task6.java

public class TSPSolver {
    // Method to solve the TSP using the Nearest Neighbor Algorithm
    public static List<Integer> solveTSP(int[][] distances) {
        List<Integer> tour = new ArrayList<>();
        Set<Integer> visited = new HashSet<>();
        // Start from city 0
        int currentCity = 0;
        tour.add(currentCity);
        visited.add(currentCity);
        while (visited.size() < distances.length) {
            int nextCity = findNearestNeighbor(currentCity, visited,
                    distances);
        }
        // Return to the starting city
        tour.add(0);
        return tour;
    }

    // Method to find the nearest unvisited neighbor of a given city
    private static int findNearestNeighbor(int currentCity, Set<Integer> visited, int[][] distances) {
        int nearestNeighbor = -1;
        int minDistance = Integer.MAX_VALUE;
        for (int city = 0; city < distances.length; city++) {
            if (!visited.contains(city) && distances[currentCity][city] < minDistance) {
                nearestNeighbor = city;
                minDistance = distances[currentCity][city];
            }
        }
        return nearestNeighbor;
    }
}

/*
The provided code is a Java method named findNearestNeighbor. This method is designed to find the nearest unvisited city from a given city in a Traveling Salesman Problem (TSP) scenario. The TSP is a classic algorithmic problem in the field of computer science and operations research, focusing on optimization. In this problem, a salesman is given a list of cities and must determine the shortest route that allows him to visit each city once and return to his original location.

The findNearestNeighbor method takes three parameters: currentCity, visited, and distances.

currentCity is an integer representing the current city the salesman is in.
visited is a set of integers representing the cities that have already been visited.
distances is a 2D array representing the distances between each pair of cities.
The method initializes two variables: nearestNeighbor and minDistance. nearestNeighbor is set to -1 as a placeholder value, and minDistance is set to Integer.MAX_VALUE, the maximum possible value for an integer in Java. These variables are used to keep track of the nearest unvisited city and the distance to that city.

The method then enters a for loop that iterates over all the cities (represented by the length of the distances array). For each city, it checks if the city has not been visited and if the distance from the currentCity to this city is less than minDistance. If both conditions are true, it updates nearestNeighbor to the current city and minDistance to the distance to this city.

After checking all cities, the method returns nearestNeighbor, which is the nearest unvisited city. If no unvisited cities are found, the method will return -1.
 */

 /*
  What is the purpose of the distances array in the findNearestNeighbor method?
  
  The distances array in the findNearestNeighbor method represents the distances between different cities in a Traveling Salesman Problem (TSP).

In the context of the TSP, each city is represented by an index in the distances array, and the value at distances[i][j] represents the distance from city i to city j.

In the findNearestNeighbor method, the distances array is used to find the nearest unvisited city from the current city. The method iterates over all cities and checks the distance from the current city to each unvisited city. If the distance is less than the minimum distance found so far, the method updates the nearest neighbor and the minimum distance.

Here's a snippet of the code that does this:

for (int city = 0; city < distances.length; city++) {    
    if (!visited.contains(city) && distances[currentCity][city] < minDistance) {        
        nearestNeighbor = city;        
        minDistance = distances[currentCity][city];    
    }
}

In this snippet, distances[currentCity][city] is the distance from the current city to the city being checked in the loop. If this city has not been visited and its distance is less than the minimum distance found so far (minDistance), then this city is considered as the nearest neighbor.


  */

  /*
   
    What is the purpose of the visited set in the findNearestNeighbor method?
    The visited set in the findNearestNeighbor method is used to keep track of the cities that have already been visited in the Traveling Salesman Problem (TSP).

In the context of the TSP, the algorithm needs to visit each city exactly once. Therefore, it's important to keep track of which cities have already been visited to avoid visiting them again. This is the role of the visited set.

In the findNearestNeighbor method, the visited set is used to filter out the cities that have already been visited when finding the nearest unvisited city. The method iterates over all cities and checks if a city has not been visited and if its distance from the current city is less than the minimum distance found so far. If both conditions are met, the method updates the nearest neighbor and the minimum distance.

Here's a snippet of the code that does this:

for (int city = 0; city < distances.length; city++) {    
    if (!visited.contains(city) && distances[currentCity][city] < minDistance) {        
        nearestNeighbor = city;        
        minDistance = distances[currentCity][city];    
    }
}

In this snippet, !visited.contains(city) checks if the city has not been visited. 
If this city has not been visited and its distance from the current city is less than the minimum distance found so far (minDistance), then this city is considered as the nearest neighbor.
   */