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A Solution to Google Hash Code 2019

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# Google Hash Code Problem 2019

This solution will get around 717698 points (712155 in the compentition; #851 Worldwide / #39 in UK)

## Qualification Problem

The problem statement is 
```
Given a list of photos and the tags associated with each photo, arrange the photos into
a slideshow that is as interesting as possible.
```
They score a slideshow by considering each transition between slides. The score will *minimum* of these three values 
  * the number of common tags between two consecutive slides or
  * the number of tags that only appears in the first slide or
  * the number of tags that only appears in the next slide
 
 Each slide could consist of
  * one horizontal photo
  * two vertical photos

*** the detail version please go to [official website](https://hashcodejudge.withgoogle.com/#/home)

### (tiny) Analysing Problem

The idea behide this is a simple greedy algorithm.

To maximize score; we found that the optimal solution is that the consecutive slides A, B should have these properties.
  * n(A) = n(B)
  * n(A intersect B) = n(A-B) = n(B-A)
  * so only about half of tags in A should be found in B
  
** n(A) = a number of tags in photo A

So we knew that a number of tags is quite useful.

### How did we solve it?
We started with seperating photos into two lists; vertical photos and horizontal photos

We thought that it would be easier to seperate problem into two parts
* Arranging Slides 
* Grouping Vertical Photos to form a slide

---------------

So, firstly, we ignored the vertical photos. We focused on how to arrange that maximize the score.

One simple idea we found is that 
1. order all photos by its number of tags (just this you could get more than 100k points)
2. optimize it by using a **sliding window**

The sliding window N is that
* starting with position 0 then you are going to find the next slide which will maximize your score from the next N slides
* then move that slide to position 1
* do it again until the final slide

The bigger N will get the better score but I believe that it will be limited around 800k points

---------------

The second part is to group vertical photos into a slide

We also used a simple solution by
1. order all photos by its number of tags
2. group the largest with the smallest and the second largest with the second smallest and so on.

This will give you roughtly the same size photos (in term of the number of tags)

Then combine two part together; grouping all vertical photos into slides then arrange them.

Hope it helps. **#HashCodeSolved**

## Go further
I believe that it could be improved a little bit more by apply thw same sliding window logic to group vertical photos. One idea is trying to apply this condition
  * max(A union B) // maximize a number of common tags within two verticle photos
  * min(H - n(A)) // H is the largest size of horizontal photos; I want to make sure that all vertical slides have the same number of tags.

## Practice Problem

I found very clear explanation from [http://flothesof.github.io/preparing-hashcode-2018.html](http://flothesof.github.io/preparing-hashcode-2018.html) so this is just a Java implementation from with tiny changes within the same idea.

# Our Team
* Pakawat Nakwijt [@chameleonTK](https://github.com/chameleonTK)
* Kenny Ng [@KennyNgZW](https://github.com/KennyNgZW)
* Praneeth Kumar Venkatapuram [@Praneethiq](https://github.com/Praneethiq) 
* Ajwad Rathore

from University of St. Andrews

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