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133. Clone Graph

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.

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 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.

Solutions

Solution 1: Hash Table + DFS

We use a hash table \(\textit{g}\) to record the correspondence between each node in the original graph and its copy, and then perform depth-first search.

We define the function \(\text{dfs}(node)\), which returns the copy of the \(\textit{node}\). The process of \(\text{dfs}(node)\) is as follows:

  • If \(\textit{node}\) is \(\text{null}\), then the return value of \(\text{dfs}(node)\) is \(\text{null}\).
  • If \(\textit{node}\) is in \(\textit{g}\), then the return value of \(\text{dfs}(node)\) is \(\textit{g}[node]\).
  • Otherwise, we create a new node \(\textit{cloned}\) and set the value of \(\textit{g}[node]\) to \(\textit{cloned}\). Then, we traverse all the neighbor nodes \(\textit{nxt}\) of \(\textit{node}\) and add \(\text{dfs}(nxt)\) to the neighbor list of \(\textit{cloned}\).
  • Finally, return \(\textit{cloned}\).

In the main function, we return \(\text{dfs}(node)\).

The time complexity is \(O(n)\), and the space complexity is \(O(n)\). Here, \(n\) is the number of nodes.

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"""
# 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 typing import Optional


class Solution:
    def cloneGraph(self, node: Optional["Node"]) -> Optional["Node"]:
        def dfs(node):
            if node is None:
                return None
            if node in g:
                return g[node]
            cloned = Node(node.val)
            g[node] = cloned
            for nxt in node.neighbors:
                cloned.neighbors.append(dfs(nxt))
            return cloned

        g = defaultdict()
        return dfs(node)

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/*
// Definition for a Node.
class Node {
    public int val;
    public List<Node> neighbors;
    public Node() {
        val = 0;
        neighbors = new ArrayList<Node>();
    }
    public Node(int _val) {
        val = _val;
        neighbors = new ArrayList<Node>();
    }
    public Node(int _val, ArrayList<Node> _neighbors) {
        val = _val;
        neighbors = _neighbors;
    }
}
*/

class Solution {
    private Map<Node, Node> g = new HashMap<>();

    public Node cloneGraph(Node node) {
        return dfs(node);
    }

    private Node dfs(Node node) {
        if (node == null) {
            return null;
        }
        Node cloned = g.get(node);
        if (cloned == null) {
            cloned = new Node(node.val);
            g.put(node, cloned);
            for (Node nxt : node.neighbors) {
                cloned.neighbors.add(dfs(nxt));
            }
        }
        return cloned;
    }
}

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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) {
        unordered_map<Node*, Node*> g;
        auto dfs = [&](this auto&& dfs, Node* node) -> Node* {
            if (!node) {
                return nullptr;
            }
            if (g.contains(node)) {
                return g[node];
            }
            Node* cloned = new Node(node->val);
            g[node] = cloned;
            for (auto& nxt : node->neighbors) {
                cloned->neighbors.push_back(dfs(nxt));
            }
            return cloned;
        };
        return dfs(node);
    }
};

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/**
 * Definition for a Node.
 * type Node struct {
 *     Val int
 *     Neighbors []*Node
 * }
 */

func cloneGraph(node *Node) *Node {
    g := map[*Node]*Node{}
    var dfs func(node *Node) *Node
    dfs = func(node *Node) *Node {
        if node == nil {
            return nil
        }
        if n, ok := g[node]; ok {
            return n
        }
        cloned := &Node{node.Val, []*Node{}}
        g[node] = cloned
        for _, nxt := range node.Neighbors {
            cloned.Neighbors = append(cloned.Neighbors, dfs(nxt))
        }
        return cloned
    }
    return dfs(node)
}

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/**
 * Definition for _Node.
 * class _Node {
 *     val: number
 *     neighbors: _Node[]
 *
 *     constructor(val?: number, neighbors?: _Node[]) {
 *         this.val = (val===undefined ? 0 : val)
 *         this.neighbors = (neighbors===undefined ? [] : neighbors)
 *     }
 * }
 *
 */

function cloneGraph(node: _Node | null): _Node | null {
    const g: Map<_Node, _Node> = new Map();
    const dfs = (node: _Node | null): _Node | null => {
        if (!node) {
            return null;
        }
        if (g.has(node)) {
            return g.get(node);
        }
        const cloned = new _Node(node.val);
        g.set(node, cloned);
        for (const nxt of node.neighbors) {
            cloned.neighbors.push(dfs(nxt));
        }
        return cloned;
    };
    return dfs(node);
}

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/**
 * // Definition for a _Node.
 * function _Node(val, neighbors) {
 *    this.val = val === undefined ? 0 : val;
 *    this.neighbors = neighbors === undefined ? [] : neighbors;
 * };
 */

/**
 * @param {_Node} node
 * @return {_Node}
 */
var cloneGraph = function (node) {
    const g = new Map();
    const dfs = node => {
        if (!node) {
            return null;
        }
        if (g.has(node)) {
            return g.get(node);
        }
        const cloned = new _Node(node.val);
        g.set(node, cloned);
        for (const nxt of node.neighbors) {
            cloned.neighbors.push(dfs(nxt));
        }
        return cloned;
    };
    return dfs(node);
};

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/*
// Definition for a Node.
public class Node {
    public int val;
    public IList<Node> neighbors;

    public Node() {
        val = 0;
        neighbors = new List<Node>();
    }

    public Node(int _val) {
        val = _val;
        neighbors = new List<Node>();
    }

    public Node(int _val, List<Node> _neighbors) {
        val = _val;
        neighbors = _neighbors;
    }
}
*/

public class Solution {
    public Node CloneGraph(Node node) {
        var g = new Dictionary<Node, Node>();
        Node Dfs(Node n) {
            if (n == null) {
                return null;
            }
            if (g.ContainsKey(n)) {
                return g[n];
            }
            var cloned = new Node(n.val);
            g[n] = cloned;
            foreach (var neighbor in n.neighbors) {
                cloned.neighbors.Add(Dfs(neighbor));
            }
            return cloned;
        }
        return Dfs(node);
    }
}

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