Optimal respective add, mul, div (a, b, c) to reach target number

optcalc.lua

-- Given the target number n
-- Starting with accumulator at 0
-- what is the optimal number of times
-- you can add a, multiply by b, or divide by
-- c to reach the target number?

-- Output is in Java, but it can be any language that
-- supports integer division.
-- (or use // in Lua 5.3 <3)

local MOD,floor = 1000000,math.floor
local a,b,c,n = 1, 3, 2, 197
local q,d,o = {0},{0},{'0'}
local opc = { '+'..a,'*'..b,'/'..c }
while (#q > 0) do
	if (d[n+1]) then break end
	local cur = table.remove(q, 1)
	local new = { cur+a, cur*b, floor(cur/c) }
	for i = 1, 3 do
		local nmod = new[i] >= MOD
		if (nmod) then new[i] = new[i] % MOD end
		if (not d[new[i]+1]) then
			table.insert(q, new[i])
			d[new[i]+1] = d[cur+1] + 1
			local nop = o[cur+1] or '0'
			if (i > 1) then
				nop = ('(%s)'):format(nop)
			end
			nop = nop .. opc[i]
			if (nmod) then
				nop = ('(%s)%%%d'):format(nop,MOD)
			end
			o[new[i]+1]=nop
		end
	end
end
print('optimal ops ' .. d[n+1])
print('System.out.println('..o[n+1]..')')