Sort Instructors by Schedule Overlap | Dataford Interview Questions

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Problem

Outschool wants to rank instructors for a parent based on how much their teaching availability overlaps with the parent's requested schedule. Given a parent's schedule and a list of instructors, return instructor names ordered by decreasing total overlap.

Each schedule is an array of half-open intervals [start, end), where start and end are integer time units. Intervals within a schedule may be unsorted or overlapping. Merge them before calculating overlap so no time is counted twice. If two instructors have equal overlap, preserve their original input order.

Formal Specification

Implement sort_instructors(instructors, parent_schedule).

instructors is a list of objects with a string name and an array schedule.
parent_schedule is an array of [start, end] intervals.
Return a list of instructor names sorted by total overlap in descending order.
An interval contributes min(end1, end2) - max(start1, start2) when that value is positive.

Constraints

0 <= len(instructors) <= 10^4
Each schedule contains at most 10^4 intervals
0 <= start < end <= 10^9
Intervals may be unsorted or overlapping
Instructor names are unique
Equal-overlap instructors retain their original order

Function Signature

def sort_instructors(instructors, parent_schedule):