Subtraction
by Isai Damier

#======================================================================
# Author: Isai Damier
# Title: Subtraction
# Project: geekviewpoint
# Package: algorithms
#
# Statement:
#   Given two sets of bits, x and y, find their difference.
#
# Sample Input:  0010010010
# Sample Output: 0010010011
#
# Technical Details: The subtraction of two sets is the subset
#   comprising the elements that appear in the minuend x and not in the
#   subtrahend y. For example if s1 = [a,b,f,h,k] and s2 = [b,c,d,f,h,i]
#   then the subtraction of s1 and s2 is [a,k]. For two sets of bits the
#   subtraction is a two steps process. First, the negative of the
#   second set is calculated. Then the bitwise AND of the result and the
#   first set is taken. For example if x = 0110101 and y=0101100 then
#   the subtraction of x and y follows:
#
#    step_1: z = negative y = ~y = 1010011.
#    step_2: x AND z = x & z = x & (~y) = 0010001
#====================================================================== 
 def subtraction( x, y ) :
  return x & ~y
import unittest
from algorithms import bitwise as bits

class Test( unittest.TestCase ):

    def testSubtraction( self ):
        x = int( "0101100", 2 )
        y = int( "0110101", 2 )
        u = int( "0001000", 2 )
        self.assertEquals( u, bits.subtraction( x, y ) )

        x = int( "0101100", 2 )
        y = int( "0110101", 2 )
        u = int( "0010001", 2 )
        self.assertEquals( u, bits.subtraction( y, x ) )