=begin
editStringAdder.rb
* contains a working edit string adder implementation (product operator)
* is ruby, hence can be treated as pseudocode
* eventual deployment may be javascript, unsure
* is a piece of a cheap as free HTML visualizer none the less
* induced from examples in Robert Edgar, MUSCLE, BMC Bioinformatics
=end

=begin
Example inputs...
U = [6, -1, 4]
V = [7, -1, 3, -2, 1]
P = U
Q = [5, -1, 5, -2, 1]
X = [-1, 5, -3, 4]
Y = [-6, 2, -2, 6, -5, 5]
D = [10]
E = [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1]
=end

=begin
w edit_product u, v
returns the edit string product for u * v where u, v are lists of integers
this operation is equal to the application of edit string u followed by v
example...
edit_product [6, -1, 4], [7, -1, 3, -2, 1] -> [6, -1, -1, 3, -2, 1]
requires edit_cleanup u
=end
def estring_product(u, v)
    w = []
    uu_replacement = nil
    ui = 0
    vi = 0
    v.each do |vv|
        if vv < 0
            w << vv
        elsif vv > 0
            vv_left = vv
            uu = uu_replacement != nil ? uu_replacement : u[ui]
            uu_replacement = nil
            until vv_left == 0
                if vv_left >= uu.abs
                    w << uu
                    vv_left -= uu.abs
                    ui += 1
                    uu = u[ui]
                else
                    if uu > 0
                        w << vv_left
                        uu -= vv_left
                    elsif uu < 0
                        w << -vv_left
                        uu += vv_left
                    end
                    vv_left = 0
                    uu_replacement = uu
                end
            end
        end
        vi += 1
    end
    return estring_collapse(w)
end

=begin
v edit_cleanup u
returns a cleaned up edit string for u where u is a list of integers--
consecutive positive or negative numbers are summed into one element
example...
[6, -1, -1, 3, -2, 1] -> [6, -2, 3, -2, 1]
required by edit_product u, v
=end
def estring_collapse(u)
    v = []
    u.each do |uu|
        if v[-1] == nil
            v << uu
        elsif (v[-1] <=> 0) == (uu <=> 0)
            v[-1] += uu
        else
            v << uu
        end
    end
    return v
end

=begin
Example inputs again...
puts (edit_product U, V).inspect
puts (edit_product P, Q).inspect
puts (edit_product X, Y).inspect
puts (edit_product D, E).inspect
=end