# Iterative solution in Ruby

• ``````def add_operators(num, target)
return [] if num.empty?

split = Array(0...num.size).each_with_object({}) do |spt, memo|
subnum = num.slice(spt...num.size)
memo[subnum] =
if subnum[0] == '0'
[[0, subnum.slice(1..-1)]]
else
Array(1..subnum.size).map do |subspt|
[subnum.slice(0...subspt).to_i, subnum.slice(subspt..-1)]
end
end
end

rnumbers = Array(1..num.size).map { |spt| num[-spt..-1] }
rcache = rnumbers.each_with_object({}) { |n, memo| memo[n] = [] }

out = []
rnumbers.each do |number|
q, c = [[[nil], number, '']], rcache[number]

until q.empty?
deque, istream, ostream = q.shift

split[istream].each do |lnum, rnum|
if rnum.empty?
deque.push(lnum); _calculate_(deque, :'\$')
if number == num
out << "#{ostream}#{lnum}" if deque[-1] == target
else
c << [deque[-1], "#{ostream}#{lnum}"]
end; next
end

rcache[rnum].each do |v, e|
de = deque.dup; de.push(lnum); _calculate_(de, :+)
de.push(v); _calculate_(de, :'\$')
if number == num
out << "#{ostream}#{lnum}+#{e}" if de[-1] == target
else
c << [de[-1], "#{ostream}#{lnum}+#{e}"]
end
end

de = deque.dup; de.push(lnum); _calculate_(de, :-)
q << [de, rnum, "#{ostream}#{lnum}-"]

de = deque.dup; de.push(lnum); _calculate_(de, :*)
q << [de, rnum, "#{ostream}#{lnum}*"]
end
end
end

out
end

private def _calculate_(deque, next_op)
case next_op
when :+, :-, :'\$'
while true
case deque[0]
when nil; break
when :+; deque.push(deque.pop + deque.pop)
when :-; deque.push(- deque.pop + deque.pop)
when :*; deque.push(deque.pop * deque.pop)
end
deque.shift
end
deque.unshift(next_op)
when :*
if deque[0] == :*
deque.shift
deque.push(deque.pop * deque.pop)
end
deque.unshift(next_op)
end
end``````

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