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#!/usr/bin/env ruby

# terver.rb
# 
# Copyright Abandoned, 2007, Vadim A. Kazantsev aka V.A.KeRneL 
# <[email protected]>, Moscow, Russia.
# 
# This file is part of `terver-rb' package.
# 
# This file has been placed into the public domain by the author and may be 
# freely used for any purpose private or commercial.
# 
# I would appreciate it, as a courtesy, if this notice is left in all copies 
# and derivative works.  Thank you.
# 
# The author makes no warranty of any kind with respect to this product and 
# explicitly disclaims any implied warranties of merchantability or fitness 
# for any particular purpose.

# Written by Vadim A. Kazantsev aka V.A.KeRneL 
# <[email protected]>, Moscow, Russia.

# 
# Created:       2007-Feb-11 20:36:00
# Last modified: 2007-Jun-11 19:12:00
# Version 1.0.0
# 

require "mathn"

include Math

# 
# Extend standard class Integer with some new methods...
# 
class Integer
    
    # 
    # In mathematics, the factorial of a non-negative integer n is the 
    # product of all positive integers less than or equal to n.  This is 
    # written as n! and pronounced "n factorial", or colloquially "n shriek", 
    # "n bang" or "n crit".  The notation n! was introduced by Christian 
    # Kramp in 1808.
    # 
    # Definition: 
    # 
    #   n! := 1 * 2 * ... * (n - 1) * n   (if n > 0)
    #   0! := 1
    # 
    def fact()
        #return 1 if self.zero?
        (2..self).inject(1) { |prod, val| prod * val }
    end  # Integer#fact()
    
end  # class Integer

# 
# See description of Integer#fact.
# 
def fact(n)
    #return 1 if (n == 0)
    (2..n).inject(1) { |prod, val| prod * val }
end  # fact()

# 
# In combinatorial mathematics, a combination is an un-ordered collection of 
# unique elements.  (An ordered collection is called a permutation.)  Given 
# S, the set of all possible unique elements, a combination is a subset of 
# the elements of S.  The order of the elements in a combination is not 
# important (two lists with the same elements in different orders are 
# considered to be the same combination).  Also, the elements cannot be 
# repeated in a combination (every element appears uniquely once).  This is 
# because combinations are defined by the elements contained in them, so the 
# set {1, 1, 1} is the same as {1}.  For example, from a 52-card deck any 5 
# cards can form a valid combination (a hand).  The order of the cards 
# doesn't matter and there can be no repetition of cards.
# 
# The number of k-combinations (each of size k) from a set S with n elements 
# (size n) is the binomial coefficient.
# 
# Definition: 
# 
#              n    /n\         n!       
#   C(n, k) = C  = (   ) = ------------- 
#              k    \k/     k! (n - k)!  
# 
def c(n, k)
    (n.fact / (k.fact * (n - k).fact)).to_i
end  # c()
alias C c

# terver.rb ends here.