We Keep Coding

Using BFS to find number of possible paths for an object on a grid

I have a matrix that represents a grid and would like to find out all possible places an object can move to.
An object can only move horizontally or vertically.
Let's assume that the example below is the grid I'm looking at, which is represented as a 2d matrix. The object is the *, the 0s are empty spaces that an object can move to, and the 1s are walls which the object cannot jump over or go on to.
What is the best way to find all possible movements of this object provided that it can only move horizontally or vertically?
I'd like to print a message saying: "There are 9 places the object can go to." The 9 is for the example below, but I would like it to work for any configuration of the below grid. So all I have to do is give the current coordinates of the * and it will give me the number of possible positions it can move to.
A thing to note is that the *'s original position is not considered in the calculations, which is why for the example below the message would print 9 and not 10.
I have a isaWall method that tells me if the cell is a wall or not. The isaWall method is in a Cell class. Each cell is represented by its coordinates. I looked into using Algorithms like BFS or DFS, but I didn't quite understand how to implement them in this case, as I am not too familiar with the algorithms. I thought of using the Cells as nodes of the graph, but wasn't too sure how to traverse the graph because from the examples I saw online of BFS and DFS, you would usually have a destination node and source node (the source being the position of the *), but I don't really have a destination node in this case. I would really appreciate some help.
00111110
01000010
100*1100
10001000
11111000
EDIT: I checked the website that was recommend in the comments and tried to implement my own version. It unfortunately didn't work. I understand that I have to expand the "frontier" and I basically just translated the expansion code to Java, but it still doesn't work. The website continues explaining the process, but in my case, there is no destination cell to go to. I'd really appreciate an example or a clearer explanation pertaining to my case.
EDIT2: I'm still quite confused by it, can someone please help?

