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 Go (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
)

func nextInt(scanner *bufio.Scanner) int {
	scanner.Scan()
	num, _ := strconv.Atoi(scanner.Text())
	return num
}

func scanIntArray() []int {
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	n := nextInt(sc)
	result := []int{}
	for i := 0; i < n; i++ {
		result = append(result, nextInt(sc))
	}

	return result
}

type Input struct {
	id    int
	left  int
	right int
}

type Element struct {
	id      int
	parent  int
	sibling int
	degree  int
	depth   int
	height  int
	left    *Element
	right   *Element
}

var maxDepth int
var elements []Element

func main() {
	// assemble input
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	n := nextInt(sc)
	inputs := []Input{}

	inputTable := NewHashTable()
	childTable := NewHashTable()

	for i := 0; i < n; i++ {
		id := nextInt(sc)
		left := nextInt(sc)
		right := nextInt(sc)
		input := Input{id, left, right}
		inputs = append(inputs, input)
		inputTable.Put(id, input)
		childTable.Put(input.left, true)
		childTable.Put(input.right, true)
	}

	// find root
	var rootInput Input
	for _, input := range inputs {
		_, exist := childTable.Find(input.id)
		if !exist {
			rootInput = input
			break
		}
	}

	// assemble tree
	leftElement := Element{id: rootInput.left}
	rightElement := Element{id: rootInput.right}
	rootElement := Element{id: rootInput.id, parent: -1, sibling: -1, depth: 0, left: &leftElement, right: &rightElement}

	assembleTree(&rootElement, inputTable)

	// print
	flat(rootElement)
	sort.Slice(elements, func(i, j int) bool {
		return elements[i].id < elements[j].id
	})

	for _, elem := range elements {
		printElement(elem)
	}
}

func printElement(element Element) {
	if element.id == -1 {
		return
	}
	degree := 0
	if element.left.id != -1 {
		degree++
	}
	if element.right.id != -1 {
		degree++
	}

	height := getMaxDepthLeaf(element, element.depth) - element.depth

	elementType := "root"
	if element.parent != -1 {
		if element.left.id != -1 || element.right.id != -1 {
			elementType = "internal node"
		} else {
			elementType = "leaf"
		}
	}

	fmt.Printf("node %v: parent = %v, sibling = %v, degree = %v, depth = %v, height = %v, %v\n",
		element.id, element.parent, element.sibling, degree, element.depth, height, elementType)

}

func getMaxDepthLeaf(element Element, maxDepth int) int {
	max := maxDepth
	if element.left.depth > max {
		max = element.left.depth
	}

	if element.right.depth > max {
		max = element.right.depth
	}

	if element.left.id != -1 {
		left := getMaxDepthLeaf(*element.left, max)
		if left > max {
			max = left
		}
	}

	if element.right.id != -1 {
		right := getMaxDepthLeaf(*element.right, max)
		if right > max {
			max = right
		}
	}

	return max
}

func flat(element Element) {
	elements = append(elements, element)
	if element.left != nil {
		flat(*element.left)
	}
	if element.right != nil {
		flat(*element.right)
	}
}

func assembleTree(element *Element, inputTable HashTable) {
	if element.depth > maxDepth {
		maxDepth = element.depth
	}

	// assemble left and children of left
	if element.left.id != -1 {
		leftInputOrg, _ := inputTable.Find(element.left.id)
		leftInput := leftInputOrg.(Input)
		leftElement := Element{id: element.left.id,
			left:    &Element{id: leftInput.left, sibling: leftInput.right},
			right:   &Element{id: leftInput.right, sibling: leftInput.left},
			depth:   element.depth + 1,
			parent:  element.id,
			sibling: element.right.id}
		element.left = &leftElement
		assembleTree(&leftElement, inputTable)
	}

	// assemble right and children of right
	if element.right.id != -1 {
		rightInputOrg, _ := inputTable.Find(element.right.id)
		rightInput := rightInputOrg.(Input)
		rightElement := Element{id: element.right.id,
			left:    &Element{id: rightInput.left, sibling: rightInput.right},
			right:   &Element{id: rightInput.right, sibling: rightInput.left},
			depth:   element.depth + 1,
			parent:  element.id,
			sibling: element.left.id}

		element.right = &rightElement
		assembleTree(&rightElement, inputTable)
	}
}

// ======= Hashtable =======

// HashTable is HashTables
type HashTable struct {
	hashtable []*element
	length    int
}

type element struct {
	key int
	val interface{}
}

// NewHashTable generate HashTable
func NewHashTable() HashTable {
	length := 1046527
	return HashTable{make([]*element, length), length}
}

// Put new value
func (h *HashTable) Put(key int, val interface{}) {
	new := element{key, val}
	hash := abs(key % h.length)

	index := 0
	for {
		// double hash
		if h.hashtable[((1+hash%(h.length-1))*index+hash)%h.length] == nil {
			h.hashtable[((1+hash%(h.length-1))*index+hash)%h.length] = &new
			break
		} else {
			index++
		}
	}
}

func abs(x int) int {
	if x < 0 {
		return -x
	}
	return x
}

// Find new value
func (h *HashTable) Find(key int) (val interface{}, ok bool) {
	hash := abs(key % h.length)
	index := 0
	for {
		target := h.hashtable[((1+hash%(h.length-1))*index+hash)%h.length]
		if target == nil {
			return Input{}, false
		}

		if target.key == key {
			return h.hashtable[((1+hash%(h.length-1))*index+hash)%h.length].val, true
		}
		index++
	}
}