Automatic problem generation

Automatic Problem
Generation
A new approach to Mathematical analysis
Presented by: Abhishek Dey. Developer. Architect.

What is a problem?
▪ Take a typical example (Algebra):
𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0 is a quadratic equation. Resolve the factors.
Approach:
1. We multiply a*c and resolve the common factors.
2. We manipulate them and try to rearrange equation to satisfy constraint b.
3. 𝑎𝑥2 + 𝑏′ 𝑥 + 𝑏 − 𝑏′ 𝑥 + 𝑐 = 0 where b’ is a constant.
9/5/2015Prepared by: Abhishek Dey, Developer, Cloud Architect. 2

Human Analysis Vs. Machine Analysis
Factorize a*c.
I. assume expr=a*c
II. take a suitable integer x and divide expr/x
III. if remainder is divisible by x, continue
(expr-x)/x else, check for a new divisor y
(expr-x)/y.
IV. repeat unless expr reduces to a prime
number or 1.

Computer’s Algorithm:
▪ Has to start from 2 and continue checking up to a*c-1 times.
▪ Iterator 𝑖 ≔ 2 to 𝑖 ≔ 𝑒𝑥𝑝𝑟 − 1
– If 𝑒𝑥𝑝𝑟%𝑖 ≔ 0, then
▪ 𝑒𝑥𝑝𝑟 ≔ 𝑒𝑥𝑝𝑟/𝑖
– Else
▪ 𝑖 + +
▪ Do you think this is smart ? 

A better approach
▪ Fundamental Law of Arithmetic:
– Every composite number can be expressed as a product of primes.
▪ This makes the algorithm faster and smarter.
Number Number of Divisors
Prime 2
Square of a prime 3
Cube of a prime 4

Problem with Machines
▪ They generate random figures.
– Can you solve 48885𝑥2
+ 3287𝑥 + 95670 = 0 ?
– Probably. But not in a limited time.
▪ The generated problem may not have a unique solution.
▪ Some problems such as Matrix Chain multiplication, Bellman Ford,
Dijkstra may require a lot of processing power.

Where there is will, there is a unique
solution
▪ Processing Queue:
– We use a distributed processing model.
– Some problems from our end, others from customer’s end.
– We maintain a processing queue.
– A worker role that keeps record of all the distributed tasks
going on.
Example:
Say, we have a customer X who wants 10 questions on
quadratic equations.The server supplies 5 of them and
the remaining is generated in his system and backed up
in our server.

Architecture of the back end
Backend
Database
ProcessingQueueWrites data
Contacts tracker
We areTrackers!
We keep track of
jobs

Determining a unique solution
▪ We form aTree.
▪ Trace all paths that can be followed.
▪ If we reach a wrong node, we trace
back using Backtracking.
▪ Finally the correct path is determined.
▪ If the tree is too complex we use
Union-Find algorithm.
▪ This also helps us to know the
difficulty level of a problem.

Another problem has come up!
▪ When a user chooses a level of difficulty for
the generated problems, what do we mean
by EASY or HARD?
▪ EASY is a relative term.
▪ So, we employ 2 things:
– A Machine Learning mechanism based on
sentiment analysis.
– Feedback from live customers.
– What is MACHINE LEARNING?? :O

Achieved Throughput
0
5000000
10000000
15000000
20000000
25000000
30000000
35000000
40000000
500 1000 10,000 1,00,000 10,00,000 20,00,000
NO.OFQUESTIONS
NO. OF DEVICES
NO. OF DEVICES
No. of devices

What’s the point?
We hate these
situations!
We want a
solution.
Maybe unique.


The UI and UX:
▪ Users will be offered:
– Choose number of questions.
– Choose difficulty level of questions.
– If not satisfied with response, option to discard
question by just a slide.
– The experience is sleek and hassle free.
▪ What we shall get:
– We are Opensource. Not just FREE.
– Entire profits from advertisements.
– You contribute your processing power. (a little bit.)
– Build a platform for teachers.

To all the teachers,
on Teacher’s Day
ThankYou.
uriosity
ommitment
ommunityC

Automatic problem generation

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