While BFS/DFS are commonly used to find connections between a start and end point, that isn't really what they are. BFS/DFS are "graph traversal algorithms," which is a fancy way of saying that they find every point reachable from a start point. DFS (Depth First Search) is easier to implement, so we'll use that for your needs (note: BFS is used when you need to find how far away any point is from the start point, and DFS is used when you only need to go to every point).
I don't know exactly how your data is structured, but I'll assume your map is an array of integers and define some basic functionality (for simplicity's sake I made the start cell 2):
Map.java
import java.awt.*;
public class Map {
public final int width;
public final int height;
private final Cell[][] cells;
private final Move[] moves;
private Point startPoint;
public Map(int[][] mapData) {
this.width = mapData[0].length;
this.height = mapData.length;
cells = new Cell[height][width];
// define valid movements
moves = new Move[]{
new Move(1, 0),
new Move(-1, 0),
new Move(0, 1),
new Move(0, -1)
};
generateCells(mapData);
}
public Point getStartPoint() {
return startPoint;
}
public void setStartPoint(Point p) {
if (!isValidLocation(p)) throw new IllegalArgumentException("Invalid point");
startPoint.setLocation(p);
}
public Cell getStartCell() {
return getCellAtPoint(getStartPoint());
}
public Cell getCellAtPoint(Point p) {
if (!isValidLocation(p)) throw new IllegalArgumentException("Invalid point");
return cells[p.y][p.x];
}
private void generateCells(int[][] mapData) {
boolean foundStart = false;
for (int i = 0; i < mapData.length; i++) {
for (int j = 0; j < mapData[i].length; j++) {
/*
0 = empty space
1 = wall
2 = starting point
*/
if (mapData[i][j] == 2) {
if (foundStart) throw new IllegalArgumentException("Cannot have more than one start position");
foundStart = true;
startPoint = new Point(j, i);
} else if (mapData[i][j] != 0 && mapData[i][j] != 1) {
throw new IllegalArgumentException("Map input data must contain only 0, 1, 2");
}
cells[i][j] = new Cell(j, i, mapData[i][j] == 1);
}
}
if (!foundStart) throw new IllegalArgumentException("No start point in map data");
// Add all cells adjacencies based on up, down, left, right movement
generateAdj();
}
private void generateAdj() {
for (int i = 0; i < cells.length; i++) {
for (int j = 0; j < cells[i].length; j++) {
for (Move move : moves) {
Point p2 = new Point(j + move.getX(), i + move.getY());
if (isValidLocation(p2)) {
cells[i][j].addAdjCell(cells[p2.y][p2.x]);
}
}
}
}
}
private boolean isValidLocation(Point p) {
if (p == null) throw new IllegalArgumentException("Point cannot be null");
return (p.x >= 0 && p.y >= 0) && (p.y < cells.length && p.x < cells[p.y].length);
}
private class Move {
private int x;
private int y;
public Move(int x, int y) {
this.x = x;
this.y = y;
}
public int getX() {
return x;
}
public int getY() {
return y;
}
}
}
Cell.java
import java.util.LinkedList;
public class Cell {
public final int x;
public final int y;
public final boolean isWall;
private final LinkedList<Cell> adjCells;
public Cell(int x, int y, boolean isWall) {
if (x < 0 || y < 0) throw new IllegalArgumentException("x, y must be greater than 0");
this.x = x;
this.y = y;
this.isWall = isWall;
adjCells = new LinkedList<>();
}
public void addAdjCell(Cell c) {
if (c == null) throw new IllegalArgumentException("Cell cannot be null");
adjCells.add(c);
}
public LinkedList<Cell> getAdjCells() {
return adjCells;
}
}
Now to write our DFS function. A DFS recursively touches every reachable cell once with the following steps:
Mark current cell as visited
Loop through each adjacent cell
If the cell has not already been visited, DFS that cell, and add the number of cells adjacent to that cell to the current tally
Return the number of cells adjacent to the current cell + 1
You can see a visualization of this here. With all the helper functionality we wrote already, this is pretty simple:
MapHelper.java
class MapHelper {
public static int countReachableCells(Map map) {
if (map == null) throw new IllegalArgumentException("Arguments cannot be null");
boolean[][] visited = new boolean[map.height][map.width];
// subtract one to exclude starting point
return dfs(map.getStartCell(), visited) - 1;
}
private static int dfs(Cell currentCell, boolean[][] visited) {
visited[currentCell.y][currentCell.x] = true;
int touchedCells = 0;
for (Cell adjCell : currentCell.getAdjCells()) {
if (!adjCell.isWall && !visited[adjCell.y][adjCell.x]) {
touchedCells += dfs(adjCell, visited);
}
}
return ++touchedCells;
}
}
And that's it! Let me know if you need any explanations about the code.

