Stabbing Number Problem

Given intervals, find the point covered by the maximum number of intervals.

function maxStabbingPoint(intervals)
    events := []
    for interval in intervals
        events.add((interval.low, +1))
        events.add((interval.high + 1, -1))

    sort events by position

    maxCount := 0
    count := 0
    bestPoint := null

    for (pos, delta) in events
        count := count + delta
        if count > maxCount then
            maxCount := count
            bestPoint := pos

    return bestPoint

The +1 offset on high ensures we count endpoints correctly for closed intervals.

Time: $O(n \log n)$. Space: $O(n)$.