import java.util.ArrayList;

import java.util.Comparator;

class Train

$\{$

$$ int trainId;

$$ String arrivalTime;

$$ String departureTime;

$$ public Train

$($

int trainId, String arrivalTime, String departureTime

$)$

$\{$

$$ this.trainId

$=$

$$trainId;

$$ this.arrivalTime

$=$

$$arrivalTime;

$$ this.departureTime

$=$

$$departureTime;

$$

$\}$

$\}$

class TrainScheduleManager

$\{$

$$ ArrayList trains;

$$ public TrainScheduleManager

$($

$)$

$\{$

$$ this.trains

$=$

$$new ArrayList

$<$

$>$

$($

$)$

;

$$

$\}$

$$ public void addTrain

$($

int trainId, String arrivalTime, String departureTime

$)$

$\{$

$$ Train newTrain

$=$

$$new Train

$($

trainId

$,$

$$arrivalTime$,$ departureTime

$)$

;

$$ int index

$=$

$$binarySearchInsertPosition

$($

arrivalTime

$)$

;

$$ trains.add

$($

index

$,$

$$newTrain

$)$

;

$$

$\}$

$$ private int binarySearchInsertPosition

$($

String targetArrivalTime

$)$

$\{$

$$ int low

$=$

$0$

;

$$ int high

$=$

$$trains$.$size

$($

$)$

$-$

$1$

;

$$ while

$($

low

$<$

$=$

$$high

$)$

$\{$

$$ int mid

$=$

$$low

$+$

$($

high

$-$

$$low

$)$

$/$

$2$

;

$$ String midArrivalTime

$=$

$$trains$.$get

$($

mid

$)$

$.$

arrivalTime;

$$ if

$($

midArrivalTime

$.$

compareTo

$($

targetArrivalTime

$)$

$<$

$0$

$)$

$\{$

$$ low

$=$

$$mid

$+$

$1$

;

$$

$\}$

$$else if

$($

midArrivalTime

$.$

compareTo

$($

targetArrivalTime

$)$

$>$

$0$

$)$

$\{$

$$ high

$=$

$$mid

$-$

$1$

;

$$

$\}$

$$else

$\{$

$$

$/$

$/$

$$Handle cases where arrival times are the same

$($

unlikely for this problem

$)$

$$ low

$=$

$$mid

$+$

$1$

;

$/$

$/$

$$Insert after duplicates

$($

if any

$)$

$$

$\}$

$$

$\}$

$$ return low;

$/$

$/$

$$Insert position

$$

$\}$

$$ public void removeTrain

$($

int trainId

$)$

$\{$

$$ for

$($

int i

$=$

$0$

; i

$<$

$$trains$.$size

$($

$)$

; i

$+$

$+$

$)$

$\{$

$$ if

$($

trains

$.$

get

$($

i

$)$

$.$

trainId

$=$

$=$

$$trainId

$)$

$\{$

$$ trains.remove

$($

i

$)$

;

$$ break;

$$

$\}$

$$

$\}$

$$

$\}$

$$ public void displaySchedule

$($

$)$

$\{$

$$ for

$($

Train train : trains

$)$

$\{$

$$ System.out.println

$($

$"$

Train ID:

$"$

$+$

$$train$.$trainId

$+$

$$

$"$

$|$

$$Arrival:

$"$

$+$

$$train$.$arrivalTime

$+$

$$

$"$

$|$

$$Departure:

$"$

$+$

$$train$.$departureTime

$)$

;

$$

$\}$

$$

$\}$

$\}$

public class Main

$\{$

$$ public static void main

$($

String

$[$

$]$

$$args

$)$

$\{$

$$ TrainScheduleManager manager

$=$

$$new TrainScheduleManager

$($

$)$

;

$$ manager.addTrain

$($

$1$

$,$

$"$

$0$

$8$

:

$0$

$0$

$"$

$,$

$"$

$0$

$8$

:

$3$

$0$

$"$

$)$

;

$$ manager.addTrain

$($

$2$

$,$

$"$

$0$

$9$

:

$0$

$0$

$"$

$,$

$"$

$0$

$9$

:

$3$

$0$

$"$

$)$

;

$$ manager.addTrain

$($

$3$

$,$

$"$

$0$

$9$

:

$3$

$0$

$"$

$,$

$"$

$1$

$0$

:

$0$

$0$

$"$

$)$

;

$$ manager.addTrain

$($

$4$

$,$

$"$

$1$

$0$

:

$0$

$0$

$"$

$,$

$"$

$1$

$0$

:

$3$

$0$

$"$

$)$

;

$$ System.out.println

$($

$"$

Initial Train Schedule:"

$)$

;

$$ manager.displaySchedule

$($

$)$

;

$$ manager.removeTrain

$($

$2$

$)$

;

$$ System.out.println

$($

$"$

Updated Train Schedule after removing Train

$2$

:

$"$

$)$

;

$$ manager.displaySchedule

$($

$)$

;

$$

$\}$

$\}$

describe the algotithm used to solve this problem