sarvex / puzzles-exercises Goto Github PK

ABSTRACT:

This project contains the solutions for some puzzles and exercises found on the internet.


RESOLVED PROBLEMS:

At the moment of this writing only the railroad exercise was solved.


ASSUMPTIONS:

Railroad:
- There is one route from city A to city B. i.e.: having AB5 and AB4 is not valid.
- Some assumptions where made regarding the possible size of a given graph for a rail road circuit.
E.g.: the total cities might be up to thousands. But, never millions.
The outgoing routes from a given cities might be up to some hundreds.
This should be more than enough for the most of the train routes.
The main problem is that if the graph is too big, it might required different algorithms or parallelization.


CODE:

All the code is in Scala and it uses SBT as the building tool.

Requirements:

- JVM 1.6
- Scala 2.9.1
- SBT 0.11.0 (https://github.com/harrah/xsbt/wiki)


GENERAL DESIGN CONSIDERATIONS:

The main idea of the design is to split the graph definition, the algorithms being used (Dijkstra, DFS, etc)
and the actual rail road logic in different places.

The graph model tries to follow the standard Scala model for collections.
E.g.: mutable graphs are in a separated mutable package. Methods names are similar etc.


HOW TO RUN THE EXERCISES:

There are two options: tests and interactive.

Tests:
1. Open a console
2. Go to the project folder and run: sbt test
3. SBT will build the project and at the end it will run the tests.
4. The tests are bases on the Specifications framework. You should see a human friendly report.
5. Look for the output for the RoutingMapSpec class.
This class contains all the user acceptance criteria as described in the specifications.

Interactive:
1. Open a console
2. Go to the project folder and run: sbt. Once you are in the interactive shell execute "run"
3. SBT will build the project and at the end it will show you a prompt like "railroad>".
4. The description of the commands are shown in the console.
5. Note: this is a very basic client and you should write the commands as explained.


INTELLIJ

You can generate the IntelliJ project by running: sbt gen-idea


==========================================================================================


PROBLEM ONE: TRAINS

Problem: The local commuter railroad services a number of towns in
Kiwiland. Because of monetary concerns, all of the tracks are 'one-way.'
That is, a route from Kaitaia to Invercargill does not imply the existence
of a route from Invercargill to Kaitaia.  In fact, even if both of these
routes do happen to exist, they are distinct and are not necessarily the
same distance!

The purpose of this problem is to help the railroad provide its customers
with information about the routes.  In particular, you will compute the
distance along a certain route, the number of different routes between two
towns, and the shortest route between two towns.

Input:  A directed graph where a node represents a town and an edge
represents a route between two towns.  The weighting of the edge
represents the distance between the two towns.  A given route will never
appear more than once, and for a given route, the starting and ending town
will not be the same town.

Output: For test input 1 through 5, if no such route exists, output 'NO
SUCH ROUTE'.  Otherwise, follow the route as given; do not make any extra
stops!  For example, the first problem means to start at city A, then
travel directly to city B (a distance of 5), then directly to city C (a
distance of 4).

1. The distance of the route A-B-C.
2. The distance of the route A-D.
3. The distance of the route A-D-C.
4. The distance of the route A-E-B-C-D.
5. The distance of the route A-E-D.
6. The number of trips starting at C and ending at C with a maximum of 3
stops.  In the sample data below, there are two such trips: C-D-C (2
stops). and C-E-B-C (3 stops).
7. The number of trips starting at A and ending at C with exactly 4 stops.
In the sample data below, there are three such trips: A to C (via B,C,D);
A to C (via D,C,D); and A to C (via D,E,B).
8. The length of the shortest route (in terms of distance to travel) from
A to C.
9. The length of the shortest route (in terms of distance to travel) from
B to B.
10. The number of different routes from C to C with a distance of less
than 30.  In the sample data, the trips are: CDC, CEBC, CEBCDC, CDCEBC,
CDEBC, CEBCEBC, CEBCEBCEBC.

Test Input:

For the test input, the towns are named using the first few letters of the
alphabet from A to D.  A route between two towns (A to B) with a distance
of 5 is represented as AB5.

Graph: AB5, BC4, CD8, DC8, DE6, AD5, CE2, EB3, AE7

Expected Output:

Output #1: 9
Output #2: 5
Output #3: 13
Output #4: 22
Output #5: NO SUCH ROUTE
Output #6: 2
Output #7: 3
Output #8: 9
Output #9: 9
Output #10: 7

==========

PROBLEM TWO: SALES TAXES

Basic sales tax is applicable at a rate of 10% on all goods, except books,
food, and medical products that are exempt. Import duty is an additional
sales tax applicable on all imported goods at a rate of 5%, with no
exemptions.

When I purchase items I receive a receipt which lists the name of all the
items and their price (including tax), finishing with the total cost of
the items, and the total amounts of sales taxes paid.  The rounding rules
for sales tax are that for a tax rate of n%, a shelf price of p contains
(np/100 rounded up to the nearest 0.05) amount of sales tax.

Write an application that prints out the receipt details for these
shopping baskets...

INPUT:

Input 1:
1 book at 12.49
1 music CD at 14.99
1 chocolate bar at 0.85

Input 2:
1 imported box of chocolates at 10.00
1 imported bottle of perfume at 47.50

Input 3:
1 imported bottle of perfume at 27.99
1 bottle of perfume at 18.99
1 packet of headache pills at 9.75
1 box of imported chocolates at 11.25

OUTPUT

Output 1:
1 book : 12.49
1 music CD: 16.49
1 chocolate bar: 0.85
Sales Taxes: 1.50
Total: 29.83

Output 2:
1 imported box of chocolates: 10.50
1 imported bottle of perfume: 54.65
Sales Taxes: 7.65
Total: 65.15

Output 3:
1 imported bottle of perfume: 32.19
1 bottle of perfume: 20.89
1 packet of headache pills: 9.75
1 imported box of chocolates: 11.85
Sales Taxes: 6.70
Total: 74.68

==========

PROBLEM THREE: MARS ROVERS


A squad of robotic rovers are to be landed by NASA on a plateau on Mars.
This plateau, which is curiously rectangular, must be navigated by the
rovers so that their on-board cameras can get a complete view of the
surrounding terrain to send back to Earth.

A rover's position and location is represented by a combination of x and y
co-ordinates and a letter representing one of the four cardinal compass
points. The plateau is divided up into a grid to simplify navigation. An
example position might be 0, 0, N, which means the rover is in the bottom
left corner and facing North.

In order to control a rover, NASA sends a simple string of letters. The
possible letters are 'L', 'R' and 'M'. 'L' and 'R' makes the rover spin 90
degrees left or right respectively, without moving from its current spot.
'M' means move forward one grid point, and maintain the same heading.

Assume that the square directly North from (x, y) is (x, y+1).

INPUT:
The first line of input is the upper-right coordinates of the plateau, the
lower-left coordinates are assumed to be 0,0.

The rest of the input is information pertaining to the rovers that have
been deployed. Each rover has two lines of input. The first line gives the
rover's position, and the second line is a series of instructions telling
the rover how to explore the plateau.

The position is made up of two integers and a letter separated by spaces,
corresponding to the x and y co-ordinates and the rover's orientation.

Each rover will be finished sequentially, which means that the second
rover won't start to move until the first one has finished moving.


OUTPUT
The output for each rover should be its final co-ordinates and heading.

INPUT AND OUTPUT

Test Input:
5 5
1 2 N
LMLMLMLMM
3 3 E
MMRMMRMRRM

Expected Output:
1 3 N
5 1 E