KDJ

// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("KDJ", "KDJ", overlay=false)

//@function Calculates KDJ (K, D, J) lines - enhanced Stochastic Oscillator
//@param high Series of high prices
//@param low Series of low prices
//@param close Series of close prices
//@param length Lookback period for highest/lowest calculation
//@param signal Smoothing period for K and D lines
//@returns Tuple [K line, D line, J line]
//@optimized Uses Wilder's RMA smoothing and deque min/max for highest/lowest, O(n) amortized
kdj(series float high, series float low, series float close, simple int length, simple int signal) =>
    if length <= 0 or signal <= 0
        runtime.error("Length and signal must be greater than 0")
    if length > 500
        runtime.error("Length exceeds maximum of 500")

    float alpha = 1.0 / signal
    float beta = 1.0 - alpha
    var bool warmupK = true
    var bool warmupD = true
    var float eK = 1.0
    var float eD = 1.0
    var float k = 0.0
    var float d = 0.0
    var float resultK = 50.0
    var float resultD = 50.0

    var int lastLength = 0
    var array<int> maxDeque = array.new_int(0)
    var array<int> minDeque = array.new_int(0)
    var array<float> highBuffer = array.new_float(0)
    var array<float> lowBuffer = array.new_float(0)

    if length != lastLength
        lastLength := length
        maxDeque := array.new_int(0)
        minDeque := array.new_int(0)
        highBuffer := array.new_float(length, na)
        lowBuffer := array.new_float(length, na)
        warmupK := true
        warmupD := true
        eK := 1.0
        eD := 1.0
        k := 0.0
        d := 0.0
        resultK := 50.0
        resultD := 50.0

    if not na(high) and not na(low) and not na(close)
        int currentBar = bar_index
        int slot = currentBar % length

        array.set(highBuffer, slot, high)
        array.set(lowBuffer, slot, low)

        while array.size(maxDeque) > 0 and array.get(maxDeque, 0) <= currentBar - length
            array.shift(maxDeque)

        while array.size(minDeque) > 0 and array.get(minDeque, 0) <= currentBar - length
            array.shift(minDeque)

        while array.size(maxDeque) > 0 and array.get(highBuffer, array.get(maxDeque, array.size(maxDeque) - 1) % length) <= high
            array.pop(maxDeque)

        while array.size(minDeque) > 0 and array.get(lowBuffer, array.get(minDeque, array.size(minDeque) - 1) % length) >= low
            array.pop(minDeque)

        array.push(maxDeque, currentBar)
        array.push(minDeque, currentBar)

        float highest = high
        float lowest = low
        if array.size(maxDeque) > 0
            highest := array.get(highBuffer, array.get(maxDeque, 0) % length)
        if array.size(minDeque) > 0
            lowest := array.get(lowBuffer, array.get(minDeque, 0) % length)

        float price_range = highest - lowest

        float rsv = price_range > 0 ? 100.0 * (close - lowest) / price_range : 50.0

        k := alpha * rsv + beta * k
        d := alpha * k + beta * d

        if warmupK
            eK *= beta
            float cK = 1.0 / (1.0 - eK)
            resultK := math.max(0.0, math.min(100.0, cK * k))
            warmupK := eK > 1e-10
        else
            resultK := math.max(0.0, math.min(100.0, k))

        if warmupD
            eD *= beta
            float cD = 1.0 / (1.0 - eD)
            resultD := math.max(0.0, math.min(100.0, cD * d))
            warmupD := eD > 1e-10
        else
            resultD := math.max(0.0, math.min(100.0, d))

    float j = 3.0 * resultK - 2.0 * resultD

    [resultK, resultD, j]

// ---------- Main loop ----------

// Inputs
i_length = input.int(9, "Length", minval=1, maxval=500)
i_signal = input.int(3, "Signal", minval=1, maxval=50)

// Calculation
[k, d, j] = kdj(high, low, close, i_length, i_signal)

// Plot
plot(k, "K", color=color.blue, linewidth=2)
plot(d, "D", color=color.red, linewidth=2)
plot(j, "J", color=color.yellow, linewidth=2)

hline(80, "Overbought K", color=color.red, linestyle=hline.style_dotted)
hline(70, "Overbought D", color=color.orange, linestyle=hline.style_dotted)
hline(50, "Midline", color=color.gray, linestyle=hline.style_solid)
hline(30, "Oversold D", color=color.lime, linestyle=hline.style_dotted)
hline(20, "Oversold K", color=color.green, linestyle=hline.style_dotted)