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Graph - Example

Graph - Example


Leetcode 133. Clone Graph

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.

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.


Analysis:

This is a classic and also fundamental question in graph.

Before we try to clone a graph, let think about how to traversal a graph. Either dfs or bfs would work.

So we can add the cloning node during graph traversal.

The tricky part is how to maintain the edges between nodes, which connects the nodes together, or to form a graph.

One solution is to use a hash_map, which maps the node-to-node relationship between the original and the cloned graphs. With this map, it would be easy to re-construct the edges between the nodes in the cloned graph.

1. Only create the node when it does not exist, or is NULL;

2. Just need to add the neighbors nodes to each node in the cloned graph as that in the original graph.


See the code below:

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

    Node() {}

    Node(int _val, vector<Node*> _neighbors) {
        val = _val;
        neighbors = _neighbors;
    }
};
*/
class Solution {
public:
    Node* cloneGraph(Node* node) {
        if(!node) return node;
        Node* copy = new Node(node->val, {});
        unordered_map<Node*, Node*> mp;
        mp[node] = copy;
        queue<Node*> q;
        q.push(node);
        while(q.size()) {
            auto t = q.front();
            q.pop();
            for(auto &a : t->neighbors) {
                if(!mp.count(a)) {
                    mp[a] = new Node(a->val, {});
                    q.push(a);
                }
                mp[t]->neighbors.push_back(mp[a]);
            }
        }
        return copy;
    }
};


Upper Layer

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