dynamic programming, tsp problem, 9 cities out of 15 - dynamic

Question

I think I have some kind of TSP problem. I have matrix of distances between 15 cities:
A B C D E F G H I J K L M N O
A 0 3 8 7 8 9 4 4 2 9 5 5 7 9 9
B 9 0 6 3 8 9 3 9 5 3 3 4 8 6 8
C 1 7 0 8 3 5 4 3 1 1 7 8 2 4 3
D 1 9 7 0 4 3 5 6 8 4 3 4 2 8 9
E 5 8 3 5 0 9 7 4 9 4 5 7 4 6 2
F 5 7 9 6 2 0 3 5 3 6 6 7 4 9 2
G 3 2 8 1 1 8 0 3 4 5 2 4 7 2 6
H 1 4 7 5 5 3 8 0 1 1 7 6 5 8 1
I 5 5 6 5 5 6 6 4 0 2 1 3 4 9 5
J 4 5 4 1 3 9 2 7 9 0 6 8 1 9 9
K 3 4 6 5 9 4 9 5 2 5 0 5 1 4 2
L 8 9 5 2 6 2 9 9 4 5 5 0 3 1 5
M 5 9 7 1 5 5 5 4 6 2 1 6 0 9 2
N 9 5 7 5 7 8 6 5 2 7 1 2 9 0 1
O 7 6 9 6 9 8 4 5 6 2 9 7 7 7 0
Distance from A to B is not the same as distance from B to A.
letter in row means city from
letter in column means city to
Example:
distance from A to F is 9
distance from F to A is 5
I have to start and end in city A. I have to travel to 9 different cities, I cant visit same city twice. Travelled distance should be minimalised. I am familiar with TSP algorithm but i am not certain how to do it only for 9 cities. It should be possible to solve this by using tsp algorithm only once. Thanks for help.

Answer 1

Eventually i figured it out:
// Dynamic Programming based Java program to find shortest path with
// exactly k edges
import java.util.*;
import java.lang.*;
import java.io.*;
class knapsack{
// Define number of vertices in the graph and inifinite value
static final int V = 15;
static final int INF = Integer.MAX_VALUE;
static int numberofedges=10;
static int[][][] S=new int[15][15][15];
// A Dynamic programming based function to find the shortest path
// from u to v with exactly k edges.
static <bolean> int shortestPath(int graph[][], int u, int v, int k)
{ for(int y=0;y<15;y++){
for(int x=0;x<15;x++){
for(int z=0;z<9;z++){
S[x][y][z]=-1;
}}}
// Table to be filled up using DP. The value sp[i][j][e] will
// store weight of the shortest path from i to j with exactly
// k edges
int sp[][][] = new int[V][V][k+1];
System.out.println(Arrays.toString(S));
// Loop for number of edges from 0 to k
for (int e = 0; e <= k; e++)
{
for (int i = 0; i < V; i++) // for source
{
for (int j = 0; j < V; j++) // for destination
{
sp[i][j][e] = INF;
boolean gofind=true;
for (int x = 1; x <= e; x++) {
if (S[i][j][x] == j) {
System.out.println(S[i][j][x]);
System.out.println("TU");
gofind = false;
break;
}
}
if(gofind){
// initialize value
// from base cases
if (e == 0 && i == j) {
S[i][j][0]=0;
sp[i][j][e] = 0;
}
if (e == 1 && graph[i][j] != INF) {
S[i][j][e]=j;
sp[i][j][e] = graph[i][j];
}
// go to adjacent only when number of edges is
// more than 1
if (e > 1)
{int help=225;
for (int a = 0; a < V; a++)
{
// There should be an edge from i to a and
// a should not be same as either i or j
if (graph[i][a] != INF && i != a &&j!= a && sp[a][j][e-1] != INF)
{if(sp[i][j][e]>graph[i][a] + sp[a][j][e-1]){
help=a;
}
sp[i][j][e] = Math.min(sp[i][j][e],graph[i][a] + sp[a][j][e-1]);
if(help>16)
S[i][j][e]=j;
else
S[i][j][e]=a;
}}
}
}}
}
}
return sp[u][v][k];
}
public static void main (String[] args)
{
try {
Scanner sc = null;
sc = new Scanner(new BufferedReader(new FileReader("src/ADS2021_cvicenie5data.txt")));
/* Let us create the graph shown in above diagram*/
int[][] graph = new int[15][15];
sc.nextLine();
while(sc.hasNextLine()) {
for (int i=0; i<graph.length; i++) {
String[] line = sc.nextLine().trim().split(" ");
for (int j=0; j<line.length; j++) {
graph[i][j] = Integer.parseInt(line[j]);
}
}
}
System.out.println(Arrays.deepToString(graph));
System.out.println("Weight of the shortest path is "+ shortestPath(graph, 0, 0, numberofedges));
System.out.println(Arrays.toString(S));
}
catch (
FileNotFoundException e) {
e.printStackTrace();
}
}
}