Minmax for ConnectFour

I am trying to implement a minmax algorithm to create an AI for connect four. I'm having quite a bit of trouble with it though as I feel like I have overcomplicated things (and it doesn't work properly), perhaps someone here can help. I'm going to post my code first and then the issue I'm having with it below.
This is the initial call to the minmax algorithm
public int getColumnForMove(ConnectFour game)
{
game.minimax(2, game.getCurrentPlayer(), game);
int column = game.getBestMove();
return column;
}
This is the initial minimax method (it is inside the ConnectFour class which is not where the initial method is called from that is in a separate AI class) that is called and a subclass that holds each column the user moves into as well as the min/max'ed score if it moves into that column.
class ColumnsAndScores
{
int column;
int score;
ColumnsAndScores(int column, int score)
{
this.column = column;
this.score = score;
}
}
List<ColumnsAndScores> cas = new ArrayList<>();
public void minimax(int depth, int turn, ConnectFour game)
{
cas = new ArrayList<>();
minimaxHelper(depth, depth, turn, game);
}
The following are methods that get the min or max score from each set of possible moves:
public int getMax(List<Integer> list)
{
int max = Integer.MIN_VALUE;
int index = -1;
for (int i = 0; i < list.size(); i++)
{
if (list.get(i) > max)
{
max = list.get(i);
index = i;
}
}
return list.get(index);
}
public int getMin(List<Integer> list)
{
int min = Integer.MAX_VALUE;
int index = -1;
for (int i = 0; i < list.size(); i++)
{
if (list.get(i) < min)
{
min = list.get(i);
index = i;
}
}
return list.get(index);
}
This is the actual minimax method (it has a bunch of commented out code that shows it should return a range of values depending on how good the board is if its not a clear cut win or loss but right now I'm just trying to have it make decisions based on a win or loss (if none of that happens in the requested depth it makes a random move)).
public int minimaxHelper(int originalDepth, int depth, int turn, ConnectFour game)
{
//holds future game states
ConnectFour futureGameState;
//holds the current scores
List<Integer> scores = new ArrayList<>();
//if (not at the lowest depth)
if (depth !=0)
{
if (checkForWin(turn))
{
//return Integer.MAX_VALUE or Integer.MIN_VALUE respectively based on who's turn it is
return (turn % 2 == 0) ? Integer.MAX_VALUE : Integer.MIN_VALUE;
}
//recursively call getColumnForMove(depth--, otherTurn) for each column if the column isnt full
for (int i = 1; i <= ConnectFour.NUM_OF_COLUMNS; i++)
{
futureGameState = new ConnectFour();
futureGameState.setCurrentGameState(game.getCurrentGameState());
futureGameState.setCurrentPlayer(game.getCurrentPlayer());
if (futureGameState.isValidMove(i))
{
futureGameState.makeMove(i);
futureGameState.switchPlayer();
scores.add(minimaxHelper(originalDepth, depth - 1, futureGameState.getCurrentPlayer(), futureGameState));
}
else //if move isnt valid return the worst possible value so this column doesnt get chosen
{
return (turn % 2 == 0) ? Integer.MAX_VALUE : Integer.MIN_VALUE;
}
if (depth == originalDepth)
{
ColumnsAndScores newScore;
if (turn % 2 == 0)
newScore = new ColumnsAndScores(i, getMax(scores));
else
newScore = new ColumnsAndScores(i, getMin(scores));
cas.add(newScore);
}
}
if (turn % 2 == 0)
return getMax(scores);
else
return getMin(scores);
}
else
{
if (checkForWin(turn))
{
//return Integer.MAX_VALUE or Integer.MIN_VALUE respectively based on who's turn it is
return (turn % 2 == 0) ? Integer.MAX_VALUE : Integer.MIN_VALUE;
}
else
{
return 0;
}
//else
//if 3 in a row with 2 open spaces that have pieces under those spaces
//return 100
//else if 3 in a row with 1 open space that has a piece under that space
//return 80;
//else if 3 in a row
//return 60;
//else if 2 in a row
//return 40
//else
//return 0
}
}
and finally this is a method that is called by the AI to get the best move from the list that minimax added the ColumnAndScores too.
public int getBestMove()
{
int highestScore = Integer.MIN_VALUE;
int best = -1;
for (int i = 0; i < cas.size(); ++i) {
if (highestScore < cas.get(i).score) {
highestScore = cas.get(i).score;
best = i;
}
}
if (highestScore == 0)
return 1 + ((int) (Math.random() * 7));
else
return best;
}
While I believe there are a couple of logic errors the thing I am having the most difficulty with at the moment is that when I dofutureGameState = new ConnectFour();
futureGameState.setCurrentGameState(game.getCurrentGameState());
This should put it into a separate instance so that when I then make a move it should only last for that branch of the tree and not corrupt the actual game being played but that isn't the case. It is changing the actual state of the game being passed in.

