Compute Rolling Averages and Merge Intervals

You are given two independent pandas tasks.

1. Symmetric sliding-window average

• Input dataframe df has columns:
  • row_id INT: unique row order
  • value FLOAT: numeric value
• Process rows in ascending row_id .
• Given an integer k >= 0 , create a new column window_avg such that for row i : window_avg(i) = average(value[i-k], ..., value[i], ..., value[i+k])
• Only compute the average if 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 .

2. Merge autonomous-driving event intervals

• Input dataframe events has columns:
  • vehicle_id STRING
  • start_ts TIMESTAMP
  • end_ts TIMESTAMP
• Each row represents a time interval for an event generated by an autonomous vehicle.
• For each vehicle_id , merge intervals that overlap or touch, meaning next.start_ts <= current.end_ts .
• Return one row per merged interval with columns:
  • vehicle_id
  • merged_start_ts
  • merged_end_ts
• Assume timestamps are in the same timezone and that start_ts <= end_ts for every row.