// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Donchian Channels (DC)", "DC", overlay=true)

//@function Calculates the Donchian Channel (DC) efficiently using monotonic deques
//@param hi Source series for the highest high calculation (usually high)
//@param lo Source series for the lowest low calculation (usually low)
//@param p Lookback period (p > 0)
//@returns Tuple containing [basis, upper_band, lower_band]
//@optimized Uses monotonic deque for O(1) amortized complexity per bar
dc(series float hi, series float lo, simple int p) =>
    if p <= 0
        runtime.error("Period must be > 0")
    var float[] hbuf = array.new_float(p, na)
    var float[] lbuf = array.new_float(p, na)
    var int[] hq = array.new_int()
    var int[] lq = array.new_int()
    int idx = bar_index % p
    array.set(hbuf, idx, hi)
    array.set(lbuf, idx, lo)
    while array.size(hq) > 0 and array.get(hq, 0) <= bar_index - p
        array.shift(hq)
    while array.size(hq) > 0 and array.get(hbuf, array.get(hq, -1) % p) <= hi
        array.pop(hq)
    array.push(hq, bar_index)
    while array.size(lq) > 0 and array.get(lq, 0) <= bar_index - p
        array.shift(lq)
    while array.size(lq) > 0 and array.get(lbuf, array.get(lq, -1) % p) >= lo
        array.pop(lq)
    array.push(lq, bar_index)
    float top = array.get(hbuf, array.get(hq, 0) % p)
    float bot = array.get(lbuf, array.get(lq, 0) % p)
    [math.avg(top, bot), top, bot]

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

// Inputs
i_period = input.int(20, "Period", minval=1)
i_high = input.source(high, "High Source")
i_low = input.source(low, "Low Source")

// Calculation
[basis, upper, lower] = dc(i_high, i_low, i_period)

// Plot
plot(basis, "Basis", color=color.yellow, linewidth=2)
p1 = plot(upper, "Upper", color=color.yellow, linewidth=2)
p2 = plot(lower, "Lower", color=color.yellow, linewidth=2)
fill(p1, p2, color=color.new(color.blue, 90), title="Band Fill")