Problem:
Binary Tree

A rooted binary tree is a tree with a root node in which every node has at most two children.

Your task is to write a program which reads a rooted binary tree T and prints the following information for each node u of T:

node ID of u

parent of u

sibling of u

the number of children of u

depth of u

height of u

node type (root, internal node or leaf)

If two nodes have the same parent, they are siblings. Here, if u and v have the same parent, we say u is a sibling of v (vice versa).

The height of a node in a tree is the number of edges on the longest simple downward path from the node to a leaf.

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

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 is given in the following format:

id left right

id is the node ID, left is ID of the left child and right is ID of the right child. If the node does not have the left (right) child, the left(right) is indicated by -1.

Output

Print the information of each node in the following format:

node id: parent = p, sibling = s, degree = deg, depth = dep, height = h, type

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

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

deg, dep and h are the number of children, depth and height of the node respectively.

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.

Please follow the format presented in a sample output below.

Constraints

1 ≤ n ≤ 25

Sample Input 1

9
0 1 4
1 2 3
2 -1 -1
3 -1 -1
4 5 8
5 6 7
6 -1 -1
7 -1 -1
8 -1 -1

Sample Output 1

node 0: parent = -1, sibling = -1, degree = 2, depth = 0, height = 3, root
node 1: parent = 0, sibling = 4, degree = 2, depth = 1, height = 1, internal node
node 2: parent = 1, sibling = 3, degree = 0, depth = 2, height = 0, leaf
node 3: parent = 1, sibling = 2, degree = 0, depth = 2, height = 0, leaf
node 4: parent = 0, sibling = 1, degree = 2, depth = 1, height = 2, internal node
node 5: parent = 4, sibling = 8, degree = 2, depth = 2, height = 1, internal node
node 6: parent = 5, sibling = 7, degree = 0, depth = 3, height = 0, leaf
node 7: parent = 5, sibling = 6, degree = 0, depth = 3, height = 0, leaf
node 8: parent = 4, sibling = 5, degree = 0, depth = 2, height = 0, leaf

Reference

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

Solution in JAVA (judge verdict: Runtime Error)


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.Deque;
import java.util.InputMismatchException;
import java.util.Map;
import java.util.Queue;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class Main {

	public static void main(String[] args) throws IOException {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskX solver = new TaskX();
		solver.solve(1, in, out);
		out.close();
	}

	static class TaskX {
		public void solve(int testNumber, InputReader in, PrintWriter out) {

			int n = in.nextInt();
			int[] degrees = new int[n];
			int[] depths = new int[n];
			int[] heights = new int[n];
			String[] types = new String[n];


			// make tree
			Node pNode = new Node(in.nextInt());
			int pLeft = in.nextInt();
			int pRight = in.nextInt();
			if (pLeft != -1) {
				pNode.left = new Node(pLeft);
				pNode.left.parent = pNode;
			}
			if (pRight != -1) {
				pNode.right = new Node(pRight);
				pNode.right.parent = pNode;
			}

			for (int i = 1; i < n; i++) {
				int tNode = in.nextInt();
				int left = in.nextInt();
				int right = in.nextInt();
				Node tn = bfs(pNode, tNode);

				if (left != -1) {
					tn.left = new Node(left);
					tn.left.parent = tn;
				}
				if (right != -1) {
					tn.right = new Node(right);
					tn.right.parent = tn;
				}
			}

			// dgree depth type
			for (int i = 0; i < n; i++) {
				Node tn = bfs(pNode, i);
				int degree = tn.degree();
				String type = tn.type();
				int depth = 0;

				while (tn.parent != null) {
					tn = tn.parent;
					depth++;
				}
				degrees[i] = degree;
				depths[i] = depth;
				types[i] = type;
			}

			// height
			for (int i = 0; i < n; i++) {
				Deque<Node> stack = new ArrayDeque<>();
				Node targetNode = bfs(pNode, i);
				stack.add(targetNode);
				boolean[] visited = new boolean[n];

				int height = 0;
				int tmpHeight = 0;
				while (!stack.isEmpty()) {
					Node node = stack.peek();
					if (node.left != null && !visited[node.left.num]) {
						stack.push(node.left);
						visited[node.left.num] = true;
						tmpHeight++;
						continue;
					}
					if (node.right != null && !visited[node.right.num]) {
						stack.push(node.right);
						visited[node.right.num] = true;
						tmpHeight++;
						continue;
					}
					stack.pop();
					height = Math.max(height, tmpHeight);
					tmpHeight--;
				}
				heights[i] = height;
			}

			// print
			StringBuffer sb = new StringBuffer();
			for (int i = 0; i < n; i++) {
				Node node = bfs(pNode, i);
				sb.append("node ").append(i).append(": parent = ");
				sb.append(node.parent()).append(", sibling = ").append(node.sibling());
				sb.append(", degree = ").append(degrees[i]).append(", depth = ");
				sb.append(depths[i]).append(", height = ").append(heights[i]);
				sb.append(", ").append(types[i]);
				if (i == n - 1) {
					continue;
				}
				sb.append("\n");
			}
			out.println(sb.toString());

		}
	}

	static class Node {
		int num;
		Node parent;
		Node left;
		Node right;
		Node (int num) {
			this.num = num;
		}
		int degree() {
			int count = 0;
			if (left != null) {
				count++;
			}
			if (right != null) {
				count++;
			}
			return count;
		}
		String type() {
			String type = null;
			if (parent == null) {
				type = "root";
			} else if (left != null || right != null) {
				type = "internal node";
			} else {
				type = "leaf";
			}
			return type;
		}
		int sibling() {
			int k = -1;
			if (parent != null) {
				if (parent.left != null && parent.left.num != this.num) {
					k = parent.left.num;
				} else if (parent.right != null && parent.right.num != this.num) {
					k = parent.right.num;
				}
			}
			return k;
		}
		int parent() {
			int k = -1;
			if (parent != null) {
				k = parent.num;
			}
			return k;
		}
	}
	static Node bfs(Node pNode, int targetNum) {

		Queue<Node> q = new ArrayDeque<>();
		q.add(pNode);

		while (!q.isEmpty()) {
			Node node = q.remove();
			if (node.num == targetNum) {
				return node;
			}
			if (node.left != null) {
				q.add(node.left);
			}
			if (node.right != null) {
				q.add(node.right);
			}
		}

		return null;
	}

	static class ArrayUtils {
		public static Map<Integer, Integer> getCountMap(int[] array) {
			Map<Integer, Integer> map = new TreeMap<>();
			for (int x : array)
				map.merge(x, 1, Integer::sum);
			return map;
		}
	}

	static class InputReader {
		BufferedReader in;
		StringTokenizer tok;

		public String nextString() {
			while (!tok.hasMoreTokens()) {
				try {
					tok = new StringTokenizer(in.readLine(), " ");
				} catch (IOException e) {
					throw new InputMismatchException();
				}
			}
			return tok.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(nextString());
		}

		public long nextLong() {
			return Long.parseLong(nextString());
		}

		public int[] nextIntArray(int n) {
			int[] res = new int[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextInt();
			}
			return res;
		}

		public long[] nextLongArray(int n) {
			long[] res = new long[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextLong();
			}
			return res;
		}

		public InputReader(InputStream inputStream) {
			in = new BufferedReader(new InputStreamReader(inputStream));
			tok = new StringTokenizer("");
		}

	}

}