Hello All, I am working on a project and I am confused in travelling salesman problem in java. The problem statement is given a set of cities and the distance between every pair of cities as an adjacency matrix, the problem is to find the shortest possible route that visits every city exactly once and returns to the starting point.) I have taken this code reference from here. Can anyone explain this code summary or explain this problem with another example? How it works?

import java.util.*;
class Main{
	
static int V = 4;
static int travllingSalesmanProblem(int graph[][],
									int s)
{
    ArrayList<Integer> vertex = new ArrayList<Integer>();

    for (int i = 0; i < V; i++)
	    if (i != s)
	        vertex.add(i);

    int min_path = Integer.MAX_VALUE;
    do
    {
	    int current_pathweight = 0;
	    int k = s;
	
    	for (int i = 0; i < vertex.size(); i++)
	    {
	        current_pathweight += graph[k][vertex.get(i)];
	        k = vertex.get(i);
	    }
	    current_pathweight += graph[k][s];
	    min_path = Math.min(min_path, current_pathweight);

    } while (findNextPermutation(vertex));

    return min_path;
}
public static ArrayList<Integer> swap(ArrayList<Integer> data,int left, int right){
    int temp = data.get(left);
    data.set(left, data.get(right));
    data.set(right, temp);
    return data;
}
public static ArrayList<Integer> reverse(ArrayList<Integer> data, int left, int right)
{
    while (left < right)
    {
	    int temp = data.get(left);
	    data.set(left++, data.get(right));
	    data.set(right--, temp);
    }
    return data;
}
public static boolean findNextPermutation(ArrayList<Integer> data)
{
    if (data.size() <= 1)
	    return false;

    int last = data.size() - 2;
    while (last >= 0)   
    {
	    if (data.get(last) < data.get(last + 1))
	    {
	        break;
	    }
	    last--;
    }
    if (last < 0)
	    return false;

    int nextGreater = data.size() - 1;
    for (int i = data.size() - 1; i > last; i--) {
	    if (data.get(i) > data.get(last))
	    {
	        nextGreater = i;
	        break;
	    }
    }
    data = swap(data,nextGreater, last);
    data = reverse(data, last + 1, data.size() - 1);
    return true;
}
public static void main(String args[]){
    int graph[][] = {{0, 10, 15, 20},
	    			{10, 0, 35, 25},
		    		{15, 35, 0, 30},
		    		{20, 25, 30, 0}};
    int s = 0;
    System.out.println(travllingSalesmanProblem(graph, s));
    }
}