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puzzle :: [Integer] -> [String]
puzzle l = do i <- [1..length l-1]
let (subl, subr) = splitAt i l
(sl, vl, _) <- gen subl
(sr, vr, _) <- gen subr
if vl == vr then
return (sl ++ " = " ++ sr)
else []
gen :: [Integer] -> [(String, Rational, String)]
gen (x:[]) = return (show x, fromInteger x, "_")
gen l = do i <- [1..length l-1]
let (subl, subr) = splitAt i l
(sl, vl, opsl) <- gen subl
(sr, vr, opsr) <- gen subr
(ops, op) <- [("+", (+)), ("-", (-)), ("*", (*)), ("/", (/))]
if (ops == "/" && vr == 0) ||
(ops == "+" && (opsr == "+" || opsr == "-")) ||
(ops == "*" && (opsr == "*" || opsr == "/")) then []
else
return ((if opsl /= "_" &&
(ops == "*" || ops == "/") &&
(opsl == "+" || opsl == "-") then
"(" ++ sl ++ ")"
else sl)
++ " " ++ ops ++ " " ++
(if opsr /= "_" &&
((ops == "-" && opsr /= "*" && opsr /= "/") ||
(ops == "*" && (opsr == "+" || opsr == "-")) ||
ops == "/") then
"(" ++ sr ++ ")"
else sr), op vl vr, ops)
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