I want to define a constant FOO
in the namespace of Integer
that is similar to Float::NAN
in Float
, which is itself an instance of Float
. It will be used somewhat similar to symbols, i.e., to mark a special case (of an integer). I don't need it to be used in calculation, but I need it to have the following properties:
Its class must be Integer
or a subclass of Integer
, and it must behave so to methods related to class:
Integer::FOO.kind_of?(Integer) # => true
Optionally (if the class is Integer
):
Integer::FOO.class # => Integer
Integer === Integer::FOO # => true
Integer::FOO.instance_of?(Integer) # => true
It must be distinct from (ideally all) other integers:
Integer::FOO == 0 # => false
Ideally, I want it distinct from any other integer, but if that is not possible, I can live with a dirty hack that, say makes Integer::FOO
be identical to the largest or the smallest integer, which are the least likely to hit any random given integer.
What is the best way to go about this?
An Integer x is called special in this case when, for every positive integer y such that y > x y \gt x y>x, x f ( x ) ≤ y f ( y ) \frac{x}{f(x)} \leq \frac{y}{f(y)} f(x)x≤f(y)y holds. Where, f ( d ) f(d) f(d) denotes the sum of the digits in the decimal representation on d.
Steps to Find Special Number Find the factorial of all digits. Sum up the factorial and store it in a variable (s). Compare the sum with the given number (N). If the sum is equal to the number itself, the number (N) is a special number, else not.
What is Special Number? A number is said to be special number when the sum of factorial of its digits is equal to the number itself. Example- 145 is a Special Number as 1!+ 4!+
We call a number special number if all the digits in that number are the same. For example, 1, 11, 1111 are special numbers. We count the special numbers in order 1, 11, 111, 1111, 2, 22, 222, 2222, 3, 33, 333, 3333, and so on. We have to find out the total number of digits that are in special numbers up to k.
Ruby's metaprogramming methods make it easy to twist a generic object into the shape you desire:
class Integer
FOO = Object.new
end
Integer::FOO.define_singleton_method(:kind_of?) do |klass|
Integer.ancestors.include? klass
end
Integer::FOO.define_singleton_method(:class) do
Integer
end
Integer::FOO.define_singleton_method(:instance_of?) do |klass|
klass == Integer
end
oldteq = Integer.method(:===)
Integer.define_singleton_method(:===) do |obj|
obj == Integer::FOO ? true : oldteq.call(obj)
end
Integer::FOO.kind_of? Integer
# true
Integer::FOO.class
# Integer
Integer === Integer::FOO
# true
Integer::FOO.instance_of? Integer
# true
Integer::FOO == 0
# false
The tricky part is making sure you cover all of the use cases. My code handles all of the requirements you listed but I have no idea what kind of weird side effects such a strange object would create.
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