133 Clone Graph

133. Clone Graph

1. Question

Clone an undirected graph. Each node in the graph contains alabeland a list of itsneighbors.

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 as0. Connect node0to both nodes1and2.

2. Second node is labeled as1. Connect node1to node2.

3. Third node is labeled as2. Connect node2to node2(itself), thus forming a self-cycle.

Visually, the graph looks like the following:

       1
      / \
     /   \
    0 --- 2
         / \
         \_/

2. Implementation

(1) BFS

/**
 * Definition for undirected graph.
 * class UndirectedGraphNode {
 *     int label;
 *     List<UndirectedGraphNode> neighbors;
 *     UndirectedGraphNode(int x) { label = x; neighbors = new ArrayList<UndirectedGraphNode>(); }
 * };
 */
public class Solution {
    public UndirectedGraphNode cloneGraph(UndirectedGraphNode node) {
        if (node == null) {
            return null;
        }

        Map<UndirectedGraphNode, UndirectedGraphNode> map = new HashMap<>();
        Queue<UndirectedGraphNode> queue = new LinkedList<>();

        map.put(node, new UndirectedGraphNode(node.label));
        queue.add(node);

        while (!queue.isEmpty()) {
            UndirectedGraphNode curNode = queue.remove();

            for (UndirectedGraphNode nextNode : curNode.neighbors) {
                if (!map.containsKey(nextNode)) {
                    map.put(nextNode, new UndirectedGraphNode(nextNode.label));
                    queue.add(nextNode);
                }
                map.get(curNode).neighbors.add(map.get(nextNode));
            }
        }
        return map.get(node);
    }
}

(2) DFS

public class Solution {
    public UndirectedGraphNode cloneGraph(UndirectedGraphNode node) {
        Map<UndirectedGraphNode, UndirectedGraphNode> map = new HashMap<>();

        return dfs(node, map);
    }

    public UndirectedGraphNode dfs(UndirectedGraphNode node, Map<UndirectedGraphNode, UndirectedGraphNode> map) {
        if (node == null) {
            return null;
        }

        if (map.containsKey(node)) {
            return map.get(node);
        }

        UndirectedGraphNode copy = new UndirectedGraphNode(node.label);
        map.put(node, copy);

        for (UndirectedGraphNode neighbor : node.neighbors) {
            copy.neighbors.add(dfs(neighbor, map));
        }
        return copy;
    }
}

3. Time & Space Complexity

BFS: 时间复杂度O(n), 空间复杂度O(n)

DFS: 时间复杂度O(n), 空间复杂度O(n)