Practice problems
=================

`Project Euler <https://projecteuler.net/archives>`_ and 
`99 Scala Problems <http://aperiodic.net/phil/scala/s-99/>`_  or
`99 Python Problems <https://wiki.python.org/moin/ProblemSets/99%20Prolog%20Problems%20Solutions>`_  
contain collections of small coding problems suitable 
for functional programming - many of them are also good exercises for **nuts-flow**.


99 Problems
-----------

A few `99 Scala Problems <http://aperiodic.net/phil/scala/s-99/>`_  with solutions
using **nuts-flow**:

>>> from nutsflow import *
>>> from nutsflow import _

**P01** : Find the last element of a list.

>>> [1, 1, 2, 3, 5, 8] >> Tail(1)
[8]

  
**P02** : Find the last but one element of a list.

>>> [1, 1, 2, 3, 5, 8] >> Tail(2) >> Head(1)
[5]

  
**P03** : Find the Kth element of a list.

>>> [1, 1, 2, 3, 5, 8] >> Nth(2)
2

>>> [1, 1, 2, 3, 5, 8] >> Drop(2) >> Head(1)
[2]

  
**P04** : Find the number of elements of a list.

>>> [1, 1, 2, 3, 5, 8] >> Count()
6
  
  
**P14** : Duplicate the elements of a list.

>>> Range(5) >> Clone(2) >> Collect()
[0, 0, 1, 1, 2, 2, 3, 3, 4, 4]
  
  
**P15** : Duplicate the elements of a list a given number of times.

>>> Range(5) >> Clone(n) >> Collect()
[0, 0, 1, 1, 2, 2, 3, 3, 4, 4]

  
**P16** :  Drop every Nth element from a list.

>>> n==3
>>> lst = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k']
>>> lst >> Chunk(n, list) >> Map(Take(n-1)) >> Flatten() >> Collect()
['a', 'b', 'd', 'e', 'g', 'h', 'j', 'k']


Euler
-----

Some `Project Euler <https://projecteuler.net/archives>`_  with solutions
using **nuts-flow**.

**P1**: Multiples of 3 and 5

If we list all the natural numbers below 10 that are multiples of 
3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. 
  
Find the sum of all the multiples of 3 or 5 below 1000.
  
>>> IsMultiple = nut_filter(lambda x: x % 3 == 0 or x % 5 == 0)
>>> Range(1, 1000) >> IsMultiple() >> Sum()
233168
  
  
**P2**: Even Fibonacci numbers

Each new term in the Fibonacci sequence is generated by adding the 
previous two terms. By starting with 1 and 2, the first 10 terms will be:

  1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
  
By considering the terms in the Fibonacci sequence whose values do not 
exceed four million, find the sum of the even-valued terms.
  
>>> @nut_source
... def Fib():
...     a, b =  1, 1
...     while True:
...         a, b = b, a + b
...         yield a
>>> IsEven = nut_filter(lambda x: x%2 == 0)
>>> Fib() >> TakeWhile(_ < 4000000) >> IsEven() >> Sum()
4613732

  
**P4**: Largest palindrome product

A palindromic number reads the same both ways. The largest palindrome 
made from the product of two 2-digit numbers is 9009 = 91 × 99.

Find the largest palindrome made from the product of two 3-digit numbers.

>>> n1, n2  = 100, 1000
>>> IsPalindrom = nut_filter(lambda p: p == p[::-1])
>>> BuildString = nut_function(lambda (a, b): str(a * b))
>>> product = Product(Range(n1, n2), repeat=2)
>>> product >> BuildString() >> IsPalindrom() >> Max(int)
'906609'
  
  
**P6**: Sum square difference

The sum of the squares of the first ten natural numbers is,

  1^2 + 2^2 + ... + 10^2 = 385

The square of the sum of the first ten natural numbers is,
  
  (1 + 2 + ... + 10)^2 = 55^2 = 3025

Hence the difference between the sum of the squares of the first ten natural 
numbers and the square of the sum is 3025 − 385 = 2640.

Find the difference between the sum of the squares of the first 
one hundred natural numbers and the square of the sum.

>>> sum_sqr = Range(1, 11) >> Square() >> Sum()
>>> sqr_sum = (Range(1, 11) >> Sum())**2
>>> sqr_sum - sum_sqr
2640