Clone Graph

Clone an undirected graph. Each node in the graph contains a label and a list of its neighbors.

How we serialize an undirected graph:

Nodes are labeled uniquely.

We use # as a separator for each node, and , as a separator for node label and each neighbor of the node.

As an example, consider the serialized graph {0,1,2#1,2#2,2}.

The graph has a total of three nodes, and therefore contains three parts as separated by #.

1. First node is labeled as 0. Connect node 0 to both nodes 1 and2.
2. Second node is labeled as 1. Connect node 1 to node 2.
3. Third node is labeled as 2. Connect node 2 to node 2 (itself), thus forming a self-cycle.

Visually, the graph looks like the following:

   1
  / 
 /   
0 --- 2
     / 
     \_/

Have you met this question in a real interview? 

Yes

Example

return a deep copied graph.

/**
 * Definition for undirected graph.
 * struct UndirectedGraphNode {
 *     int label;
 *     vector<UndirectedGraphNode *> neighbors;
 *     UndirectedGraphNode(int x) : label(x) {};
 * };
 */
class Solution {
public:
    /**
     * @param node: A undirected graph node
     * @return: A undirected graph node
     */
    UndirectedGraphNode *cloneGraph(UndirectedGraphNode *node) {
        // write your code here
        
        // suppose the value of nodes are unique.
        // For every node, construct a new node of the same value. For its neighbours, first check if the neighbour has been created (value equals or not), if not, create a node and push into a queue, if so, link the it to the neighbor. 
        // To check whether the neighbour has been visited, maintain a hash map to map the original node to a newly created node.
        if (!node) return node;
        queue<UndirectedGraphNode* > qu;
        qu.push(node);
        unordered_map<UndirectedGraphNode*, UndirectedGraphNode* > um;
        UndirectedGraphNode* result = new UndirectedGraphNode(node->label);
        um[node] = result;
        while (!qu.empty()) {
            UndirectedGraphNode* temp = qu.front();
            qu.pop();
            UndirectedGraphNode* move = um[temp];
            
            for (auto neighbor : temp->neighbors) {
                // if the neighbor is not created, created it and map neighbor to a new create node, update the neighbor of move with newly created node
                if (um.find(neighbor) == um.end()) {
                    UndirectedGraphNode* newNeighbor = new UndirectedGraphNode(neighbor->label);
                    um[neighbor] = newNeighbor;
                    move->neighbors.push_back(newNeighbor);
                    qu.push(neighbor);
                } else {
                    move->neighbors.push_back(um[neighbor]);
                }
            }
        }
        return result;
    }
};