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. public class Solution {
  4.     public UndirectedGraphNode cloneGraph(UndirectedGraphNode node) {
  5.         if(node == null) return null;
  6.         // key is original node，value is copied node
  7.         HashMap<UndirectedGraphNode, UndirectedGraphNode> visited = new HashMap<>();
  8.         clone(node, visited);
  9.         return visited.get(node);
  10.     }
  11.     // DFS
  12.     private static UndirectedGraphNode clone(UndirectedGraphNode node,
  13.                                               HashMap<UndirectedGraphNode,
  14.                                                       UndirectedGraphNode> visited) {
  15.         // a copy already exists
  16.         if (visited.containsKey(node)) return visited.get(node);
  18.         UndirectedGraphNode new_node = new UndirectedGraphNode(node.label);
  19.         visited.put(node, new_node);
  20.         for (UndirectedGraphNode nbr : node.neighbors)
  21.             new_node.neighbors.add(clone(nbr, visited));
  22.         return new_node;
  23.     }
  24. }

BFS

  1. // Clone Graph
  2. // BFS，时间复杂度O(n)，空间复杂度O(n)
  3. public class Solution {
  4.     public UndirectedGraphNode cloneGraph(UndirectedGraphNode node) {
  5.         if (node == null) return null;
  6.         // key is original node，value is copied node
  7.         HashMap<UndirectedGraphNode,UndirectedGraphNode> visited = new HashMap<>();
  8.         // each node in queue is already copied itself
  9.         // but neighbors are not copied yet
  10.         Queue<UndirectedGraphNode> q = new LinkedList<>();
  11.         q.offer(node);
  12.         visited.put(node, new UndirectedGraphNode(node.label));
  13.         while (!q.isEmpty()) {
  14.             UndirectedGraphNode cur = q.poll();
  15.             for (UndirectedGraphNode nbr : cur.neighbors) {
  16.                 // a copy already exists
  17.                 if (visited.containsKey(nbr)) {
  18.                     visited.get(cur).neighbors.add(visited.get(nbr));
  19.                 } else {
  20.                     UndirectedGraphNode new_node =
  21.                             new UndirectedGraphNode(nbr.label);
  22.                     visited.put(nbr, new_node);
  23.                     visited.get(cur).neighbors.add(new_node);
  24.                     q.offer(nbr);
  25.                 }
  26.             }
  27.         }
  28.         return visited.get(node);
  29.     }
  30. }

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