The power sum challenge

Find the number of ways that a given integer, X, can be expressed as the sum of the N^{th} power of unique, natural numbers.

Input Format
The first line contains an integer X.
The second line contains an integer N.

1 \le X \le 1000
2 \le N \le 10

Output Format
Output a single integer, the answer to the problem explained above.

Sample Input 0

Sample Output 0

Explanation 0
If X = 10 and N=2, we need to find the number of ways that 10 can be represented as the sum of squares of unique numbers.

10 = 1^2 + 3^2

This is the only way in which 10 can be expressed as the sum of unique squares.

Sample Input 1

Sample Output 1

Explanation 1
100 = 10^2 = 6^2 + 8^2 = 1^2 + 3^2 + 4^2 + 5^2 + 7^2

Sample Input 2

Sample Output 2



Minimum loss challenge

Problem statement
Lauren has a chart of distinct projected prices for a house over the next n years, where the price of the house in the i^{th} year is p_i. She wants to purchase and resell the house at a minimal loss according to the following rules:

The house cannot be sold at a price greater than or equal to the price it was purchased at (i.e., it must be resold at a loss). The house cannot be resold within the same year it was purchased. Find and print the minimum amount of money Lauren must lose if she buys the house and resells it within the next years.

Note: It’s guaranteed that a valid answer exists.

Input Format
The first line contains an integer, n, denoting the number of years of house data. The second line contains space-separated long integers describing the respective values of p_1, p_2,\dots, p_n.

2\le n \le 2 \times 10^5 1 \le p_i \le 10^{16} All the prices are distinct. It’s guaranteed that a valid answer exists.

Output Format
Print a single integer denoting the minimum amount of money Lauren must lose if she buys and resells the house within the next n years.

Sample Input 0

Sample Output 0

Explanation 0
Lauren buys the house in year 1 at price p_1 = 5 and sells it in year 3 at p_3 = 3 for a minimal loss of 5 - 3 = 2.

Sample Input 1

Sample Output 1

Explanation 1
Lauren buys the house in year 2 at price p_2 = 7 and sells it in year 5 at p_5 = 5 for a minimal loss of 7 - 5 = 2.

Sample Input & Output 3

Naive approach
The naive approach is to iterate over each price p_i and compare it with all the subsequent prices, storing any new found minimum loss based on the two rules stated in the problem statement. This obviously has a running time of \mathcal{O}(n^2).

Binary Search Tree (BST) approach
We can construct a BST from the prices array. The construction has a running time of \mathcal{O}(nlogn). We then go through all the nodes. Starting at node x we traverse up (go to its parent) the BST as long as the current node is not a left child of its parent (or no parent is available). If the current node is a left child then we return the value of its parent. This value is the smallest value that is greater than the value of the original/starting node x. Searching the BST for every node has a total worst case running time of \mathcal{O}(nlogn).

Full code


Migrating WordPress site from a legacy hosting provider to AWS

Up until now my blog ( was hosted on a traditional/old fashioned hosting provider, Their service provided a fixed 10GB of hosting storage together with FTP access and a cPanel.

So here are the reasons why I switched over to AWS:
– Less expensive
– More flexible due to the fact that you can launch unlimited virtual servers, database instances, configure firewalls, load balancers, etc
– More security: my database isn’t publicly available anymore and sits in a VPC, better user management
– Literally thousands of services from CloudWatch to Lambda

Overall using AWS you have more control over your web applications.

So lets get started with the migration process!

We are going to do the following:
• Setup an EC2 instance using a Basic 64-bit Amazon Linux AMI
• Setup a S3 bucket
• Setup a MySQL RDS Instance
• Migrate old MariaDB database to new AWS DB Instance
• Install Apache Web Server, MySql, PHP, Git and Python on EC2 instance
• Install WordPress on EC2 instance
• Issue a Let’s Encrypt certificate
• Configure Apache Web Server on EC2 for HTTPS

Create an S3 bucket
We will first create an S3 bucket that we can use to store any database dumps and files so we can access them through our new EC2 instance.

