Compute window averages and merge intervals

Question

You are given two independent pandas tasks.

1. Centered sliding-window average

• Input DataFrame df with columns:
• row_id INT — unique row-order key, already sorted ascending
• value FLOAT — numeric value
• Given an integer k >= 0, add a new column window_avg such that for each row i:

window_avg(i) = average(value[i-k], ..., value[i], ..., value[i+k])

(the average of the current value plus the k values before it and the k values after it).

• Only compute the average when the row has at least k previous rows and k later rows. For the first k rows and the last k rows, set window_avg = -1.
• Return the original DataFrame with the new column window_avg (columns row_id, value, window_avg).

2. Merge autonomous-driving event intervals

• Input DataFrame of time intervals, each representing an event generated by an autonomous vehicle. Depending on the variant you are handed, the schema is one of:
• vehicle_id STRING, start_ts TIMESTAMP, end_ts TIMESTAMP, or
• vehicle_id STRING, event_type STRING, start_ts TIMESTAMP, end_ts TIMESTAMP (group by both), or
• a single table intervals with start INT and end INT.
• Assume all timestamps share the same timezone and start <= end for every row.
• Within each group (per vehicle_id, or per (vehicle_id, event_type) when event_type is present — the whole table is one group when there is no grouping column), merge intervals that overlap or touch: a later interval is merged into the current one when next.start <= current.end.
• Return one row per merged interval with the group key(s) plus merged_start / merged_end (named merged_start_ts / merged_end_ts when the inputs are timestamps), sorted by the group key(s) then merged_start.

Write pandas code for both tasks.