Stack Trace Reconstructor

Implement exclusive_time(logs) for a profiler event stream. Each log line has the form:

<timestamp> <function_name> <start|end>

Timestamps are integer monotonic ticks. end timestamps are exclusive: if the active function starts at 2 and ends at 5, it ran for 3 ticks.

Requirements

• Return a dictionary mapping function name to exclusive runtime.
• Support nested function calls with a stack.
• Support repeated calls to the same function.
• Recursive calls are valid; aggregate the exclusive time of every frame with the same function name.
• Preserve deterministic behavior for valid, sorted input.
• Raise ValueError for mismatched end events (empty stack or top name differs). The message must include the substring "mismatched".
• Raise ValueError if any call is still open after the last log line. The message must include the substring "unclosed".
• Raise ValueError for any event token other than start or end.

Example

logs = [
    "0 root start",
    "2 parse start",
    "5 parse end",
    "6 fetch start",
    "9 fetch end",
    "10 root end",
]

assert exclusive_time(logs) == {"root": 4, "parse": 3, "fetch": 3}

root runs during [0, 2), [5, 6), and [9, 10): 2 + 1 + 1 = 4 ticks. While parse or fetch is on top of the stack, that child owns the elapsed interval. The intervals add to the root call's 10 ticks without double counting.

Constraints

• Assume input is already sorted by timestamp.
• Logs describe one execution thread. Each line has exactly three whitespace-separated fields and an integer timestamp. Unknown event words and invalid nesting still require the errors above. For equal timestamps, preserve the supplied event order.
• Function names don't contain spaces.
• Zero-duration calls (start and end at the same timestamp) contribute 0 and still appear in the map.
• An empty log list returns {}.
• Idle gaps with an empty stack between sequential top-level calls attribute no exclusive time.
• Equal timestamps are valid; an ending child releases execution to its parent without adding an extra tick.
• Use standard-library Python only.