Kiln firing controller

Simulate the controller of a pottery kiln that follows a firing schedule, one thermocouple reading per minute.

The program is a list of segments run in order: "ramp <target> <rate>" raises the setpoint by rate degrees per minute up to target, and "hold <minutes>" keeps the setpoint where it is until the kiln has really stayed there for that many minutes. readings[i] is the temperature measured in minute i.

The controller keeps a setpoint sp, which starts equal to readings[0], and a heater that starts off. Handle each minute i in this order:

1. If the controller has tripped, the output is X; stop here.
2. If the program has finished, the output is . (heater off); stop here. Nothing is checked after the end.
3. Over-temperature trip: if readings[i] > sp + 30, or readings[i] >= 1300, the controller trips for good: output X. This uses sp as it was at the end of the previous minute.
4. Advance the program, but not in minute 0:

• Current segment is a ramp: only if the kiln keeps up, i.e. readings[i] >= sp - 20, set sp = min(target, sp + rate). If sp reaches target, the ramp is done.
• Current segment is a hold: only if readings[i] >= sp - 5 does this minute count towards the hold. When the count reaches the hold's minutes, the hold is done. A segment that finishes this minute lets the next segment start working from the next minute. After the last segment finishes the program is finished, but this minute's heater decision is still made.

1. Heater: with the possibly updated sp, switch the heater on if readings[i] <= sp - 3, off if readings[i] >= sp + 3, otherwise leave it as it was. Output H if it is on, . if off.

Input: program (each ramp target is above the setpoint when that ramp begins) and readings.

Output: a string with one character (H, . or X) per reading; "" if readings is empty.