To create a new instance, access the AWS Management Console and click the S3 tab. Create a new bucket and give it a name. Mine is named

Create an EC2 instance
To create a new instance, access the AWS Management Console and click the EC2 tab:

  • Choose an AMI in the classic instance wizard: I chose the Basic 64-bit Amazon Linux AMI.
  • Instance details: Select the Instance Type you want to use. I chose t2.micro.
  • Create a new key pair. Enter a name for your key pair (i.e. lucasloucacom) and download your key pair (i.e. lucasloucacom.pem).
  • Make sure you create a new security group, give it a name (e.g. and add inbound rules for SSH, HTTP and HTTPS that allow traffic from all sources.
  • Launch your instance.

Note:For security purposes you can edit the inbound rule for SSH to allow traffic only from your IP address.

Map IP Address and Domain Name
Your EC2 instance has an IP address as well as a DNS name. However, the default IP address is assigned dynamically and might change. You will keep the IP address as long as the instance is running and across reboots, but if you are forced to stop/start or anything like that you will lose it. If you have a domain name pointing to your instance, that is a bad thing. Thats why we need to associate an IP address to our instance and then map your domain name to that IP address.

To associate an IP address to your instance:
In the AWS Management Console, click Elastic IPs (left navigation bar). Click Allocate New Address, and confirm by clicking the Yes, Allocate button.
Select the newly allocated IP address and select Actions -> Associate address in the popup menu. Select the EC2 instance and click Yes, Associate

Note down the new Public DNS (e.g. of our EC2 instance. We will need it later.

Then, go to Route 53-> Hosted zones-> Create Hosted Zone. Amazon will list you four NS servers:

Note them down and login to your domain registrar. Under the DNS Manager delete the NS entries and any A records pointing to your web server. In my domain registrar I have deleted the NS and A entries and edited the names servers for my domain to point to the Route 53 provided name servers instead of my hosting providers defaults.

Back in the AWS console go to Route 53-> Hosted zones and select your newly created zone. Click on Create Record Set to setup some A records. Leave Alias to No and paste the elastic IP address of your EC2 instance into the value field. This will create a new A record pointing the domain name to the IP You can repeat this for any subdomains also. For example you can click on Create Record Set again and under Name enter www, Alias set to Yes and from the Alias Target target you can select the previously created record (e.g. That way will also point to the same IP as

Install Updates, Apache Web Server, MySql, PHP, etc
Once the instance is up and running go ahead and ssh to your EC2 instance:

In order to install the required tools and updates run the following commands:

Create a DB instance
Next, we are going to need a MySQL database for our blog.

To create a new instance, access the AWS Management Console and click the Database -> RDS tab. Then click Launch a DB Instance and select MySQL.

Then specify a username, password and database name and make sure Publicly Accessible is set to NO. Make sure you also create a new security group.

Once the instance is created, select it and under Configuration Details click on the security group (e.g. rds-launch-wizard-3). Edit the inbound rules for that group and set the Source for the MYSQL/Aurora type to the security group you created earlier for your EC2 instance (e.g. This will allow only traffic in that comes from the security group In other words only traffic that comes from our EC2 web server is allowed in.

Once created note down the endpoint address (e.g. You are going to need it later.

Install WordPress
Back in your EC2 shell:

Finaly, adjust wp-config.php to your database settings (i.e. username, passowrd, database name, host) that you created earlier.

By now you should be able to access your newly installed WordPress blog via

Export database from old blog
If your hosting server is as crapy as mine and your only option is to use phpMyAdmin then go ahead and login into your phpMyAdmin site. Then, select your blog database from the left side-bar and then go to Export. Select the Custom - display all possible options option and make sure you check the Add DROP TABLE / VIEW / PROCEDURE / FUNCTION setting. This will drop (delete) the table if it exists and recreate it in the database you are importing it to. For Format select SQL. and click Go.

Once you have your OLD_DB.sql go ahead and upload it to your S3 Bucket.

Backup wp-content from old blog
You also want to migrate any existing themes, plugins etc to your new AWS hosted blog. For that you need to migrate the contents of wp-content from your old blog into your newly installed wordpress blog. So for that you need to connect to your old hosting provider via FTP, navigate to your blog directory and download the entire wp-content directory. Archive it using:

Then go ahead and upload wp-content.tar to your S3 Bucket.

Create a new AMI access role for your EC2 instance
We need to be able to access our S3 bucket through our EC2 instance, so we can download our backed-up database and wp-content files. For that you need to login into your AWS console and navigate to your EC2 instance.