The issue is most probably caused by the implementation of ConnectFour, something like
private int[][] state;
public void setCurrentGameState(int[][] newState) {
this.state = newState;
}
That's okay, but causes your "copy" of the game state to actually reference the same int[][] state, thus any modifications to it will apply to both states. What you want is
public class ConnectFour implements Cloneable<ConnectFour> {
private static final int NUM_ROWS = 6;
private static final int NUM_COLS = 7;
private int[][] state = new int[NUM_ROWS][NUM_COLS];
// ...
public ConnectFour clone() {
int[][] stateCopy = new int[NUM_ROWS][NUM_COLS];
for (int i = 0; i < NUM_ROWS; i++)
for (int j = 0; j < NUM_COLS; j++)
stateCopy[i][j] = this.state[i][j];
ConnectFour cloned = new ConnectFour();
cloned.setCurrentGameState(stateCopy);
// copy other fields over to cloned
return cloned;
}
}

I'm just going to address one issue. You should try not to have too many per question, and include the code relevant to your question, such as your ConnectFour class here.
If you want to make a copy of the board you can modify without changing the original, you need to make a deep copy, not a copy of the reference. To make a shallow copy of your house, you make a copy of your house key. If you give it to someone, you shouldn't be surprised to see changes when you get home. To make a deep copy of your house, you get a second lot and build a new house from blueprints and photos of your house. If you give a key to the new house to someone, he/she might not notice the difference immediately, but any changes shouldn't affect you directly, and changes you make won't affect the recipient.
"Deep copy" is actually ambiguous because your object may contain object members that have object members. When you make a deep copy, you have to decide whether to make deep copies or shallow copies of any member objects. If your ConnectFour class contains an ArrayList of Move objects, each of which is a wrapper for an int representing a column, you have 3 choices:
You can copy a reference to the ArrayList.
You can make a new ArrayList with references to the same set of moves.
You can make a new ArrayList with references to copies of the moves.
Anyway, my guess is that you don't yet have nested member objects, so your deep copy method can look something like the following:
public class ConnectFour{
private int[][] board = new int[6][7];
public setCurrentGameState(int[][] state){
for(int i = 0; i<6; i++)
for(int j=0; j<7; j++)
board[i][j] = state[i][j];
}
...

When navigating a 2D array, check neighboring elements for valid path relative to point of entry?

