Red-Black Tree

I will refine this post as I code more methods. This is an attempt to learn this data structure and explain what I think I understand using pictures drawn using TEX. I use the tikz editor.

The algorithm code is based on pseudo-code from “Introduction to Algorithms” by Thomas H. Cormen et al. I use Java language features like enums etc. wherever possible.

Sample TEX code

[->,>=stealth',level/.style={sibling distance = 5cm/#1,
  level distance = 1.5cm}] 
\node [arn_n] {3}
    child{ node [arn_r] {2} 
 				child{ node [arn_nil] {NIL}}
    child{ node [arn_r] {4}
							child{ node [arn_nil] {NIL}}


public class RedBlack {

    private final Node SENTINEL= new Node();
    private Node root= new Node();

    public RedBlack() {
        root = SENTINEL;

    enum Color {

    class Node{

        public void setColor(Color color) {
            this.color = color;

        private Color color = Color.BLACK;

        Node left,right,p;
        int key;

    public void insert( RedBlack tree,
                        Node z){
        Node y =  SENTINEL;
        Node x =  tree.root;
        while( x != SENTINEL){
            y = x;
            if ( z.key < x.key){
                x = x.left;
                x = x.right;
        z.p = y;
        if( y == SENTINEL){
            tree.root = z;
        }else if ( z.key < y.key){
                z = y.left;
                z = y.right;
        z.left = z.right = SENTINEL;

I check the colors like this.

    public void inOrder(Node x){

        if( x != SENTINEL){
            System.out.println(x.key + "[" + x.color + "]");

Now this tree has to be fixed so that it conforms to the rules that govern a Red-Black tree. So I code a method to fix it. This method is based on the pseudo-code from the same book. But I think there is a bug which I haven’t found. This tree after it is fixed looks like this.

Screen Shot 2014-06-01 at 1.17.01 PM

The black height property is 2.

The black height property for the left branch is 2 but it is 3 for one of the paths on the right.

I may have to read some other book because finding this bug is going to be hard.

Actually the tree should be like this.

Hackerrank’s Service Lane

I am again posting code without asymtotic analysis. There is no standard algorithm used here. I believe this problem pertains to Range Minimum Query algorithm which I hope to explore.

It is ridiculous that the code to parse the input values is more complex than the actual brute-force algorithm. Should Hackerrank parse it for us ?

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class Solution {

    private int noOfTestCases;

    private ArrayList<Integer> widths = new ArrayList<>();
    private ArrayList<Segment> tests = new ArrayList<>();

    OutputStream outputStream = System.out;
    PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));

    public void  getInput(BufferedReader br) throws IOException {
        Scanner s = null;
        int lengthHighway = 0;
        try {
            s = new Scanner(new BufferedReader(new InputStreamReader(;

            if (s.hasNextLine()) {
                String[] s1 = s.nextLine().split("\\s+");
                lengthHighway = Integer.parseInt(s1[0]);
                noOfTestCases = Integer.parseInt(s1[1]);
            if (s.hasNextLine()) {
                String[] s1 = s.nextLine().split("\\s+");
                for( int i = 0 ; i < s1.length ; i ++){
                    widths.add( Integer.parseInt(s1[i]) );
            while (s.hasNextLine()) {
                String[] s1 = s.nextLine().split("\\s+");
                tests.add( new Segment(Integer.parseInt(s1[0]), Integer.parseInt(s1[1]) ));
        } finally {

    class Segment{

        public final int entry,exit;

        public Segment(int entry, int exit) {
            this.entry = entry;
            this.exit = exit;

    public static void main( String... argv ) throws IOException {
        Solution rm = new Solution();
        BufferedReader br = new BufferedReader(new InputStreamReader(;


   private void fit() {
        int[] vehicle = new int[]{1,2,3};

        try {
            for( Segment test : tests){
                Integer[] a  = Arrays.copyOfRange(widths.toArray(new Integer[widths.size()]), test.entry, test.exit+1);