Count super-streak segments in an event stream

You are given a time-ordered sequence of events. Each event has:

• type, a string or integer event type.
• ts, an integer timestamp in milliseconds or seconds.

A streak segment is a maximal contiguous subsequence of the input where:

1. All events have the same type.
2. For every adjacent pair in the segment, the time gap satisfies ts[i] - ts[i-1] <= T.

A streak segment is a super streak if:

• The number of events in the segment is at least N.
• The duration ts[last] - ts[first] is at least X.

Implement a function that returns the number of super streak segments.

Constraints & Assumptions

• Events are already sorted by timestamp ascending.
• T, N, and X are non-negative.
• The gap threshold is inclusive: a gap exactly equal to T continues the segment.
• A single event has duration 0.
• Count maximal streak segments, not every subarray inside a streak.

Clarifying Questions to Ask

• Can timestamps be equal?
• Can N be 0 or 1, and how should that be interpreted?
• Is the input too large to store, or can it be processed as a stream?
• Should the function return only the count or also the segment boundaries?

Part 1 - Define Segment Boundaries

When does a current streak segment end?

What This Part Should Cover

• A segment ends when the next event has a different type or the time gap exceeds T.
• The current segment must be evaluated once at the boundary.
• Maximality means you should not count subsegments separately.

Part 2 - Design The Algorithm

How would you count super streak segments efficiently?

What This Part Should Cover

• One pass through the events.
• Maintain current segment type, first timestamp, last timestamp, and count.
• Evaluate the segment at each break and after the loop.

Part 3 - Analyze Complexity And Edge Cases

What is the time and space complexity, and what edge cases matter?

What This Part Should Cover

• O(n) time and O(1) extra space.
• Empty input, single event, exact threshold gap, timestamp duplicates, X = 0, N = 1, and type changes.

Part 4 - Handle Changing Parameters Over Time

How would you adapt the solution if N, T, or X can change over time?

What This Part Should Cover

• If thresholds are attached to each event or time window, segment-breaking rules must use the active T at the relevant adjacent gap.
• For changing N or X, evaluate completed segments against the thresholds active for that segment or query.
• For many offline threshold queries, precompute segment summaries and answer queries from those summaries rather than rescanning raw events.