The nature of this problem has changed since submission, but the question isn't fit for deletion. I've answered the problem below and marked it as a community post.
I'm writing a recursive path-navigating function and the final piece I need involves knowing which cell you came from, and determining where to go next.
The Stage
You are given a 2d array where 0's denote an invalid path and 1's denote a valid path. As far as I know, you are allowed to manipulate the data of the array you're navigating, so I mark a traveled path with 2's.
The Goal
You need to recursively find and print all paths from origin to exit. There are four mazes, some with multiple paths, dead ends, or loops.
I've written code that can correctly handle all three cases, except the method for finding the next path is flawed in that it starts at a fixed location relative to your current index, and checks for a travelled path; If you encounter it, it's supposed to retreat.
While this works in most cases, it fails in a case when the first place it checks happens to be the place you came from. At this point, it returns out and ends prematurely.
Because of this, I need to find a way to intelligently start scanning (clockwise or anti-clockwise) based on where you came from, so that that place is always the last place checked.
Here is some code describing the process (note: edge cases are handled prior to this, so we don't need to worry about that):
private static void main()
{
int StartX = ;//Any arbitrary X
int StartY = ;//Any arbitrary Y
String Path = ""; //Recursive calls will tack on their location to this and print only when an exit path is found.
int[][] myArray = ;//We are given this array, I just edit it as I go
Navigator(StartX, StartY, Path, myArray);
}
private static void Navigator(int locX, int locY, String Path, int[][] myArray)
{
int newX = 0; int newY = 0;
Path = Path.concat("["+locX+","+locY+"]");
//Case 1: You're on the edge of the maze
boolean bIsOnEdge = (locX == 0 || locX == myArray.length-1 || locY == 0 || locY == myArray[0].length-1);
if (bIsOnEdge)
{
System.out.println(Path);
return;
}
int[][] Surroundings = surroundingsFinder(locX, locY, myArray);
for (int i = 0; i <= 7; i++)
{
//Case 2: Path encountered
if (Surroundings[0][i] == 1)
{
myArray[locX][locY] = 2;
newX = Surroundings[1][i];
newY = Surroundings[2][i];
Navigator(newX, newY, myArray, Path);
}
//Case 3: Breadcrumb encountered
if (Surroundings[0][i] == 2)
{
myArray[locX][locY] = 1;
return;
}
}
}
//generates 2D array of your surroundings clockwise from N to NW
//THIS IS THE PART THAT NEEDS TO BE IMPROVED, It always starts at A.
//
// H A B
// G - C
// F E D
//
static int[][] surroundingsFinder(int locX, int locY, int[][] myArray)
{
int[][] Surroundings = new int[3][8];
for (int i = -1; i <= 1; i++)
{
for (int j = -1; j <= 1; j++)
{
}
}
//Can be done simpler, is done this way for clarity
int xA = locX-1; int yA = locY; int valA = myArray[xA][yA];
int xB = locX-1; int yB = locY+1; int valB = myArray[xB][yB];
int xC = locX; int yC = locY+1; int valC = myArray[xC][yC];
int xD = locX+1; int yD = locY+1; int valD = myArray[xD][yD];
int xE = locX+1; int yE = locY; int valE = myArray[xE][yE];
int xF = locX+1; int yF = locY-1; int valF = myArray[xF][yF];
int xG = locX; int yG = locY-1; int valG = myArray[xG][yG];
int xH = locX-1; int yH = locY-1; int valH = myArray[xH][yH];
int[][] Surroundings = new int[3][8];
Surroundings[0][0] = valA; Surroundings[1][0] = xA; Surroundings[2][0] = yA;
Surroundings[0][1] = valB; Surroundings[1][1] = xB; Surroundings[2][1] = yB;
Surroundings[0][2] = valC; Surroundings[1][2] = xC; Surroundings[2][2] = yC;
Surroundings[0][3] = valD; Surroundings[1][3] = xD; Surroundings[2][3] = yD;
Surroundings[0][4] = valE; Surroundings[1][4] = xE; Surroundings[2][4] = yE;
Surroundings[0][5] = valF; Surroundings[1][5] = xF; Surroundings[2][5] = yF;
Surroundings[0][6] = valG; Surroundings[1][6] = xG; Surroundings[2][6] = yG;
Surroundings[0][7] = valH; Surroundings[1][7] = xH; Surroundings[2][7] = yH;
return Surroundings;
}
Can anyone help me with this? As you can see, surroundingsFinder always finds A first, then B all the way to H. This is fine if and only if you entered from H. But if fails on cases where you entered from A, so I need to make a way to intelligently determine where to start finding. Once I know this, I can probably adapt the logic so I no longer use a 2D array of values, as well. But so far I can't come up with the logic for the smart searcher!
NOTE: I am aware that Java does not optimize middle-recursion. It seems impossible to get tail recursion working for a problem like this.

