Find shared objects across two log files

You are given two large log files representing activity on two different days. Each line of each log has three fields:

• timestamp: a time value (you may treat it as an opaque string or integer)
• obj_id: identifier of an object (string or integer)
• client_id: identifier of a client (string or integer)

The logs are not necessarily sorted by any field.

Define an object as interesting if:

1. Its obj_id appears at least once in day 1's log and at least once in day 2's log; and
2. Across all of its appearances in both days combined, it is associated with at least two distinct client_id values.

Tasks

1. Design and implement a function that, given file handles (or streaming iterators) for the two log files, returns the set of all such interesting obj_ids.
2. For your initial, straightforward in-memory solution (you may assume both logs fit in memory), state the time and space complexity in terms of the total number of log records.
3. Follow-up (memory constrained): Now assume the logs are very large and cannot both fit into memory at once.

• You may still sequentially scan each file and you may perform external sorting.
• Describe how you would modify your approach to work under this memory constraint.
• Analyze the time and space complexity of this memory-efficient solution.