I am working on a project in which I am creating an adjacency matrix of cities and need to find and print out up to 3 of the shortest paths based on time or cost between two cities. I am struggling in figuring out what the easiest way to do this is. I am supposed to use a priority queue to store the shortest paths. If anyone has an ideas or can show me how to do this that would be great. Thanks.

import java.io.File;
import java.io.FileNotFoundException;
import java.util.*;
import java.util.Scanner;
import java.util.LinkedList;

class Destination{
    String name;
    double cost;
    double time;
    
    public String getName(){
        return name;
    }
}
class City{
    String name;
    LinkedList<Destination> reachableCities = new LinkedList<>();
    
    public void addReachableCity(String destinationName, double cost, double time){
        boolean duplicate = false;
        for(Destination element : reachableCities){
            if(element.getName().equals(destinationName)){
                duplicate = true;
            }
        }
        
        if(duplicate == false){
            Destination destination = new Destination();
            destination.name = destinationName;
            destination.cost = cost;
            destination.time = time;

            reachableCities.add(destination);
        }
    }
    
    public String getName(){
        return name;
    }
    
    public LinkedList<Destination> getDestinations(){
        return reachableCities;
    }
}

public class Main{
    public static void main(String[] args){
        Scanner scanner = new Scanner(System.in);
        System.out.println("Enter flight data input file: ");
        String flightData = scanner.nextLine();
        LinkedList<City> cities = createList(flightData);
        
        System.out.println("Enter requested flight plans input file: ");
        String requestdFlights = scanner.nextLine();
        
        printList(cities);
    }
    
    public static void findPaths(LinkedList<City> cities, String fileName){
        int numLines = 0;
        String line;
        String startCity = "";
        String destinationCity = "";
        String timeOrCost = "";
        try{
            Scanner scanner = new Scanner(file);
            numLines = Integer.parseInt(scanner.nextLine());
            for(int i = 0; i < numLines; i++){
                line = scanner.nextLine();
                int pipedCounter = 0;
                for(int j = 0; j < line.length(); j++){
                    if(pipedCounter == 0 && line.charAt(j) != '|'){
                        startCity += line.charAt(j);
                    }
                    else if(pipedCounter == 1 && line.charAt(j) != '|'){
                        destinationCity += line.charAt(j);
                    }
                    else if(pipedCounter == 2 && line.charAt(j) != '|'){
                        timeOrCost += line.charAt(j);
                    }
                    else{
                        pipedCounter++;
                    }
                }
                
                if(timeOrCost.equals("T")){
                    for(City element : cities){
                        if(element.equals(startCity)){
                            findPathTimes(element, destinationCity);
                        }
                    }
                }
            }
        }
    }
    
    public static void findPathTimes(City element, String destinationCity){
        //
    }
    public static void printList(LinkedList<City> list){
        for(City element : list){
            LinkedList<Destination> destinations = element.getDestinations();
            System.out.println(element.getName());
            for(Destination destination: destinations){
                System.out.println(destination.getName());
            }
            System.out.println();
        }
    }
    
    public static LinkedList<City> createList(String fileName) {
        String line;
        String cityName = "";
        String destinationName = "";
        String cost = "";
        String time = "";
        int numLines = 0;
        LinkedList<City> cities = new LinkedList<>();
        File file = new File(fileName);
        try {
            Scanner scanner = new Scanner(file);
            numLines = Integer.parseInt(scanner.nextLine());
            for(int i = 0; i < numLines; i++){
                line = scanner.nextLine();
                int pipedCounter = 0;
                for(int j = 0; j < line.length(); j++){
                    if(pipedCounter == 0 && line.charAt(j) != '|'){
                        cityName += line.charAt(j);
                    }
                    else if(pipedCounter == 1 && line.charAt(j) != '|'){
                        destinationName += line.charAt(j);
                    }
                    else if(pipedCounter == 2 && line.charAt(j) != '|'){
                        cost += line.charAt(j);
                    }
                    else if(pipedCounter == 3 && line.charAt(j) != '|'){
                        time += line.charAt(j);
                    }
                    else{
                        pipedCounter++;
                    }
                }
                
                boolean duplicate = false;
                for(City element : cities){
                    if(element.getName().equals(cityName)){
                        duplicate = true;
                        element.addReachableCity(destinationName, Double.parseDouble(cost), Double.parseDouble(time));
                    }
                }
                
                if(duplicate == false){
                    City city = new City();
                    city.name = cityName;
                    city.addReachableCity(destinationName, Double.parseDouble(cost), Double.parseDouble(time));
                    cities.add(city);
                }
                
                duplicate = false;
                for(City element : cities){
                    if(element.getName().equals(destinationName)){
                        duplicate = true;
                        element.addReachableCity(cityName, Double.parseDouble(cost), Double.parseDouble(time));
                    }
                }
                
                if(duplicate == false){
                    City destination = new City();
                    destination.name = destinationName;
                    destination.addReachableCity(cityName, Double.parseDouble(cost), Double.parseDouble(time));
                    cities.add(destination);
                }
                    
                cityName = "";
                destinationName = "";
                cost = "";
                time = "";
            }
        } catch (FileNotFoundException e) {
            System.err.println("File not found: " + fileName);
            return null;
        }
        return cities;
    }
}

Honestly, I created the adjacency matrix and have been lost since. I have looked into breadth first search to find the shortest path but I am struggling with how to implement it.