Hobbyist Competitive Programmer to Software Developer at HackerEarth

Prologue - Late December 2012, beginning of a new semester.

Reached college campus 2-3 days earlier only to know that we have planned to "mass bunk" the first week. Had no plans whatsoever for the 10 days that lied ahead. Took a stroll around the hostel and found a guy who, I speculated had already started studying for mid-semester exam. On later inspection I found that he was solving some mathematical puzzle on codechef.com. I had heard that name before but never bothered to browse around. He explained me that puzzle with sample input and asked me for output. It all started there, the craving for the green AC tick.

Dynamic Programming or Memoization : Simple optimizing Concept yet Effective

Dynamic Programming or Memoization is a well known technique for optimization.  It is just a method that remembers your previously calculated results and stores it somewhere so that when time comes you can use it again.

Just to begin with, a straightforward example of Memoization is calculation of Factorials. When we calculate Factorial of 5, i.e.

5! = 1*2*3*4*5 = 120

Now when you're asked to calculate Factorial of 6, a normal human being wouldn't go on like 1*2*3*4*5*6 rather he would think that "Well, I just calculated upto 5! why not simply multiply 6 to the answer of 5! " This is exactly what we are going to make our computers to do.

So, How do I make computer to remember pre-calculated results?
Answer is as simple as the question, just store them at a particular location in any array/list/vector.

Have a look at this simple Python implementation for memoized Factorial.

C/C++ and Python Program to find GCD of a list of numbers

A very easy question though, yet thought posting about it thinking it may improve my explanation prowess.

Lets get back to old school math, how did we find Greatest Common Divisor (GCD) or you may call it Highest Common Factor(HCF) of two numbers?

Assuming you know primary Maths, I'd proceed further.

Lets take an example before we go ahead.

Find GCD of 54 and 24.

Divisors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54.

Divisors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.

Common divisors of 54 and 24: 1, 2, 3, 6

The greatest of these is 6.

Hence gcd(54,24) = 6

Okay, lets write an algorithm for this. Well, one would say, there's nothing to think of any algorithm, things are crystal clear. Find out the factors of two numbers, then find common factors and then the largest of them.

But brother! There exists a better algorithm. Our Father of Geometry, Euclid, left us an algorithm already. We simply have to implement it.

Fast Power Algorithm: C/C++ and Python Code

In competitive programming, traditional way to finding power may not work sometimes.

By traditional way I mean if we have to find 2^10 (just as an example).

Or else simply by using library function after including math.h (in C) we can do it by pow(2,10)

Well, but this doesn't help us anymore when it comes to finding base to the power (base^power) where power could be anything in the range 0 to 1000000 or even greater value, same goes for base

Whilst you may think it impractical but in competitive programming questions ask us find Modulus of the answer by any prime number such as 1000000007, just to make sure answer remains in range of int data type.

i.e. pow(2,100)%1000000007 = 976371285

Lets come to the point and discuss what you have come for :)

Fast Algorithm:

result = 1
If power is odd:
    result = result*value
value = value*value
power = power/2

Yeah, I know, above algorithm more looks like a code & was nothing but a bouncer. ;)