## Clone Graph

### 描述

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

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 neighbour 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
/ \
\_/


### DFS

// Clone Graph
// DFS，时间复杂度O(n)，空间复杂度O(n)
class Solution {
public:
UndirectedGraphNode *cloneGraph(const UndirectedGraphNode *node) {
if(node == nullptr) return nullptr;
// key is original node，value is copied node
unordered_map<const UndirectedGraphNode *,
UndirectedGraphNode *> visited;
clone(node, visited);
return visited[node];
}
private:
// DFS
static UndirectedGraphNode* clone(const UndirectedGraphNode *node,
unordered_map<const UndirectedGraphNode *,
UndirectedGraphNode *> &visited) {
if (visited.find(node) != visited.end()) return visited[node];

UndirectedGraphNode *new_node = new UndirectedGraphNode(node->label);
visited[node] = new_node;
for (auto nbr : node->neighbors)
new_node->neighbors.push_back(clone(nbr, visited));
return new_node;
}
};


### BFS

// Clone Graph
// BFS，时间复杂度O(n)，空间复杂度O(n)
class Solution {
public:
UndirectedGraphNode *cloneGraph(const UndirectedGraphNode *node) {
if (node == nullptr) return nullptr;
// key is original node，value is copied node
unordered_map<const UndirectedGraphNode *,
UndirectedGraphNode *> copied;
// each node in queue is already copied itself
// but neighbors are not copied yet
queue<const UndirectedGraphNode *> q;
q.push(node);
copied[node] = new UndirectedGraphNode(node->label);
while (!q.empty()) {
const UndirectedGraphNode *cur = q.front();
q.pop();
for (auto nbr : cur->neighbors) {
if (copied.find(nbr) != copied.end()) {
copied[cur]->neighbors.push_back(copied[nbr]);
} else {
UndirectedGraphNode *new_node =
new UndirectedGraphNode(nbr->label);
copied[nbr] = new_node;
copied[cur]->neighbors.push_back(new_node);
q.push(nbr);
}
}
}
return copied[node];
}
};