Problem:
Rooted Trees

A graph G = (V, E) is a data structure where V is a finite set of vertices and E is a binary relation on V represented by a set of edges. Fig. 1 illustrates an example of a graph (or graphs).

Fig. 1

A free tree is a connnected, acyclic, undirected graph. A rooted tree is a free tree in which one of the vertices is distinguished from the others. A vertex of a rooted tree is called "node."

Your task is to write a program which reports the following information for each node u of a given rooted tree T:

node ID of u

parent of u

depth of u

node type (root, internal node or leaf)

a list of chidlren of u

If the last edge on the path from the root r of a tree T to a node x is (p, x), then p is the parent of x, and x is a child of p. The root is the only node in T with no parent.

A node with no children is an external node or leaf. A nonleaf node is an internal node

The number of children of a node x in a rooted tree T is called the degree of x.

The length of the path from the root r to a node x is the depth of x in T.

Here, the given tree consists of n nodes and evey node has a unique ID from 0 to n-1.

Fig. 2 shows an example of rooted trees where ID of each node is indicated by a number in a circle (node). The example corresponds to the first sample input.

Fig. 2

Input

The first line of the input includes an integer n, the number of nodes of the tree.

In the next n lines, the information of each node u is given in the following format:

id k c1 c2 ... ck

where id is the node ID of u, k is the degree of u, c1 ... ck are node IDs of 1st, ... kth child of u. If the node does not have a child, the k is 0.

Output

Print the information of each node in the following format ordered by IDs:

node id: parent = p, depth = d, type, [c1...ck]

p is ID of its parent. If the node does not have a parent, print -1.

d is depth of the node.

type is a type of nodes represented by a string (root, internal node or leaf). If the root can be considered as a leaf or an internal node, print root.

c1...ck is the list of children as a ordered tree.

Please follow the format presented in a sample output below.

Constraints

1 ≤ n ≤ 100000

Sample Input 1

13
0 3 1 4 10
1 2 2 3
2 0
3 0
4 3 5 6 7
5 0
6 0
7 2 8 9
8 0
9 0
10 2 11 12
11 0
12 0

Sample Output 1

node 0: parent = -1, depth = 0, root, [1, 4, 10]
node 1: parent = 0, depth = 1, internal node, [2, 3]
node 2: parent = 1, depth = 2, leaf, []
node 3: parent = 1, depth = 2, leaf, []
node 4: parent = 0, depth = 1, internal node, [5, 6, 7]
node 5: parent = 4, depth = 2, leaf, []
node 6: parent = 4, depth = 2, leaf, []
node 7: parent = 4, depth = 2, internal node, [8, 9]
node 8: parent = 7, depth = 3, leaf, []
node 9: parent = 7, depth = 3, leaf, []
node 10: parent = 0, depth = 1, internal node, [11, 12]
node 11: parent = 10, depth = 2, leaf, []
node 12: parent = 10, depth = 2, leaf, []

Sample Input 2

4
1 3 3 2 0
0 0
3 0
2 0

Sample Output 2

node 0: parent = 1, depth = 1, leaf, []
node 1: parent = -1, depth = 0, root, [3, 2, 0]
node 2: parent = 1, depth = 1, leaf, []
node 3: parent = 1, depth = 1, leaf, []

Note

You can use a left-child, right-sibling representation to implement a tree which has the following data:

the parent of u

the leftmost child of u

the immediate right sibling of u

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in JAVA (judge verdict: Accepted)


import java.util.*;

public class Main{ 

	public static void main(String args[]){
		Scanner scan = new Scanner(System.in);
		//int numNode = scan.nextInt();
		TreeNodeData data = new TreeNodeData(scan.nextInt());
		//scan.nextLine();
		data.readNodeData(scan);
		Root root = data.getNodeList();
		ArrayList<AbstractNode> tree = root.connectTree();
		Collections.sort(tree);
		for(int i=0; i<tree.size();i++)
			System.out.println(tree.get(i));
		//Tree tree = new Tree(data.getNodeList());
		//tree.connectNode();
		//.out.println("scan end");
		//tree.treeView();
	}

}
class NodeData{

	private int numChild;
	private ArrayList<Integer> children;
	public NodeData(int n){
		numChild = n;
		children = new ArrayList<Integer>();
	}
	public void addChild(int c){
		children.add(c);
	}
	public boolean isLeaf(){
		return (children.size()==0);
	}
	public Iterator<Integer> getChildren(){
		return children.iterator();
	}
}
class Tree{
	int numNode;
	ArrayList<AbstractNode> tree = new ArrayList<AbstractNode>();
	HashMap<Integer, NodeData> nodeData;
	public Tree(HashMap<Integer, NodeData> nodeData){
		this.nodeData = nodeData;
		numNode = nodeData.size();
		for(int i =0; i<numNode ;i++ ){
			if(nodeData.get(i).isLeaf())
				tree.add(new Leaf(i, nodeData));
			else
				tree.add(new InternalNode(i, nodeData));
		}
	}
	public void connectNode(){
		for(int i=0; i<numNode; i++){
			for(Iterator<Integer> iter = nodeData.get(i).getChildren(); iter.hasNext();){
				int childId = iter.next();
				tree.get(i).addChild(tree.get(childId));
				tree.get(childId).setParent(tree.get(i));
			}
		}
	}
	public void treeView(){
		for(int i=0; i<numNode; i++)
			System.out.println(tree.get(i));
	}
}
class TreeNodeData{
	int numNode;
	private HashMap<Integer, NodeData> nodeData = new HashMap<Integer, NodeData>();
	int rootID;
	//

