Activity Scheduling Problem

Problem Statement

Say you are given $n$ activities with their start and finish times. Select the maximum number of activities that can be performed by a single person, assuming that a person can only work on a single activity at a time.

Mathematically, Let $S$ $=$ ${1, 2, . . . , n}$ be the set of activities that compete for a resource. Each activity $i$ has its starting time $s_i$ and finish time $f_i$ with $s_i$ $≤$ $f_i$ , namely, if selected, i takes place during time [$s_i$ , $f_i$). No two activities can share the resource at any time point. We say that activities $i$ and $j$ are compatible if their time periods are disjoint.

The activity-selection problem is the problem of selecting the largest set of mutually compatible activities.