karatedog

# factorial method
def fact(n)
  (1..n).reduce(:*)
end  

# binomial theorem, n choose k
def binomial(n,k)
  return 1 if n-k <= 0  
  return 1 if k <= 0
  fact(n) / ( fact(k) * fact( n - k ) )

karatedog

# recursive 'de Casteljau' method. The method multiplies the array's elements in pairs (1st * 2nd, 2nd * 3rd, 3rd * 4th, etc.). Output array is one element less than input array.

# test_ary = [7, 17, 23, 47, 61]

def rec(ary)
        if ary.length == 2 then 
                # base case
                return [ ary[0] * ary[1] ]
        else
                # recursive case

karatedog

#!/usr/bin/env ruby
# 2011-10-10 20:57:53 +1000

def merge_sort(a)
    return a if a.size <= 1
    l, r = split_array(a)
    result = combine(merge_sort(l), merge_sort(r))
end

karatedog

# Ruby Array's "-" (minus) method removes elements from the receiver which exist in the parameter Array

[5, 6, 1] - [2, 3, 5]

# => [6, 1]

# this #subtract method will subtract the value of the parameter Array from the value of the receiver Array, defined by the actual index.
# type mismatch, Nil, and different Array length are not handled

class Array

karatedog

# Enumerator based Logistic map, can be used as a PRNG as well.

def logistic_map(x0, r)
  return Enumerator.new do |yielder|
    number = x0.to_f
    r = r.to_f
    loop do
      yielder.yield(number)
      number = r * number * (1 - number)
    end