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E-lite 2014 Programming Senior Finals Solutions Part1

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Here is the editorial for the Senior Programming Finals. The contest can be found here

Problem1. Odd
This was a straightforward question. Only perfect square numbers have an odd number of factors. Though this can be seen by observation(and is sufficient for solving this problem), you may want to know how we formally prove this:
Assume that there is a perfect square N. Let A be the set of natural numbers which are strictly smaller than floor(square_root(N)) . Let B be the set of natural numbers derived form A such that for every element(a) belonging to A there is a corresponding element N/a in B . The sets A and B do not intersect since if they did, a=N/a => a^2=N => a is the square root of N, but the square root of N does not belong to set A and we have a contradiction. Since these sets do not intersect, the total number of factors of N is 2*k + 1(where k is the number of elements in A, and 1 extra factor is the square root of N). Thus, N had an odd number of factors.
So, we need to output the sum of the first N perfect squares(where N was given in the problem) modulo M. The formula for that is N*(N+1)*(2*N+1)/6.
Some of you had a problem outputting the answer modulo 10^9 + 7.  This is where language matters : python can easily handle large numbers and you could have just done (print ans % M) to get your solution accepted. Its different with C++ however since there can be overflows while handling large numbers, You can read more about modulo operations here. Another common mistake was using x^y over pow(x,y):  x^y does not mean x raised to power y in C++, it means x XOR y.

Problem2. Walk Over Me
This is a classic Dynamic Programming problem. First of all you would need to figure out the intersection points, since the arrays are sorted this can be done in linear time. After this is done, the recurrence is simple,
maxSum(i) = max_(over all intersections j<i){ maxSum(j) + branchSum(j..i) }
For the people who got interviewed, the above recurrence is what I wanted as an answer: when we are given the optimal solutions to 1..i-1, we can find the optimal solution to i using the above recurrence.

Problem3. Mad Scientist
This was a tough problem to solve if you are not familiar with graphs. Unfortunately, some people jumped to this problem without attempting the first one(!). How you choose the problems pretty much decides how well you do in a programming contest.
For each pair of chemicals which can react, we add an edge in the graph. Once we have this information in a graph, we can find the “connected components” of this graph. When two chemicals are in a connected component, it basically means there is a sequence of links by which one can reach one of the chemicals starting from the other. For example, if A reacts with B, B reacts with C, and A reacts with D, then A,B,C,D form a connected component. Note that the order of adding chemicals within a connected component does not matter, the final power after adding all the chemicals is always initialPower * 2^(Size of Component – 1). So, the solution is to form the graph and then report the answer as 2^(V-number of  distinct connected components).

Problem4. Non Zero
This was an AdHoc implementation problem. Going from the left, maintain a counter recording the position of the last zero. Whenever a nonZero element is seen, swap that element with the element at counter, and increment the counter. I think the above is better understood by some code:

nonZero

Problem 6. Knights
This was a relatively hard graph problem. Consider the N*N squares on the (chess?)board as vertices. Then find the shortest distance between each pair of vertices. I used Breadth First Search to do this. The running time of this step is O(N4). Floyd-Warshall is not recommended here, since the graph is relatively sparse, and using it will cause solutions to time out. Then we wish to find the optimal point for the knights to gather at, and the total distance they need to travel to get there. For this, we iterate over each of the N*N candidate points and for each candidate point, we sum the distance each knight would need to travel to get to that point. Then we find and print the minimum value among the so-calculated distance sums of each point. The running time of this step is O(N2*M), which simplifies to O(N4) for lazy implementations, like my own. The total running time is hence O(N4).

e-Lite 2014 Programming Prelims Result

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Senior Programming Results

The following students have qualified for the Senior Programming Finals to be held on Wednesday, 16 July 2014.

Name Class
Aditya Sengupta X-H
Neel Bakshi XI-G
G Siddharth X-K
Rahul Shekhar XI-H
Tanay Rohtagi XI-J
Aryaman Dubey X-M
Akarsh Shekhar XI-I
Manan Aggarwal X-B
Anmol Peters XI-J
Sambhav Anand XI-L
Dev Shaurya Singhal X-L
R. Sai Narayan IX-J
Varun Arora X-J
Puroo Kumar Roy X-F
Amrutavarsh X-A
Sarthak Pal X-J
Sarkush Gupta IX-A
Amogh Agarwal IX-E

 
*Non Competitive Participants.

Congratulations to all the qualifiers!

e-Lite 2014 Prelim Results

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Senior Quiz Results

The following students have qualified for the Senior Quiz Finals to be held on Thursday, 17th July 2014.

Participant 1 Name Participant 1 Class Participant 2 Name Participant 2 Class
Vishal Chanda XI-R Tushar Chawla XI-R
Anav Agarwal XI-H Siddhant Jain XI-L
Neel Bakshi XI-G Archit Aggarwal XI-G
Shivain Arora XI-Q Sambhav Anand XI-L
Tejasvin Passi X-G Rishab Jain X-G
Nitin Mathai XI-J Aditya Garg XI-J

 

Junior Quiz Results

The following students have qualified for the Junior Quiz Finals to be held on Thursday, 17th July 2014.