	public TreeNodeData(int n){
		this.numNode = n;
		//for(int i=0; i<numNode; i++)
		//	nodes.put(i, new Node(i));	
	}
	public HashMap<Integer, NodeData> getNodeData(){
		return nodeData;
	}
	public void readNodeData(Scanner scan){
		ArrayList<Integer> notParent = new ArrayList<Integer>();
		for(int i=0; i<numNode; i++){
			int id = scan.nextInt();
			int numChild = scan.nextInt();
			NodeData data = new NodeData(numChild);
			for(int j=0; j<numChild; j++){
				int childID = scan.nextInt();
				data.addChild(childID);
				notParent.add(childID);
			}
			nodeData.put(id, data);
		}
		for(int i=0; i<numNode; i++)
			if(!notParent.contains(i)){
				rootID = i;
				//System.out.println("root : "+ i);
				break;
			}
	}
	public Root getNodeList(){
		//ArrayList<AbstractNode> tree = new ArrayList<AbstractNode>();
		return new Root(rootID, nodeData);	
	}
}


class Leaf extends AbstractNode{
	public Leaf(int n, HashMap<Integer, NodeData> nodeData){
		super(n, nodeData);
	}
	@Override 
	public void addChild(AbstractNode c){
		return;
	}
	@Override 
	String getType(){
		if(parent==null)
			return "root";
		else
			return "leaf";
	}

}
class Root extends AbstractNode{
	public Root(int n, HashMap<Integer, NodeData> nodeData){
		super(n, nodeData);
	}
	@Override 
	public void addChild(AbstractNode c){
		children.add(c);
	}
	@Override 
	String getType(){
			return "root";
	}
}
class InternalNode extends AbstractNode{
	public InternalNode(int n, HashMap<Integer, NodeData> nodeData){
		super(n, nodeData);
	}
	@Override 
	public void addChild(AbstractNode c){
		children.add(c);
	}
	@Override 
	String getType(){
		if(parent==null)
			return "root";
		else
			return "internal node";
	}
}
abstract class AbstractNode implements Comparable<AbstractNode>{
	protected int id;
	protected AbstractNode parent;
	protected ArrayList<AbstractNode> children = new ArrayList<AbstractNode>();
	abstract public void addChild(AbstractNode c);
	//abstract int getDepth(AbstractNode n);
	abstract String getType();
	public AbstractNode(int id, HashMap<Integer, NodeData> nodeData){
		this.id = id;
		if(nodeData.get(id).isLeaf())
			return;
		for(Iterator<Integer> iter = nodeData.get(id).getChildren(); iter.hasNext();){
			int childId = iter.next();
			if(nodeData.get(childId).isLeaf()){
				Leaf temp = new Leaf(childId, nodeData);
				temp.setParent(this);
				this.addChild(temp);
			}else{
				InternalNode temp = new InternalNode(childId, nodeData);
				temp.setParent(this);
				this.addChild(temp);
			}
		}
	}
	public int getID(){
		return id;
	}
	public void setParent(AbstractNode p){
		this.parent = p;
	}
	public int getParentID(){
		return (parent==null)? -1 : parent.getID();
	}
	int getDepth(AbstractNode n){
		if(n.parent==null)
			return 0;
		else
			return getDepth(n.parent)+1;
	}

	String childrenID(){
		StringBuilder temp = new StringBuilder();
		temp.append("[");
		if(children.size()>0)
		for(int i=0; ; i++){
			temp.append(children.get(i).getID());
			if( i == children.size() - 1 )
				break;
			temp.append(", ");
		}
		temp.append("]");
		return new String(temp);
	}
	public void nodeInfomation(){
		System.out.println(this);
		for(int i=0; i< children.size();i++)
			children.get(i).nodeInfomation();
	}
	public ArrayList<AbstractNode> connectTree(){
		ArrayList<AbstractNode> temp = new ArrayList<AbstractNode>();
		temp.add(this);
		for(int i=0; i< children.size();i++)
			temp.addAll(children.get(i).connectTree());
		return 	temp;
	}
	@Override
	public String toString(){
		StringBuilder temp = new StringBuilder();
		temp.append("node " + this.id);
		temp.append(": parent = " + getParentID());
		temp.append(", depth = " + getDepth(this));
		temp.append(", "  + getType());
		temp.append(", "   + childrenID());
		return new String(temp);
	}
	@Override
 	public int compareTo(AbstractNode temp) {
		return this.id - temp.getID();
	}
}