Select your EC2 instance and under Actions select Instance Settings -> Attach/Replace IAM role. From there you can select an existing role or create a new one by clicking Create new IAM role. Alternatively you can create a new role by from Services -> Security, Identity & Compliance -> IAM -> Roles -> Create new role.

So go ahead and create a new role providing it the policy AmazonS3FullAccess and attach the new role to your EC2 instance.

Access S3 from EC2
OK, once you have attached an IAM role with AmazonS3FullAccess policy to your EC2 instance you can go ahead and ssh to your EC2 instance:

Once you are logged in create a directory to sync our S3 bucket into:

Then try and sync the S3 bucket using:

In order to get the correct region type:

Then configure your aws client tot use it as the default region:

Verify your configuration using:

And then go ahead and try and sync your S3 bucket again:

Your files are now accessible under

Import old database into AWS hosted database
Go ahead and ssh to your EC2 instance:

And import your old database into your AWS RDS database:

Linking to new URL and defining new domain
Next you need to update any existing old URLs in your db to your new AWS URL. For that I temporary made my DB Instance Publicly Accessible and edited the security group’s inbound rules to allow any source (i.e. That way I could access my db through a nice GUI SQL client (I used Sequel Pro) and run the following SQL:

Of course you could again ssh into your EC2 and use the mysql command.

Note: Once you are done do not forget to disable Publicly Accessible and remove the added inbound rules from the security group.

WordPress pretty permalinks on Amazon EC2 Linux instance
You will need to edit /etc/httpd/conf/httpd.conf and change AllowOverride None to AllowOverride All. So it should look like so:

Note: AllowOverride None appears two times in /etc/httpd/conf/httpd.conf and you need to change it in all cases.

Then, navigate to /var/www/html/blog and create an .htaccess file that looks like so:

Also create a .htaccess file under /var/www/html/ to route to

This will transparently redirect all requests to /blog/{requested_resource}. If you have other subfolders that need to be excluded from this redirect you can just an .htaccess file in those directories saying:

For example, I wanted to leave and it’s content alone completely so I have just added such an .htaccess file under /var/www/html/bargain.

Finally, you then need to restart apache:

You should be able to view your old posts etc under the new host

Updated WordPress site URLs
In the previous section we updated out database entries to point to our domain. That way we could continue working until the NS and A records are updated. We can run the sql script again to point to our domain name (http://lucaslouca.comNote: http and not https).

You may need to temporary make your DB Instance Publicly Accessible and edit the security group’s inbound rules to allow any source (i.e. That way you can access your db through a nice GUI SQL client (I used Sequel Pro) and run the following SQL:

Enable HTTPS
We already enabled any HTTPS traffic in our We now need to configure our Apache server to also listen on port 443 in order for us to be able to access our blog via HTTPS. For that we first need to obtain a CA-signed certificate. We will use Let’s Encrypt for our CA.

Add the following to your /etc/httpd/conf/httpd.conf:

Install python and git on your EC2:

Get the letsencrypt client:

Create a config file that will be used for new certificates and renewals. It contains the private key size and your email address.

Important: Before you run letsencrypt temporary disable /var/www/html/.htaccess:

Run letsencrypt:

Note: If you are trying to letsencrypt your AWS domain (e.g. and you are getting an error its because happens to be on the blacklist of Let’s Encrypt.

Enable /var/www/html/.htaccess and clean up:

The certificates are located at /etc/letsencrypt/live/ and the last thing is to update your webserver’s configuration. So edit your /etc/httpd/conf.d/ssl.conf file:

Restart apache:

Try and access It should work!

Finally, add the renew command in a crontab. Refresing your webserver command should also be here.

Updated WordPress site URLs
In the previous section we updated out database entries to point to our domain. Now that we got HTTPS up and running we can update our WordPress site URLs to point to HTTPS.

You may need to temporary make your DB Instance Publicly Accessible and edit the security group’s inbound rules to allow any source (i.e. That way you can access your db through a nice GUI SQL client and run the following SQL:

Note: Once you are done do not forget to disable Publicly Accessible for your db instance and remove the added inbound rules from the security group.

