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 #.

  • First node is labeled as 0. Connect node 0 to both nodes 1 and 2.
  • Second node is labeled as 1. Connect node 1 to node 2.
  • 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.        1
  2.       / \
  3.      /   \
  4.     0 --- 2
  5.          / \
  6.          \_/

分析

广度优先遍历或深度优先遍历都可以。

DFS

  1. // Clone Graph
  2. // DFS，时间复杂度O(n)，空间复杂度O(n)
  3. class Solution {
  4. public:
  5.     UndirectedGraphNode *cloneGraph(const UndirectedGraphNode *node) {
  6.         if(node == nullptr) return nullptr;
  7.         // key is original node，value is copied node
  8.         unordered_map<const UndirectedGraphNode *,
  9.                             UndirectedGraphNode *> visited;
  10.         clone(node, visited);
  11.         return visited[node];
  12.     }
  13. private:
  14.     // DFS
  15.     static UndirectedGraphNode* clone(const UndirectedGraphNode *node,
  16.             unordered_map<const UndirectedGraphNode *,
  17.             UndirectedGraphNode *> &visited) {
  18.         // a copy already exists
  19.         if (visited.find(node) != visited.end()) return visited[node];
  21.         UndirectedGraphNode *new_node = new UndirectedGraphNode(node->label);
  22.         visited[node] = new_node;
  23.         for (auto nbr : node->neighbors)
  24.             new_node->neighbors.push_back(clone(nbr, visited));
  25.         return new_node;
  26.     }
  27. };

BFS

  1. // Clone Graph
  2. // BFS，时间复杂度O(n)，空间复杂度O(n)
  3. class Solution {
  4. public:
  5.     UndirectedGraphNode *cloneGraph(const UndirectedGraphNode *node) {
  6.         if (node == nullptr) return nullptr;
  7.         // key is original node，value is copied node
  8.         unordered_map<const UndirectedGraphNode *,
  9.                             UndirectedGraphNode *> copied;
  10.         // each node in queue is already copied itself
  11.         // but neighbors are not copied yet
  12.         queue<const UndirectedGraphNode *> q;
  13.         q.push(node);
  14.         copied[node] = new UndirectedGraphNode(node->label);
  15.         while (!q.empty()) {
  16.             const UndirectedGraphNode *cur = q.front();
  17.             q.pop();
  18.             for (auto nbr : cur->neighbors) {
  19.                 // a copy already exists
  20.                 if (copied.find(nbr) != copied.end()) {
  21.                     copied[cur]->neighbors.push_back(copied[nbr]);
  22.                 } else {
  23.                     UndirectedGraphNode *new_node =
  24.                             new UndirectedGraphNode(nbr->label);
  25.                     copied[nbr] = new_node;
  26.                     copied[cur]->neighbors.push_back(new_node);
  27.                     q.push(nbr);
  28.                 }
  29.             }
  30.         }
  31.         return copied[node];
  32.     }
  33. };

原文: https://soulmachine.gitbooks.io/algorithm-essentials/content/cpp/graph/clone-graph.html