133. Clone Graph (Graph, Map; DFS)

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

OJ's undirected graph serialization:

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 and 2.
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
         / 
         \_/
思路：对neughbors的每个节点，如果还没创建，DFS
所以需要一个map标示节点是否已创建
每次递归内容为创建该节点，并递归创建邻节点。

struct UndirectedGraphNode {
    int label;
    vector<UndirectedGraphNode *> neighbors;
    UndirectedGraphNode(int x) : label(x) {};
};

class Solution {
public:
    UndirectedGraphNode *cloneGraph(UndirectedGraphNode *node) {
        if(!node) return NULL;
        UndirectedGraphNode *current;
        map<UndirectedGraphNode*,UndirectedGraphNode*> flag; //前一个元素是节点在原Graph中的地址，后一个元素是节点在新拷贝的图中的位置
        UndirectedGraphNode *root = cloneNode(node,flag);
        return root;
    }
    
    UndirectedGraphNode * cloneNode(UndirectedGraphNode *source, map<UndirectedGraphNode*,UndirectedGraphNode*> &flag)
    {
        if(flag.find(source)!= flag.end()) return flag[source];

        //如果map中没有该节点，那么创建该节点
        UndirectedGraphNode *target = new UndirectedGraphNode(source->label); 
        flag[source] = target;

        for(vector<UndirectedGraphNode *>::iterator it = source->neighbors.begin(); it < source->neighbors.end(); it++ )
        {
            UndirectedGraphNode *newRoot = cloneNode(*it, flag); //深度优先，先递归处理它的某一个邻居，再处理其他邻居
            target->neighbors.push_back(newRoot);
        }
        return target; //返回已经处理好的节点
    }
};