Schedule With Narrowest Slot | Dataford Interview Questions

Headway needs to place a new patient appointment within a provider's working hours. Given existing appointments, find the narrowest available time slot that can fit the requested duration.

Appointments may overlap or touch, and they are not guaranteed to be sorted. Return the new appointment as [start, end], where start and end are integer minutes from midnight. If multiple slots have the same smallest available gap, choose the earliest one. Return [] if no gap is large enough.

Formal Specification

Implement find_narrowest_slot(appointments, work_start, work_end, duration), where appointments is a list of [start, end] intervals, and the remaining arguments are integers. The function returns a two-element list representing the scheduled appointment, or an empty list when scheduling is impossible. Schedule the appointment at the beginning of the selected free gap.

Constraints

0 <= len(appointments) <= 10^5
work_start < work_end
0 < duration <= work_end - work_start
Every appointment satisfies work_start <= start < end <= work_end
Appointment times are integer minutes from midnight

Function Signature

def find_narrowest_slot(appointments, work_start, work_end, duration):

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