Give Apache apache access to the folders
An issue still exists when you try to update/install plugins etc. The issue is that apache does not have access to the folders. The default permission is given to the ec2-user in the AMI.

Run this in your EC2 shell and you should be good to go:

Thats it guys!!


Word in string challenge

Problem statement
We say that a string, s, contains the word hackerrank if a subsequence of the characters in s spell the word hackerrank. For example, haacckkerrannkk does contain hackerrank, but haacckkerannk does not (the characters all appear in the same order, but it’s missing a second r).

More formally, let p_0, p_1, \dots, p_9 be the respective indices of h, a, c, k, e, r, r, a, n, k in string s. If p_0 \textless p_1, \textless p_2 \dots \textless p_9 is true, then s contains hackerrank.

You must answer q queries, where each query i consists of a string, s_i. For each query, print YES on a new line if s_i contains hackerrank; otherwise, print NO instead.

Input Format
The first line contains an integer denoting q (the number of queries).
Each line i of the q subsequent lines contains a single string denoting s_i.

Output Format
For each query, print YES on a new line if s_i contains hackerrank; otherwise, print NO instead.

Sample Input 0

Sample Output 0



Recursive Digit Sum challenge

Problem statement
We define super digit of an integer x using the following rules:

  • If x has only 1 digit, then its super digit is x.
  • Otherwise, the super digit of x is equal to the super digit of the digit-sum of x. Here, digit-sum of a number is defined as the sum of its digits.

For example, super digit of 9875 will be calculated as:

You are given two numbers n and k. You have to calculate the super digit of P.

P is created when number n is concatenated k times. That is, if n = 123 and k = 3, then P=123123123.

Input Format
The first line contains two space separated integers, n and k.

1 \le n \textless 10^{100000}
1 \le k \le 10^{5}

Output Format
Output the super digit of P, where P is created as described above.

Sample Input 0

Sample Output 0

Explanation 0
Here n=148 and k=3, so P=148148148.

Sample Input 1

Sample Output 1



Random video chat website using WebRTC

Seing as how many people are interested in my video-conference-webrtc project, I have decided to develop a random video chat website using WebRTC. The project is called rtcrandom and is hosted on GitHub. A live demo is also available at


RTCRandom is an online (video)chat website that allows users to socialize with others without the need to register. The service       randomly pairs users in one-on-one chat sessions where they chat anonymously using the names “You” and “Stranger”.

For the project I have used GitHub for my online project hosting service using Git, issue tracking, collaboration and wikis. Node.js and JavaScript are the main programming languages used for development. For continuous integration I am using Jenkins with OpenShift as my hosting service. The wiki is available here.

I not going into great detail explaining the code. I will rather give you a brief overview on how rtcrandom works and leave the pleasure of examining the code to you.

For the back-end Node.js is used with Express as the web application framework. I used winston for logging and EJS as the templating language for the views.

For the front-end simple HTML with JavaScript (jQuery, and CSS is used. In order to add WebRTC support for browsers like Safari (which does not support WebRTC yet) I have used the Temasys WebRTC adapter. If you do not wish to use such an adapter see release v0.1-alpha.

Main components
On the back-end the main component is server.js and on the front-end the magic happens in public/js/room.js, which is loaded by the views/room.ejs view.

How does the matching work
When a client first loads the page a bidirectional event-based communication is created between the client’s browser and the back-end using I call this the default communication channel. The default communication channel is used by the client to let the server know, that the client wants to find a new chat partner etc. It also allows the server to inform a client about a new chat partner etc.

So once a client wants to find a new (or initial) communication partner he triggers a next event through the default communication channel, letting the server know about its ID and that he wants a new chat partner. The ID is a random hash that is generated once on client-side. The server then puts the client’s request into a queue and checks if the queue has at least two requests (note: no client is put twice in the queue). If at least two requests are in the queue (one from a different client and one from our current client), the two clients are polled from the queue. The server then generates a random room name (a random six digit alphanumeric string) and sends it to the two clients via the default communication channel.

