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: Accepted)

import java.util.Arrays;

import java.io.IOException;
import java.io.InputStream;
import java.util.NoSuchElementException;

 class FS {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        } else {
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }

    private int readByte() {
        return hasNextByte() ? buffer[ptr++] : -1;
    }

    private boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }

    private void skipUnprintable() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
    }

    public boolean hasNext() {
        skipUnprintable();
        return hasNextByte();
    }

    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public int nextInt() {
        return (int) nextLong();
    }

    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b)) {
                return minus ? -n : n;
            } else {
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
}

public class Main {
    static BinTree bt[];
    static int par[];

    public static void main(String[] args) {
        FS fs = new FS();
        int n = fs.nextInt();
        bt = new BinTree[n];
        par = new int[n];
        for (int i = 0; i < n; i++) {
            int id = fs.nextInt();
            int left = fs.nextInt();
            int right = fs.nextInt();
            if (left!=-1)par[left] = id + 1;
            if (right!=-1) par[right] = id + 1;
            bt[i] = new BinTree(id, left, right);
        }
        Arrays.sort(bt);
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < n; i++) {
            BinTree binTree = bt[i];
            int sibling = -1;
            if (par[binTree.id] - 1 >= 0) {
                if (bt[par[binTree.id] - 1].left == binTree.id) sibling = bt[par[binTree.id] - 1].right;
                else sibling = bt[par[binTree.id] - 1].left;
            }
            int degree = 0;
            if (binTree.left != -1) degree++;
            if (binTree.right != -1) degree++;

            int depth = 0;
            int x = binTree.id;
            while (par[x] - 1 != -1) {
                depth++;
                x = par[x] - 1;
            }
            int height = getHeight(binTree);
            String type = "internal node";
            if (par[binTree.id]-1 == -1) type = "root";
            else if (binTree.left == -1 && binTree.right == -1) type = "leaf";
            sb.append("node ").append(binTree.id).append(": parent = ").append(par[binTree.id] - 1).append(", sibling = ")
                    .append(sibling).append(", degree = ").append(degree).append(", depth = ")
                    .append(depth).append(", height = ").append(height).append(", ").append(type).append("\n");
        }
        System.out.print(sb);
    }

    private static int getHeight(BinTree binTree) {
        if (binTree.left == -1 && binTree.right == -1) {
            return 0;
        }
        if (binTree.left == -1) return getHeight(bt[binTree.right]) + 1;
        else if (binTree.right == -1) return getHeight(bt[binTree.left]) + 1;
        else return Math.max(getHeight(bt[binTree.right]) + 1, getHeight(bt[binTree.left]) + 1);
    }

    static class BinTree implements Comparable<BinTree> {
        int id;
        int left;
        int right;

        public BinTree(int id, int left, int right) {
            this.id = id;
            this.left = left;
            this.right = right;
        }

        @Override
        public int compareTo(BinTree o) {
            if (this.id > o.id) return 1;
            else return -1;
        }
    }
}