Find common active intervals across cameras

You are now processing data from multiple security cameras.

You are given:

• An integer N , the number of cameras.
• A threshold value T (a real number).
• For each camera i (0-indexed), a vector (array) of time-stamped motion readings:
  • readings[i] is an array of pairs [time, motion_level] for camera i .
  • For each camera, its readings are sorted by strictly increasing time .

For a single camera, define its active intervals as in the previous question:

• A camera is considered "active" at a reading if motion_level > T .
• Consecutive active readings in that camera's array form one continuous active interval from the first active reading's time to the last active reading's time.

For this problem, we are interested in time intervals during which all cameras are simultaneously active.

Task:

1. For each camera, compute its list of active intervals using the above rule.
2. Given all cameras' active interval lists, compute all maximal time intervals during which every camera is active (i.e., the intersection of all cameras' active periods).

Return a list of intervals [start_time, end_time] representing all such overlapping intervals where all N cameras are active at the same time.

Assumptions:

• Each camera's reading list can have different lengths and different timestamp ranges.
• If there is no time when all cameras are active together, return an empty list.

Follow-up discussion:

• Suppose the number of cameras N becomes very large (e.g., thousands or more), and each has many readings.
  • What is the time and space complexity of your approach?
  • Where is the bottleneck in your solution (e.g., per-camera processing vs. multi-camera interval intersection)?
  • How might you optimize or restructure the solution to handle a very large number of cameras or very high data volume (e.g., streaming processing, pre-aggregation, or indexing of intervals)?