Once each client receives the new room name, they send a message to the server via the default channel that they want to join the room. The client whose message arrives first at the server creates and joins the room and the second client simply joins the new room. The peer that simply joins the new room gets notified by the server that it just joined, so that it can broadcast the message to the default channel saying that it is a new participant that joined the room and wants to receive a WebRTC offer to open up a peer-to-peer WebRTC communication with the other client in the room (the one that created the room). The room creator then receives the new participant message in the default channel and creates an offer for the joining peer. This offer will be send via a private communication channel which both clients open using the room name as namespace. The room creator then sends the offer through this channel, which the other peer receives and responds to with an answer. Further WebRTC related communication messages to build the WebRTC peer-to-peer connection between the two clients are also exchanged through the private channel. Once a peer-to-peer connection is establish the video stream and chat messages are exchanged directly between the two clients (no server required).

Note: when a peer disconnects from one peer (e.g. because it wants to chat with a different person) the disconnect event is not immediately received by the other peer, due to WebRTC delays. This is why the disconnecting peer also sends a disconnect notification message to the other peer via the private channel, so that it can update its view. The notification is send using the private channel because it tends to be faster than waiting for the WebRTC notifications.

The source code is available here. A live demo is available at


Crossword Puzzle challenge

Problem statement
A 10 \times 10 Crossword grid is provided to you, along with a set of words (or names of places) which need to be filled into the grid. The cells in the grid are initially, either + signs or - signs. Cells marked with a + have to be left as they are. Cells marked with a - need to be filled up with an appropriate character.

Input Format
The input contains 10 lines, each with 10 characters (which will be either + or - signs).
After this follows a set of words (typically nouns and names of places), separated by semi-colons (;).

There will be no more than ten words. Words will only be composed of upper-case A-Z characters. There will be no punctuation (hyphen, dot, etc.) in the words.

Output Format
Position the words appropriately in the 10 \times 10 grid, and then display the 10 \times 10 grid as the output. So, your output will consist of 10 lines with 10 characters each.

Sample Input 0

Sample Output 0

Sample Input 1

Sample Output 1



Password Cracker challenge

Problem statement
There are N users registered on a website Each of them have a unique password represented by pass[1], pass[2], \dots, pass[N]. As this a very lovely site, many people want to access those awesomely cute pics of the kittens. But the adamant admin don’t want this site to be available for general public. So only those people with passwords can access it.

Yu being an awesome hacker finds a loophole in their password verification system. A string which is concatenation of one or more passwords, in any order, is also accepted by the password verification system. Any password can appear 0 or more times in that string. He has access to each of the N passwords, and also have a string loginAttempt, he has to tell whether this string be accepted by the password verification system of the website.

For example, if there are 3 users with password {abra, ka, dabra}, then some of the valid combinations are abra (pass[1]), kaabra (pass[2]+pass[1]), kadabraka (pass[2]+pass[3]+pass[2]), kadabraabra (pass[2]+pass[3]+pass[1]) and so on.

Input Format
First line contains an integer T, the total number of test cases. Then T test cases follow.
First line of each test case contains N, the number of users with passwords. Second line contains N space separated strings, pass[1] pass[2] \dots pass[N], representing the passwords of each user. Third line contains a string, loginAttempt, for which Yu has to tell whether it will be accepted or not.

1 \le T \le 10
1 \le N \le 10
pass[i] \ne pass[j], 1 \le i \textless j \le N
1 \le length(pass[i]) \le 10, where\ i \in \left[1,N\right]
1 \le length(loginAttempt) \le 2000
loginAttempt and pass[i] contains only lowercase latin characters (‘a’-‘z’).

Output Format
For each valid string, Yu has to print the actual order of passwords, separated by space, whose concatenation results into loginAttempt. If there are multiple solutions, print any of them. If loginAttempt can’t be accepted by the password verification system, then print WRONG PASSWORD.

Sample Input 0

Sample Output 0

Explanation 0
Sample Case #00: wedowhatwemustbecausewecan is the concatenation of passwords {we, do, what, we, must, because, we, can}. That is

Note that any password can repeat any number of times.

Sample Case #01: We can’t create string helloworld using the strings {hello",planet`}.

Sample Case #02: There are two ways to create loginAttempt (abcd). Both pass[2] = "abcd" and pass[1] + pass[3] = "ab cd" are valid answers.

Sample Input 1

Sample Output 1

We can solve this problem recursively and use memoization to avoid running out of time. The basic algorithm goes as follows:
– Iterate over all indices i of loginAttempt:
– Split loginAttempt into two parts left = loginAttempt.substring(0,i) and right = loginAttempt.substring(i).
– Call isValid(left) and isValid(right).
– If both calls return true, then loginAttempt is valid.

