Clone Graph

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

Nodes are labeled uniquely.

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
         /          \_/

這題只需一邊遍歷一遍復制就可以了。

因此至少可以用三種方法：

1、廣度優先遍歷(BFS)

2、深度優先遍歷(DFS)

2.1、遞歸

2.2、非遞歸

解法一：廣度優先遍歷

變量說明：

映射表m用來保存原圖結點與克隆結點的對應關系。

映射表visited用來記錄已經訪問過的原圖結點，防止循環訪問。

隊列q用於記錄廣度優先遍歷的層次信息。

 1 /**
 2  * Definition for undirected graph.
 
 3  * struct UndirectedGraphNode {
 4  *     int label;
 5  *     vector<UndirectedGraphNode *> neighbors;
 6  *     UndirectedGraphNode(int x) : label(x) {};
 7  * };
 8  */
 9 class Solution {
10 public:
11     UndirectedGraphNode *cloneGraph(UndirectedGraphNode *node) {
12         if(node == NULL)
13             return NULL;
14         // map from origin node to copy node
15         unordered_map<UndirectedGraphNode *, UndirectedGraphNode *> m;
16         unordered_map<UndirectedGraphNode *, bool> visited;
17         queue<UndirectedGraphNode*> q;
18         q.push(node);
19         while(!q.empty())
20         {// BFS
21             UndirectedGraphNode* front = q.front();
22             q.pop();
23             
24             if(visited[front] == false)
25             {
26                 visited[front] = true;
27                 
28                 UndirectedGraphNode* cur;
29                 if(m.find(front) == m.end())
30                 {
31                     cur = new UndirectedGraphNode(front->label);
32                     m[front] = cur;
33                 }
34                 else
35                 {
36                     cur = m[front];
37                 }
38                 for(int i = 0; i < front->neighbors.size(); i ++)
39                 {
40                     if(m.find(front->neighbors[i]) == m.end())
41                     {
42                         UndirectedGraphNode* nei = new UndirectedGraphNode(front->neighbors[i]->label);
43                         m[front->neighbors[i]] = nei;
44                         cur->neighbors.push_back(nei);
45                             
46                         q.push(front->neighbors[i]);
47                     }
48                     else
49                     {
50                         cur->neighbors.push_back(m[front->neighbors[i]]);
51                     }
52                 }
53             }
54         }
55         return m[node];
56     }
57 };

解法二：遞歸深度優先遍歷(DFS)

 1 /**
 2  * Definition for undirected graph.
 3  * struct UndirectedGraphNode {
 4  *     int label;
 5  *     vector<UndirectedGraphNode *> neighbors;
 6  *     UndirectedGraphNode(int x) : label(x) {};
 7  * };
 8  */
 9 class Solution {
10 public:
11     map<UndirectedGraphNode *, UndirectedGraphNode *> m;
12     
13     UndirectedGraphNode *cloneGraph(UndirectedGraphNode *node) 
14     {
15         if(node == NULL)
16             return NULL;
17         
18         if(m.find(node) != m.end())   //if node is visited, just return the recorded nodeClone
19             return m[node];
20             
21         UndirectedGraphNode *nodeClone = new UndirectedGraphNode(node->label);
22         m[node] = nodeClone;
23         for(int st = 0; st < node->neighbors.size(); st ++)
24         {
25             UndirectedGraphNode *temp = cloneGraph(node->neighbors[st]);
26             if(temp != NULL)
27                 nodeClone->neighbors.push_back(temp);
28         }
29         return nodeClone;
30     }
31 };

解法三：非遞歸深度優先遍歷(DFS)

深度優先遍歷需要進行鄰居計數。如果鄰居已經全部訪問，則該節點訪問完成，可以出棧，否則就要繼續處理下一個鄰居。

 1 /**
 2  * Definition for undirected graph.
 3  * struct UndirectedGraphNode {
 4  *     int label;
 5  *     vector<UndirectedGraphNode *> neighbors;
 6  *     UndirectedGraphNode(int x) : label(x) {};
 7  * };
 8  */
 9 
10 struct Node
11 {
12     UndirectedGraphNode *node;
13     int ind;    //next neighbor to visit
14     Node(UndirectedGraphNode *n, int i): node(n), ind(i) {}
15 };
16 
17 class Solution {
18 public:
19     UndirectedGraphNode *cloneGraph(UndirectedGraphNode *node) {
20         if(node == NULL)
21             return NULL;
22         // map from origin node to copy node
23         unordered_map<UndirectedGraphNode *, UndirectedGraphNode *> m;
24         unordered_map<UndirectedGraphNode *, bool> visited;
25         stack<Node*> stk;
26         Node* newnode = new Node(node, 0);
27         stk.push(newnode);
28         visited[newnode->node] = true;
29         while(!stk.empty())
30         {// DFS
31             Node* top = stk.top();
32             UndirectedGraphNode* topCopy;
33             if(m.find(top->node) == m.end())
34             {
35                 topCopy = new UndirectedGraphNode(top->node->label);
36                 m[top->node] = topCopy;
37             }
38             else
39                 topCopy = m[top->node];
40 
41             if(top->ind == top->node->neighbors.size())
42                 //finished copying its neighbors 
43                     stk.pop();
44             else
45             {
46                 while(top->ind < top->node->neighbors.size())
47                 {
48                     if(m.find(top->node->neighbors[top->ind]) == m.end())
49                     {
50                         UndirectedGraphNode* neiCopy = new UndirectedGraphNode(top->node->neighbors[top->ind]->label);
51                         m[top->node->neighbors[top->ind]] = neiCopy;
52                         topCopy->neighbors.push_back(neiCopy);
53                         if(visited[top->node->neighbors[top->ind]] == false)
54                         {
55                             visited[top->node->neighbors[top->ind]] = true;
56                             Node* topnei = new Node(top->node->neighbors[top->ind], 0);
57                             stk.push(topnei);
58                         }
59                         top->ind ++;
60                         break;
61                     }
62                     else
63                     {
64                         topCopy->neighbors.push_back(m[top->node->neighbors[top->ind]]);
65                         top->ind ++;
66                     }
67                 }
68             }
69         }
70         return m[node];
71     }
72 };

轉自：http://www.cnblogs.com/ganganloveu/p/4119462.html

133. Clone Graph (3 solutions)——無向無環圖復制