
                dst->neighbors.push_back(visited[neighbor]);
            }
        }
        return visited[node];
    }
};

BFS⚓︎

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/*
// Definition for a Node.
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;
    }
};
*/

class Solution {
public:
    Node* cloneGraph(Node* node) {
        if (!node) return nullptr;

        unordered_map<Node*, Node*> visited;

        queue<Node*> q;
        q.push(node);
        visited[node] = new Node(node->val);

        while (!q.empty()) {
            auto curr = q.front();
            q.pop();

            for (auto& neighbor : curr->neighbors) {
                if (!visited.count(neighbor)) {
                    visited[neighbor] = new Node(neighbor->val);
                    q.push(neighbor);
                }
                visited[curr]->neighbors.emplace_back(visited[neighbor]);
            }
        }

        return visited[node];
    }
};