Design a Balloon Festival Simulator

Implement a class BalloonFestival with the following API and rules.

Goal Track hot air balloons (yours and competitors), evolving wind fields, and balloon stability over time. When inspected at a timestamp, return the sorted names of your team’s balloons that are stable and flying at or above the highest stable competitor balloon.

Initialization init(yourBalloonNames: list[str])

• Registers the set of balloon names that belong to your team; all other names that appear later are competitors.
• Each balloon name is unique.
• Constraint: 1 ≤ len(yourBalloonNames) < 2^20.

Operations BalloonAscended(timestamp: float, balloonName: str, altitude: float) -> bool

• Marks a balloon as ascended to the given altitude and updates its state.
• Balloons are stable by default upon ascending.
• Returns True if the state was updated successfully; otherwise False.

BalloonDescended(timestamp: float, balloonName: str) -> bool

• Marks a balloon as descended to the ground and resets its stability to the default.
• Returns True on success; otherwise False.

SetWindSpeed(timestamp: float, altitude: float, windSpeed: float) -> bool

• Updates the wind speed centered at the given altitude.
• Constraints: 0 < altitude < 2^15, 0 ≤ windSpeed < 2^5.
• Returns True on success; otherwise False.

InspectBalloons(timestamp: float) -> list[str]

• Returns the sorted names of your team’s balloons that are stable at the given timestamp and whose altitudes are ≥ the highest stable competitor balloon at that timestamp. If none qualify, return [].

Stability Rules

• A balloon becomes immediately unstable if the wind speed at its altitude exceeds 15 m/s.
• An unstable balloon regains stability only after it has remained at an altitude where the wind speed is ≤ 15 m/s for at least 300 seconds (inclusive).

Wind Model

• Wind from multiple defined altitudes adds cumulatively.
• Let WindSpeedAtAltitude be the wind defined at WindAltitude, and h be a balloon’s current altitude.
• The contribution from that wind source at altitude h is: WindSpeed(h) = WindSpeedAtAltitude / (1 + ((h - WindAltitude) / 100)^

• The total wind speed at altitude h is the sum of contributions from all defined wind sources at the inspection time.

Requirements

• Design data structures and algorithms to support the above operations correctly and efficiently over many events.