The Solution
The initial goal was to print, from start to end, all of the paths that exit the array.
An earlier rendition of the script wrote "0" on treaded locations rather than "2", but for some reason I imagined that I needed the "2" and I needed to differentiate between "treaded path" and "invalid path".
In fact, due to the recursive nature of the problem, I discovered that you can in fact solve the problem writing only 0's as you go. Also, I no longer needed to keep track of where I came from and instead of checking clockwise over a matrix, I was iterating from left to right down the 3x3 matrix surrounding me, skipping my own cell.
Here is the completed code for such a solution. It prints to console upon finding an exit (edge) and otherwise traces itself around the maze, complete with recursion. To start the function, you are given a square 2D array of 0's and 1's where 1 is a valid path and 0 is invalid. You are also given a set of coordinates where you are "dropped in" (locX, locY) and an empty string that accumulates coordinates, forming a path that is later printed out (String Path = "")
Here is the code:
static void Navigator(int locX, int locY, int[][] myArray, String Path)
{
int newX = 0;
int newY = 0;
Path = Path.concat("["+locX+","+locY+"]");
if ((locX == 0 || locX == myArray.length-1 || locY == 0 || locY == myArray[0].length-1))
{//Edge Found
System.out.println(Path);
pathCnt++;
myArray[locX][locY] = 1;
return;
}
for (int row = -1; row <= 1; row++)
{
for (int col = -1; col <= 1; col++)
{
if (!(col == 0 && row == 0) && (myArray[locX+row][locY+col] == 1))
{ //Valid Path Found
myArray[locX][locY] = 0;
Navigator(locX+row, locY+col, myArray, Path);
}
}
}
//Dead End Found
myArray[locX][locY] = 1;
return;
} System.out.println(Path);
pathCnt++;
swamp[locX][locY] = 1;
return;
}
for (int row = -1; row <= 1; row++)
{
for (int col = -1; col <= 1; col++)
{
if (!(col == 0 && row == 0) && (swamp[locX+row][locY+col] == 1))
{ //Valid Path Found
swamp[locX][locY] = 0;
Navigator(locX+row, locY+col, swamp, Path);
}
}
}
//Dead End Found
swamp[locX][locY] = 1;
return;
}
As you may determine yourself, every time we "enter" a cell, we have 8 neighbors to check for validity. First, to save on run time and to avoid going out of the array during our for loop (it can't find myArray[i][j] if i or j point it outside, and it will error out), we check for edges. Since we're given the area of our swamp we use a truth comparison statement that essentially says ("(am I on the top or left edge?) or (am I on the bottom or right edge?)"). If we ARE on an edge, we print out the Path we're holding (thanks to deep copy, we have a unique copy of the original Path that only prints if we're on an edge, and includes our full set of coordinates).
If we aren't on an edge, then we start looking around us. We start at top left and move horizontally to bottom right, with a special check to make sure we're not checking where we're standing.:
A B C
D . E
F G H
This loop checks only for 1's and only calls the function up again should that happen. Why? Because it is the second-to-last case. There is only one extra situation that will occur, and if we reach the end of the function it means we hit that case. Why write extra code (checking for 0's to specifically recognize it?
So, as I just mentioned, if we exit the for loop, it means we didn't encounter any 1's at all. It means we're surrounded by zeros! It means we've hit a dead end, and that means that all we have to do is error our away out of that instance of the function, ergo the final return;.
All in all, the final function is simple. But coming from no background and having to realize the patterns and meanings of these cases, and after several failed attempts at this, it can take quite a bit of work. I was several days at work on perfecting this.
Happy coding, Everyone!

Your issue seems to be with:
if (Surroundings[0][i] == 2)
{
myArray[locX][locY] = 1;
return;
}
Perhaps this should be changed to:
if (Surroundings[0][i] == 2)
{
// not sure why you need this if it's already 1
myArray[locX][locY] = 1;
// go to next iteration of the "i" loop
// and keep looking for next available path
continue;
}
Your recursive method will automatically return when none of the surrounding cells satisfy the condition if (Surroundings[0][i] == 1).
PS: It's conventional to name your variables using small letter as the first character. For example: surroundings, path, startX or myVar