Participant 1 Name Participant 1 Class Participant 2 Name Participant 2 Class
Sumay Mishra VIII-A Gursher Aujla VIII-A
Sameer Chaddha VIII-I Aditya Batra VII-J
Nishil Rajan VIII-A Kushagra Kshatri VIII-A
Anusha Shekhar VIII-A Nishka Bhushan VIII-A
Yashwardhan Kumar VIII-I Anshul Vardhan VIII-I
Udit Malik VIII-A Arihan Bothra VIII-A

 

Hardware Results

The following students have qualified for the Hardware Finals to be held on Friday, 18th July 2014

 

Name Class
Nitin Mathai XI-J
Aditya Garg XI-J
Harshil Kashyap XI-I
Siddhant Jain XI-L
Pranav Sharma IX-D

*Non Competitive Participants.

Congratulations to all the qualifiers!

Exun e-Lite 2014 Onsite Events

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The Onsite Events of Exun e-Lite 2014 will comprise the following :

Quiz: Power up that grey matter and sharpen that neural network because this is the ultimate battle of the brains! And not a very easy one at that! You’ll be asked to recall everything ranging from modern gadgets, to latest software to popular internet phenomena! There will be 2 participants per team.

  • Eligibility: Senior(9th to 11th) & Junior(6th to 8th)
  • Participation: 2 per team

Group Discussion: Quick-thinking, confidence and coherence backed up by statistical data and facts ensure heated debates and discussions about topics that will be given on the spot. Make your point and accommodate other’s opinions to come out at the top!

  • Eligibility: Junior(6th to 8th)
  • Participation: Individual

Programming: Make sure to include all your header files as you make your way through two rounds of intense programming.
No prior knowledge of programming is required for the preliminary rounds of the Programming event and therefore, if you think you’re good at solving puzzles and can work your way around patterns and sequences, then, have a crack at the paper, you must!
The senior event participants shall be required to qualify a logic-based written prelim round following which they shall face a grueling onsite final.
The junior event shall include only one logic based written round.

  • Eligibility: Senior(9th to 11th) & Junior(6th to 8th)
  • Participation: Senior(Individual), Junior(Individual)

Hardware Event: Power up your cores and overclock that grey matter, because you’re in for some serious hands-on competition! Participants will be tested on their knowledge of the most essential part of technology, Hardware! Identify components belonging to a plethora of devices and show-off all your know-how about the latest in the tech world. Participation will be individual.

  • Eligibility: Senior( 9th to 11th)
  • Participation: Individual

Registrations are now closed.
NO ONSITE REGISTRATIONS SHALL BE ENTERTAINED.

For further queries, contact us at exunclan@gmail.com or elite2014@exunclan.com

Exun e-Lite 2014 Creative Event

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The Exun Clan presents Exun e-Lite 2014 Creative Event, open to all students from classes 6th to 11th. The event entails the following sub-events :

  • Web Design and Development:

    For those of you who inspect each and every element on each and every web page you come across in order to analyse how it was built using only plain and simple HTML/CSS; for those of you who judge organisations by the how beautiful their websites look, we present an opportunity to show to us your creativity and skills. A series of online interactive sessions – designed and delivered by present Exun members – on the nuances of web design as well as the practical aspect – the use of a multitude of languages to develop applications for the web – awaits, at the end of which you will be given a task to complete. Based on submissions to this task, the Exun clan will be inducting members to its Design team.

  • Digital Imaging:

    If design is what you are absolutely passionate about; if all of your time on the internet eventually lands you onto websites like Abduzeedo and Behance, then the Digital Imaging event is the place to be. A series of online interactive sessions – designed and delivered by present Exun members – on how to harness your inherent creativity with the help of amazing software awaits, at the end of which you will be given a task to complete. Based on submissions to this task, the Exun clan will be inducting members to its Design team.

  • Audio – Video

    If you imagine Head-Up Displays while day dreaming in class or are particularly inspired by the magical technology that can make Transformers seem real – get ready to animate text and shapes into something that makes an impact. A series of online interactive sessions – designed and delivered by present Exun members – on how to create videos and manipulate sounds into pieces of art that make audiences stand up and applaud – awaits, at the end of which you will be given a task to complete. Based on submissions to this task, the Exun clan will be inducting members to its Video team.

Sessions will start in the last week of June, and the date for submission of entries is the 13th July, 2014. Follow lnexun.com for important updates.
Registrations are now closed.

Amity CyberBuzz 2014

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Amity Cyberbuzz 2014 was held on 2nd May 2014 at Amity International School, Gurgaon. The individual results are as follows:-

    Quiz – Winners

  • Akshay Gupta
  • Saumitra Khullar
    Movie Making – Runners Up

  • Arkin Gupta
  • Chaitanya Vaish
  • Devansh Gandhi
  • Zorawar Singh
  • Saumitra Khullar
  • Anumay Mishra
    Cryptex – Runners Up

  • Whole Team

Congratulations to all the winners!