Full code


How to setup Let’s Encrypt (SSL) Certificate on OpenShift

In previous posts I have described how to deploy a Node.js application to OpenShift. Now its time to add a custom alias to our Node.js application so that it is accessible through a custom domain, like Currently it is accessible only through Off course we also want valid SSL certificates for our custom domain For that we need to get a certificate (a type of file) from a Certificate Authority (CA). Let’s Encrypt is a free, automated, and open certificate authority brought to you by the non-profit Internet Security Research Group (ISRG). So obviously we will use that.

Create alias via OpenShift web console
From the Applications section choose your application (e.g. testnode) and then click on change alias. For Domain Name enter your custom domain. Mine is Leave the rest of the fields blank and click Save.

To successfully use this alias, you must have an active CNAME record with your DNS provider. The alias is and the destination app is

My provider is So I went ahead, logged in and under Subdomains -> New Sub Domain I have created a new subdomain Then under DNS Configuration for, I was able to set the CNAME record to for * ( included).

And thats it!

Create certificates
We will need a valid certificate and its corresponding private key to upload to OpenShift for the new domain Under Mac OS X I have used certbot. So go ahead and install certbot:

Once installed run:

OK, that didn’t work. Obviously Let’s Encrypt wants us to prove that we are the truthful owners of The way it verifies ownership is trying to load the above URL ( and compare the received result with the expected result.

We need to modify our Node.js application to return the hash Let’s Encrypt requires when the above URL is GET. In my router.js I have added the below code snippet:

The above code reads the hash from the requested URL and returns it. OK, lets try it one more time.

Hmmmm, that didn’t work either. At this point I should probably read the manual. But apparently when the URL is requested, it expects xxxxxxxxxxx.yyyyyyyyyyy as a result. So I went and modified my router.js again:

Giving it a try again, I finally got my certificates:

The generated certificate and private key is located under /etc/letsencrypt/archive/test.testnode.comc/cert1.pem and /etc/letsencrypt/archive/ respectively.

Upload certificates to OpenShift
For this we will use the OpenShift client tools:

Thats it! Our application is now accessible through


Reading SPIEGEL Plus articles

DISCLAIMER: The information below is for information purposes only.

I happened to be browsing on SPIEGEL Online the other day and noticed that articles published for non SPIEGEL Plus subscribers were still partially available on the article’s page in readable form while the largest portion of the text was blurred out and available only for paying subscribers.

So the first thing I did was to take a closer look at the blurred out text (which was just underneath an overlay with a CSS filter style). I noticed that the text structure was resembling an ordinary paragraph style (if I can express it like that), with the words just being gibberish:

In the above example you can see that the letter ‘/’ is used three consecutive times or that it is often followed by a space. This made me think that ‘/’ may be a replacement for the character ‘.’.

Another fun fact is that SPIEGEL Plus articles are only partially encrypted so that the reader can develop an interest for the article and then hopefully (for them) decide to buy it. The particular article that I happen to be reading was an interview like article, where SPIEGEL interviewed a guy named Butter, with SPIEGEL asking a question and Butter answering it. Fortunately for me this was a repeating pattern with participant names being styled in bold text in both the plain and encrypted text for easy detection. I could easily see that SPIEGEL: was always matching to TQJFHFM; and Butter: to Cvuufs; in the cipher text. Using this I could easily see that the letter ‘E’ was matching to ‘F’, ‘e’ to ‘f’, ‘:’ to ‘;’…

This made me think that this cipher was nothing more than a simple substitution cipher where each letter in the original message is replaced with some other predefined letter. Taking a look at the following ASCII table one can easily see that the ASCII code x of the plain text character has been replaced with the character represented by the ASCII code x+1: ‘E’ (ASCII 69) has been replace with F (ASCII 70), etc.

This cipher is also known as Caesar cipher. Anyhow, I thought it might be fun to write a small Firefox extension that I can use to view those articles. The extension basically removes the blurring overlay and replaces the encrypted text with their plain text version.

The source code is available here. If you don’t know how to temporary install a Firefox extension you can refer to this guide.