$1\mathrm{.}2$ Problem $2[30$ pts $]$

Problem $2.$ You're organizing a university event spanning multiple days with student volunteers scheduled for

various shifts. Each shift occurs during a specific time interval, and some shifts may overlap.

Your task is to select a supervising committee $($a subset of students$)$ so that:

Each shift not in the committee is partially overlapped by at least one committee member's shift.

The goal is to form the smallest possible committee that ensures every shift is observed.

Problem:

Design an efficient algorithm that, given $n$ shifts, finds the smallest supervising committee such that each shift is

covered by at least one overlapping committee member.

Example:

If the shifts are:

Shift $1$: $4$ PM $8$ PM

Shift $2$: $6$ PM $10$ PM

Shift $3$: $9$ PM $11$ PM

The smallest committee would consist of just the second shift, as it overlaps with both the first and third

shifts.