137.克隆图

描述

克隆一张无向图，图中的每个节点包含一个 label 和一个列表 neighbors。数据中如何表示一个无向图？http://www.lintcode.com/help/graph/你的程序需要返回一个经过深度拷贝的新图。这个新图和原图具有同样的结构，并且对新图的任何改动不会对原图造成任何影响。

样例

比如，序列化图 {0,1,2#1,2#2,2} 共有三个节点, 因此包含两个个分隔符#。

第一个节点label为0，存在边从节点0链接到节点1和节点2
第二个节点label为1，存在边从节点1连接到节点2
第三个节点label为2，存在边从节点2连接到节点2(本身),从而形成自环。
我们能看到如下的图：

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

代码

1. 3steps

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

        // use bfs algorithm to traverse the graph and get all nodes.
        ArrayList nodes = getNodes(node);
        
        // copy nodes, store the old->new mapping information in a hash map
        HashMap mapping = new HashMap<>();
        for (UndirectedGraphNode n : nodes) {
            // 创建hashmap将原图和新图之间结点对应关系存在hashmap中
            mapping.put(n, new UndirectedGraphNode(n.label));    
            
        }
        
        // copy neighbors(edges)
        for (UndirectedGraphNode n : nodes) {
            // 复制的新的结点,不能写newNode = n这样复制的是引用，我们需要的是deep copy
            UndirectedGraphNode newNode = mapping.get(n); 
            // neighbors是定义好的存储整型下标的数组     
            for (UndirectedGraphNode neighbor : n.neighbors) { 
                // 复制相邻结点，复制相邻结点和复制的结点建立边的关系          
                UndirectedGraphNode newNeighbor = mapping.get(neighbor);     
                newNode.neighbors.add(newNeighbor);        
            }
        }

        // 从输入的结点开始逐渐返回图中每个结点对应的信息
        return mapping.get(node);                      
    }
    
    // 用bfs由点到面得到所有结点信息，返回一个包含所有结点的数组
    private ArrayList getNodes(UndirectedGraphNode node) {
        Queue queue = new LinkedList();
         // HashSet不允许有相同元素，如果b已是集合中元素，再执行set.add(b)无效
        HashSet set = new HashSet<>();          
        
        queue.offer(node);
        set.add(node);
        // bfs利用队列来控制遍历图中结点的顺序
        while (!queue.isEmpty()) {
            UndirectedGraphNode head = queue.poll();
            for (UndirectedGraphNode neighbor : head.neighbors) {
                if(!set.contains(neighbor)){
                    set.add(neighbor);
                    queue.offer(neighbor);
                }
            }
        }

        // 所有结点都已添加到 set，此处用深度拷贝是因为外边要用ArrayList，而此处是hashset
        return new ArrayList(set);
    }
}

2. two steps

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

        ArrayList nodes = new ArrayList();
        HashMap map
            = new HashMap();

        // clone nodes    
        nodes.add(node);
        map.put(node, new UndirectedGraphNode(node.label));

        int start = 0;
        while (start < nodes.size()) {
            UndirectedGraphNode head = nodes.get(start++);
            for (int i = 0; i < head.neighbors.size(); i++) {
                UndirectedGraphNode neighbor = head.neighbors.get(i);
                if (!map.containsKey(neighbor)) {
                    map.put(neighbor, new UndirectedGraphNode(neighbor.label));
                    nodes.add(neighbor);
                }
            }
        }

        // clone neighbors
        for (int i = 0; i < nodes.size(); i++) {
            UndirectedGraphNode newNode = map.get(nodes.get(i));
            for (int j = 0; j < nodes.get(i).neighbors.size(); j++) {
                newNode.neighbors.add(map.get(nodes.get(i).neighbors.get(j)));
            }
        }

        return map.get(node);
    }
}

3. Non-Recursion DFS

/**
 * Definition for undirected graph.
 * class UndirectedGraphNode {
 *     int label;
 *     ArrayList neighbors;
 *     UndirectedGraphNode(int x) { label = x; neighbors = new ArrayList(); }
 * };
 */
class StackElement {
    public UndirectedGraphNode node;
    public int neighborIndex;
    public StackElement(UndirectedGraphNode node, int neighborIndex) {
        this.node = node;
        this.neighborIndex = neighborIndex;
    }
}

public class Solution {
    /**
     * @param node: A undirected graph node
     * @return: A undirected graph node
     */
    public UndirectedGraphNode cloneGraph(UndirectedGraphNode node) {
        if (node == null) {
            return node;
        }

        // use dfs algorithm to traverse the graph and get all nodes.
        ArrayList nodes = getNodes(node);
        
        // copy nodes, store the old->new mapping information in a hash map
        HashMap mapping = new HashMap<>();
        for (UndirectedGraphNode n : nodes) {
            mapping.put(n, new UndirectedGraphNode(n.label));
        }
        
        // copy neighbors(edges)
        for (UndirectedGraphNode n : nodes) {
            UndirectedGraphNode newNode = mapping.get(n);
            for (UndirectedGraphNode neighbor : n.neighbors) {
                UndirectedGraphNode newNeighbor = mapping.get(neighbor);
                newNode.neighbors.add(newNeighbor);
            }
        }
        
        return mapping.get(node);
    }
    
    private ArrayList getNodes(UndirectedGraphNode node) {
        Stack stack = new Stack();
        HashSet set = new HashSet<>();
        stack.push(new StackElement(node, -1));
        set.add(node);
        
        while (!stack.isEmpty()) {
            StackElement current = stack.peek();
            current.neighborIndex++;
            // there is no more neighbor to traverse for the current node
            if (current.neighborIndex == current.node.neighbors.size()) {
                stack.pop();
                continue;
            }
            
            UndirectedGraphNode neighbor = current.node.neighbors.get(
                current.neighborIndex
            );
            // check if we visited this neighbor before
            if (set.contains(neighbor)) {
                continue;
            }
            
            stack.push(new StackElement(neighbor, -1));
            set.add(neighbor);
        }
        
        return new ArrayList(set);
    }
}