Merge K Drone Telemetry Streams Into a Running Altitude Timeline

A fleet of K drones each logs altitude-change events locally: every event is [timestamp, delta], meaning the drone's altitude changed by delta at that timestamp. Each drone's own log is already sorted by timestamp (non-decreasing), but the K logs were recorded independently and have no ordering relationship with each other. A drone is identified purely by where its log sits in the logs list — the first entry is drone 0, and so on up to K - 1.

Replay every event from every drone as a single chronological stream, tracking one shared absolute altitude that starts at 0 and changes by each event's delta as it's processed. Return the altitude recorded immediately after each event, in the order the events were processed.

Function Signature

def running_altitude(logs: list[list[list[int]]]) -> list[int]:

Rules

• Processing order. Earlier timestamps always go before later ones. For a tie between two different drones, whichever drone appears earlier in logs goes first. For a tie within the very same drone's own log, its existing order wins (it's already sorted, so this is just its natural sequence). Put differently, sort the full key (timestamp, drone_index, position_within_that_drones_log) ascending.
• Running altitude. Begins at 0 before anything is processed. Each event, as it's handled, adjusts the running total by its own delta, and that updated total becomes the next entry written to the result — so the result ends up exactly as long as the combined event count across every drone.
• Negative deltas. delta can be negative, and altitude can go below zero; it is never floored at 0.
• Empty logs. A drone that logged nothing simply never shows up in the merged stream. In the degenerate case where every drone (or the whole fleet) has nothing logged, the output is an empty list.

Example

logs = [
    [[1, 10], [1, -3], [5, 2]],
    [[1, 4], [3, -1]],
]
running_altitude(logs) -> [10, 7, 11, 10, 12]

Processing order: drone 0's two events at timestamp 1 (in their own log order: +10 then -3) come before drone 1's event at timestamp 1 (+4), since drone 0 has the lower index; then drone 1's event at timestamp 3 (-1); then drone 0's event at timestamp 5 (+2). Running altitude: 10, 7, 11, 10, 12.

Constraints

• 0 <= K == len(logs) <= 10^4
• 0 <= N <= 10^5; N denotes however many events the whole fleet logged once every drone's entries are counted together.
• Every event is [timestamp, delta] with 0 <= timestamp <= 10^9 and -10^6 <= delta <= 10^6.
• Within a single drone's log, timestamps are non-decreasing (ties within one log are possible).
• The running altitude always stays within [-10^11, 10^11], which exceeds a 32-bit signed range — use 64-bit accumulation in a fixed-width language (plain int in Python needs no special handling).
• The output has exactly N entries and is uniquely determined by the rules above.