Python Excercises (Task 0)

Create a file solution.py with the functions described below. Add also a file called test.py that will test these functions in a manner of your choice.

Preparation

First fork this repository, by clicking the nice Fork button on the top of the page. Then you'll have your own copy of the repository. You can open it in your favorite Python editor.

Create the needed files and add them to your repository (git add solution.py test.py). Then, push them to your fork at github (git push). You should see yourself in the network graph. Now you are ready to solve the problems at hand.

Testing

You should test your functions before you submit them to us. Especially in this task, notice the places where we say that it needs to work for high n or something. These are simple excercises, but they need a bit of thinking to do them right!

After you've solved all the excercises, push them all to your fork. Check if all your changes are visible on github.com and create a Pull Request (a nice green button on top of your fork page). The pull request will be automagickly tested with Travis-CI. The results will show as a green checkmark or a sad red x.

IMPORTANT: In this task, you cannot use scipy, numpy, or matplotlib

Open source and public work

Yes, we know that you can open another person's fork and copy the solutions. Yay, you got an green checkmark for free! You can be proud of yourself. Have another one. Freshly copy-pasted from google images.

If you copy your homework in school,
don't be suprised that when you grow up,
you'll get paid with money from monopoly
— Ancient Chinese Proverb

Excercise 1

Create a function Newton(n,m) which for integers n and m will return an integer equal to the the binomial coefficient n over m. Which is equal to:

Do it so that the result will be still good for high values of n, for example:

> Newton(200,2)
19900

Excercise 2

Create a function Pascal(n) which will return a list of n rows of elements of the Pascal triangle. The result should be a list of length n. The elements of this list should be also lists, of increasing length (from 1 to n). For example:

> Pascal(4)
[ [1], [1,1], [1,2,1], [1,3,3,1] ]

Excercise 3

Create a function LotOfHash(n) which will print one line for each row of the Pascal Triangle, in which all the odd numbers will be printed as #. For example:

> LotOfHash(6)
#
##
# #
####
#   #
##  ##

Consider how to do it for high values of n

Excercise 4

Write a function PowerModulo(a,b,n) which will calculate the reminder of a^b with respect to division by n:

![a^b mod n](https://latex.codecogs.com/gif.latex?a^b\\quad\\text{mod }n)

For example:

> PowerModulo(2,3,10) # 8 mod 10 = 8
8
> PowerModulo(2,4,10) # 16 mod 10 = 6
6
> PowerModulo(2,5,10) # 32 mod 10 = 2
2

Implement is so that the value can be calculated for very high numbers (including b), for example:

> PowerModulo(2,200,100)
76

Clue: To calculate a^(2^k) you need only k multiplications

Excercise 5

Write a function Intersect(a,b) that for two tuples a=[x1,y1,r1] and b=[x2,y2,r1] will return a list of points of intersection of two circles, one with center at (x1,y1) and radious r1 and the other at (x2,y2) and radious r2. For example:

> Intersect( (0,0,5), (6,0,5) )
[ (3, 4), (3,-4) ]
> Intersect( (0,0,5), (10,0,5) )
[ (5, 0) ]
> Intersect( (0,0,5), (15,0,5) )
[ ]

taraspiotr / python_task0