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: Memory Limit Exceeded)

import java.util.Scanner;
public class Main {
    public static void main (String[] args) {
	Scanner scan = new Scanner(System.in);
	int n = Integer.parseInt(scan.nextLine());
	Node[] nodes = new Node[n];
	for (int i = 0; i < n; i++) {
	    nodes[i] = new Node(i);
	}
	
	String[] input;
	int id, k, childId;
	int[] a;
	for (int i = 0; i < n; i++) {
	    input = scan.nextLine().split(" ");
	    id = Integer.parseInt(input[0]);
	    k = Integer.parseInt(input[1]);
	    nodes[id].k = k;
	    if (k == 0) {
		nodes[id].type = 1;
	    } else {
		a = new int[k];
		for (int j = 0; j < k; j++) {
		    childId = Integer.parseInt(input[2+j]);
		    a[j] = childId;
		    nodes[childId].parent = id;
		}
		nodes[id].c = a;
	    }
	}

	for (int i = 0; i < n; i++) {
	    nodes[i].depth = setDepth(i, nodes);
	}
	
	StringBuilder sb = new StringBuilder();

	for (int i = 0; i < n; i++) {
	    sb.append("node " + i);
	    sb.append(": parent = " + nodes[i].parent);
	    sb.append(", depth = " + nodes[i].depth);
	    sb.append(", ");
	    if (nodes[i].type == -1) {
		sb.append("root, ");
	    } else if (nodes[i].type == 0) {
		sb.append("internal node, ");
	    } else if (nodes[i].type == 1) {
		sb.append("leaf, ");
	    }
	    sb.append("[");
	    if (nodes[i].k != 0) {
		sb.append(nodes[i].c[0]);
	    }
	    for (int j = 1; j < nodes[i].k; j++) {
		sb.append(", " + nodes[i].c[j]);
	    }
	    sb.append("]\n");
	}
	System.out.print(sb);

    }
    public static int setDepth (int id, Node[] nodes) {
	if (nodes[id].depth >= 0) return nodes[id].depth;
	if (nodes[id].parent == -1) {
	    nodes[id].type = -1;
	    return nodes[id].depth = 0;
	}
	return nodes[id].depth = setDepth(nodes[id].parent, nodes)+1;
    }
    
}

class Node {
    int id;
    int parent;
    int depth;
    int type; //-1: root, 0: internal node, 1: leaf
    int k;
    int[] c;
    Node (int id) {
	this.id = id;
	this.parent = -1;
	this.depth = -1;
	this.type = 0;
    }
}