JAVA - Go game algorithm

I am trying to implement an algorithm to clear dead stones in my Go game.
I hear that floodfill is the best to achieve this as using it recursively would be most effiecient and easier to implement.
I am having trouble using it within my code and was wondering how I should go about implementing it.
This is one of my classes, it is pretty self explanatory.
import java.io.*;
public class GoGame implements Serializable {
int size;
char[][] pos; // This is the array that stores whether a Black (B) or White (W) piece is stored, otherwise its an empty character.
public GoGame(int s){
size = s;
}
public void init() {
pos = new char[size][size];
for (int i=0;i<size;i++) {
for (int j=0;j<size;j++) {
pos[i][j] = ' ';
}
}
}
public void ClearAll() {
for (int i=0;i<size;i++) {
for (int j=0;j<size;j++) {
pos[i][j] = ' ';
}
}
}
public void clear(int x, int y) {
pos[x][y]=' ';
}
public void putB(int x, int y) { //places a black stone on the board+array
pos[x][y]='B';
floodfill(x,y,'B','W');
}
public void putW(int x, int y) { //places a white stone on the board+array
pos[x][y]='W';
floodfill(x,y,'W','B');
}
public char get(int x, int y) {
return pos[x][y];
}
public void floodfill(int x, int y, char placed, char liberty){
floodfill(x-1, y, placed, liberty);
floodfill(x+1, y, placed, liberty);
floodfill(x, y-1, placed, liberty);
floodfill(x, y+1, placed, liberty);
}
}
x and y are the coordinates of the square, placed is the character of the stone put down, liberty is the other character
Any help would be amazing!

while the other answers are technically correct, you are also missing a lot more logic related to go. what you need to do is, i think (on a B move):
for each W neighbour of the move:
check that W group to see if it has any liberties (spaces)
remove it if not
flood fill is useful for finding the extent of a group of stones, but your routine needs a lot more than that (i'm simplifying here, and also trying to guess what this routine is used for - see comments below this answer).
given the above, a flood fill that identifies all the stones in a group would be something like this (note that it uses a second array for the fill, because you don't want to be changing pos just to find a group):
public void findGroup(int x, int y, char colour, char[][] mask) {
// if this square is the colour expected and has not been visited before
if (pos[x][y] == colour && mask[x][y] == ' ') {
// save this group member
mask[x][y] = pos[x][y];
// look at the neighbours
findGroup(x+1, y, colour, mask);
findGroup(x-1, y, colour, mask);
findGroup(x, y+1, colour, mask);
findGroup(x, y-1, colour, mask);
}
}
you can call that to identify a single group (and copy it into mask), so it will help you identify the members of a W group that neighbour a B move (for example), but it is only a small part of the total logic you need.
finally, note that if you want to do something with every stone in a group you have two options. you can call a routine like the one above, and then loop over mask to find the group, or you can put the action you want to do directly inside the routine (in which case you still use mask to control the extent of the flood fill in the test && mask[x][y] == ' ' but you don't use it as a result - all the work is done by the time the routine returns).
(programming something to handle go correctly, following all the rules, is actually quite complex - you've got a lot of work ahead... :o)

I'd use false proof for that. Here is how I find captured stones:
private static final int SIZE = 8;
private static final int VACANT = 0; //empty point
private static final int MY_COLOR = 1; //Black
private static final int ENEMY_COLOR = 2; //White
private static final int CHECKED = 50; //Mark for processed points
private static final int OUT = 100; //points out of the board
private static boolean isCaptured(int col, int row, int[][] board) {
boolean result = !isNotCaptured(col, row, board);
cleanBoard(board);
return result;
}
private static boolean isNotCaptured(int col, int row, int[][] board) {
int value = board[col][row];
if (!(value == MY_COLOR || value == CHECKED))
return true;
int top = row < SIZE - 1 ? board[col][row + 1] : OUT;
int bottom = row > 0 - 1 ? board[col][row - 1] : OUT;
int left = col > 0 ? board[col - 1][row] : OUT;
int right = col < SIZE - 1 ? board[col + 1][row] : OUT;
if (top == VACANT || right == VACANT || left == VACANT || bottom == VACANT)
return true;
board[col][row] = CHECKED;
return (top == MY_COLOR && isNotCaptured(col, row + 1, board))
|| (bottom == MY_COLOR && isNotCaptured(col, row - 1, board))
|| (left == MY_COLOR && isNotCaptured(col - 1, row, board))
|| (right == MY_COLOR && isNotCaptured(col + 1, row, board));
}
private static void cleanBoard(int[][] board) {
for (int i = 0; i < SIZE; i++) {
for (int j = 0; j < SIZE; j++) {
if (board[i][j] == CHECKED)
board[i][j] = MY_COLOR;
}
}
}
Then you can call method like this:
isCaptured(5, 4, board)

