Develop a pseudocode for an algorithm; analyze your pseudocode mathematically; implement the

code for the algorithm of your choice; test your implementation; and describe your results.

The Problem: Matching Group Schedules

The group schedule matching takes two or more arrays as input. The arrays represent slots that are

already booked and the login$/$logout time of group members. It outputs an array containing intervals

of time when all members are available for a meeting for a minimum duration expected.

Mathematical notation of the problem.

Hint: you will be good even if you don$$t understand mathematical notations of the problem.

Group Schedule Problem

input: arrays $$ of related elements comprising the time intervals and an array $,$

representing the daily active periods of all members. $.$ U is a global set of all arrays. The

problem can be represented as:

$=$

$$

$=1$

$$

output: a set of HashMap, $,$ such that r$$ U

The group schedule matching takes the following inputs:

$1.$ Busy$\_$Schedule: An array list that represents the person's existing schedule $($they can$$t plan

any other engagement during these hours$)$

Hint: Array may be $2$D or maybe a list, ArrayList.

$2.$ Working$\_$period: Daily working periods of group members. $($login$,$ logout$)$

Just two entries $[$login$,$ logout$]$

$3.$ Duration of the meeting It outputs a list of list containing intervals of time when all

members are available for a meeting for the minimum duration of the meeting required.

An analogy for the question:

Assume you and your group members provide your schedules and daily availability. The goal is

to find a time slot when all of you are free for a meeting, considering the provided schedules and

the minimum duration required for the meeting.

Sample Input

Enter person$1\_$Schedule $=[[7$:$00,8$:$30],[12$:$00,13$:$00],[16$:$00,18$:$00]]$

person$1\_$DailyAct $=[9$:$00,19$:$00]$

Enter person$2\_$Schedule $=[[9$:$00,10$:$30],[12$:$20,13$:$30],[14$:$00,15$:$00],[16$:$00,17$:$00]]$

person$2\_$DailyAct $=[9$:$00,18$: $30]$

Enter duration$\_$of$\_$meeting $=30$

Sample output

$[[10$:$30,12$:$00],[15$:$00,16$:$00],[18$:$00,18$:$30]$