You are building a stability tracker for a hot-air balloon festival. Over time, balloons change altitude, wind-field anchors are updated, and inspectors request a list of your team's rewarded balloons. Implement the function `solution(yourBalloonNames, operations)` that **simulates a stream of operations in order** and returns the list of results they produce. --- ## Function contract ```python def solution(yourBalloonNames, operations): ... ``` - **`yourBalloonNames`** — a list of **unique** strings naming the balloons that belong to your team. - **`operations`** — a list of operations, each a tuple whose first element is the operation name (see below). They are processed **strictly in the given order**. - **Return value** — a list built by appending one result per operation **that produces output**: - `BalloonAscended`, `BalloonDescended`, `SetWindSpeed` → append the returned **bool**. - `InspectBalloons` → append the returned **list of strings**. Every operation appends exactly one entry, so the output list has the same length as `operations`. ### Balloon ownership - **Your team balloons**: the names in `yourBalloonNames`. - **Competitor balloons**: any other name that first appears in a later operation. A balloon's state is created the first time it ascends. --- ## Timestamps Every operation carries a `timestamp` (float). **Each operation's timestamp must be ≥ the timestamp of the most recent operation that was *accepted*** — an operation whose timestamp is *less than* that last-accepted timestamp is an **ordering violation**. Equal timestamps are allowed. A rejected (out-of-order) operation has no effect and does **not** become the new baseline; the next operation is still compared against the most recent *accepted* timestamp. On an ordering violation, the operation returns `False` (or `[]` for `InspectBalloons`). Each accepted operation (including `InspectBalloons`) first **advances time** to its timestamp, applying any pending stability recoveries (see *Stability rules*) before the operation itself runs. --- ## Operations ### `("BalloonAscended", timestamp, balloonName, altitude)` → `bool` Records that `balloonName` is airborne at `altitude`. This is used for both the first ascent **and** for **changing altitude while already airborne**. On a successful (non-no-op) ascent or altitude change: - The balloon becomes airborne at the new `altitude`. - Its stability is **reset to stable**, then **immediately re-evaluated** against the wind at that altitude and timestamp: if the wind there exceeds the threshold it flips to **unstable** right away; otherwise it stays **stable**. Returns `False` (no state change) if **any** of these hold: - the timestamp ordering is violated, **or** - `altitude` is out of bounds, **or** - the balloon is already airborne **and** the new `altitude` equals its current altitude (a no-op ascent). Otherwise returns `True`. ### `("BalloonDescended", timestamp, balloonName)` → `bool` Records that `balloonName` has landed. - The balloon becomes not-airborne and is ignored by inspections. - Its stability resets to stable for the next ascent. Returns `False` (no state change) if: - the timestamp ordering is violated, **or** - the balloon is already on the ground (not currently airborne). Otherwise returns `True`. ### `("SetWindSpeed", timestamp, altitude, windSpeed)` → `bool` Sets or replaces a **wind anchor** at `altitude` with base magnitude `windSpeed`. - Anchors at multiple distinct altitudes may coexist; their contributions **add cumulatively** (see *Wind physics*). - Setting an anchor at an altitude that already has one **overwrites** its base speed. - After the change, **every airborne balloon is re-evaluated** for stability at the new wind field. Returns `False` (no state change) if: - the timestamp ordering is violated, **or** - `altitude` is out of bounds, **or** - `windSpeed` is out of bounds. Otherwise returns `True`. ### `("InspectBalloons", timestamp)` → `list[str]` Returns the **lexicographically sorted** names of **your team's** balloons that are **all** of: - airborne, **and** - currently stable, **and** - at altitude **≥** the **maximum altitude among all currently stable competitor balloons**. Return `[]` if: - the timestamp ordering is violated, **or** - there are **no currently stable competitor balloons** at that timestamp. --- ## Wind physics Let each wind anchor have altitude `A` and base speed `s`. The aggregate wind speed at altitude `h` is the sum over all current anchors: ``` WindSpeed(h) = Σ s / ( 1 + ((h - A) / 100)^2 ) ``` --- ## Stability rules Let `THRESHOLD = 15` and `RECOVERY = 300` seconds. Each balloon is either **stable** or **unstable**. - A **stable** balloon becomes **unstable** the moment `WindSpeed(currentAltitude) > THRESHOLD`. - An **unstable** balloon can **regain stability** only after it has stayed **continuously** at altitudes where `WindSpeed ≤ THRESHOLD` for at least `RECOVERY` seconds (inclusive), measured from the start of that uninterrupted safe period. Any interruption — the wind rising above the threshold again, an altitude change, or a descent — restarts the clock. The recovery clock applies **only** to balloons that are currently unstable; a stable balloon at a safe altitude has no clock running and simply remains stable. - On `BalloonAscended`, stability is **reset to stable**, then immediately re-evaluated against the current wind. If the new altitude is unsafe (`WindSpeed > THRESHOLD`) the balloon becomes **unstable** at once and a fresh recovery period begins from that timestamp; if the altitude is safe, the balloon simply stays **stable** (no recovery clock). - On `BalloonDescended`, the balloon is not airborne and its stability resets to stable for the next ascent. - When `SetWindSpeed` changes the wind field, each airborne balloon flips to unstable immediately if its altitude is now unsafe; if it is already unstable, its recovery period begins / continues when its altitude is now safe, or its clock is cleared when its altitude is unsafe. --- ## Constraints - `1 ≤ len(operations) < 2^20`. - `0 < altitude < 2^15` (for both balloon altitude and wind-anchor altitude). - `0 ≤ windSpeed < 2^5`. - Timestamps are floats and must be nondecreasing across all accepted operations. - `yourBalloonNames` contains unique strings.