I think that BFS will be better for this case because you need to explore the neighbors first, so that if any of them is captured then the point is captured.

As others pointed out, there is also a "ko rule" in Go which roughly means that you are not allowed to capture back immediately when a single stone is captured (simplified). In summary, you may want to use an existing library for this.
I recommend the brugo repository, which is available in maven.
<!-- https://mvnrepository.com/artifact/be.brugo/brugo -->
<dependency>
<groupId>be.brugo</groupId>
<artifactId>brugo</artifactId>
<version>0.1.0</version>
</dependency>
It roughly works like this.
(warning: code not tested)
// create a starting position
Position position = new Position(boardSize, komi);
// play a move
Intersection whereToPlay = Intersection.valueOf(4,4);
IntStatus colorToPlay = IntStatus.BLACK;
Position position2 = position.play(whereToPlay, colorToPlay);
// watch the result.
IntStatus[][] matrix = position2.getMatrix()
It also contains objects to export to Load/Save SGF. The loading of SGF files does not only support UTF-8 but also Asian encodings. Here is a screenshot that shows how difficult this is to implement yourself:
If you also plan to use javafx, then run this demo: brugo.go.ui.javafx.goban.GobanComponentDemo
Enough to get you started.

NullPointerException returning an array that will filled in a different method

I am getting a NullPointerException when the getCave method is called when it tries to return the 2D array. I have not been able to find a solution online. I can get the program to run without the exception by replacing the return with a new Cave that is not an array but that would not fit my needs. Here is a simplified version of my code:
import java.util.Random;
public class Board {
public static final int DEFAULT_ROWS = 10;
public static final int DEFAULT_COLS = 10;
Cave[][] caveArray = new Cave[DEFAULT_ROWS+2][DEFAULT_COLS+2];
public Board(int rows, int cols){
Random rand = new Random();
for (int j = 1; j < (cols+1); j++) {
for (int i = 1; i < (rows+1); i++) {
Cave temp;
temp = new Cave(i, j);
int rnum = rand.nextInt(100)+1;
if (rnum > 50) {
caveArray[i][j]=temp;
caveArray[i][j].makeBlocked();
}
else if(rnum <=50) {
caveArray[i][j]=temp;
caveArray[i][j].makeOpen();
}
}
}
}
public Cave getCave(int r, int c){
return caveArray[r][c];
}
}
here is the caller:
private void newGame() {
// Set up the game board.
gameBoard = new Board(DEFAULT_ROWS, DEFAULT_COLS);
// Set up the 3 characters.
characters = new ArrayList<Character>();
// Add the adventurer (always in the top left).
characters.add(new Adventurer(gameBoard.getCave(0, 0)));
selected = 0; // Initially select the adventurer.
}
which calls:
public class Adventurer extends Character{
Adventurer(Cave initLoc) {
super(initLoc);
}
which calls:
public abstract class Character implements CaveWorker{
protected Cave location;
public Character(Cave initLoc){
location = initLoc;
location.setOccupied(true);
}

The only explanation that I can offer without observing a stack trace (those are really helpful, more times than not) is that if you attempt to index into caveArray[0][c], or even caveArray[r][0] there's not going to be anything there.
You have two options - either use the fact that arrays will start at index 0 (it's not so bad), or preemptively place a Cave object in row 0 and column 0 that serves no real purpose. Aligning with (0,0) would be the easier choice, though.