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 C++14 (judge verdict: Accepted)

#include <iostream>
#include <vector>
using namespace std;

struct rootedTree {
	struct node {
		int bro, chi, par;
	};

	vector<int> dep;
	vector<node> tree;

	rootedTree(int n) :
		dep(n),
		tree(n, { -1, -1, -1 })
	{}

	int getBrother(int a) {
		return tree[a].bro;
	}

	int getChild(int a) {
		return tree[a].chi;
	}

	int getDepth(int a) {
		return dep[a];
	}

	int getParent(int a) {
		return tree[a].par;
	}

	vector<int> getChildren(int a) {
		int b = tree[a].chi;
		vector<int> res;
		while (b != -1) {
			res.push_back(b);
			b = tree[b].bro;
		}
		return res;
	}

	void setBrother(int a, int newBro) {
		tree[a].bro = newBro;
	}

	void setChild(int a, int newChi) {
		tree[a].chi = newChi;
	}

	void setParent(int a, int newPar) {
		tree[a].par = newPar;
	}

	void updateDepth(int a, int b) {
		dep[a] = b;
		if (tree[a].bro != -1) updateDepth(tree[a].bro, b);
		if (tree[a].chi != -1) updateDepth(tree[a].chi, b + 1);
	}
};

int main() {
	int n, id, k, c, tmp1;
	cin >> n;
	rootedTree rt(n);
	for (int i = 0; i < n; ++i) {
		cin >> id >> k;
		for (int j = 0; j < k; ++j) {
			cin >> c;
			if (j) rt.setBrother(tmp1, c);
			else rt.setChild(id, c);
			tmp1 = c;
			rt.setParent(c, id);
		}
	}
	for (int i = 0; i < n; ++i) {
		if (rt.getParent(i) == -1) {
			tmp1 = i;
			break;
		}
	}
	rt.updateDepth(tmp1, 0);
	for (int i = 0; i < n; ++i) {
		vector<int> tmp2 = rt.getChildren(i);
		cout << "node " << i << ": parent = " << rt.getParent(i) << ", depth = " << rt.getDepth(i) << ", ";
		if (rt.getParent(i) == -1) cout << "root, [";
		else if (rt.getChild(i) == -1) cout << "leaf, [";
		else cout << "internal node, [";
		if (!tmp2.empty()) cout << tmp2[0];
		for (int j = 1; j < tmp2.size(); ++j) cout << ", " << tmp2[j];
		cout << "]" << endl;
	}
}