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How to avoid stackoverflow error for n = 8 in N Rooks problem

I want to solve N Rooks problem in N x N board using recursion with max N = 8. My code works fine for N = 2, 3, 4, 5, 6, 7. But when N = 8 it gives so many possible results starting with the first row of 1 0 0 0 0 0 0 0 then gives stackoverflow error before checking other possible results starting with the first row of 0 1 0 0 0 0 0 0.
I know about general recursion like fibonacci series, factorial, etc. and I can trace them down. Then I came across a new form of recursion called backtracking recursion. Then I sarted to learn the logic behind this form of recursion and read some pseudocode algorithms. Acually this form of recursion seemed to me a little bit harder to construct than normal recursion.
public class NRooks {
/**
* In this code r = which row, c = which column.
* lastY method just returns column c of last placed rook in
* a given row r in order to remove it.
* row.length, col.length, board.length have no special meaning. They all
* equal to the dimension of board N.
* main() method always initiates first row(r = 0). Therefore in main()
* method r remains 0 and c changes as you can see in putRook(0, i).
* So solve() method always begins from second row(r = 1).
*/
private static int found = 0;
private static int[][] board;
private static int[] row;
private static int[] col;
public static void putRook(int r, int c) {
board[r][c] = 1;
row[r] = 1;
col[c] = 1;
}
public static void removeRook(int r, int c) {
board[r][c] = 0;
row[r] = 0;
col[c] = 0;
}
public static boolean isValid(int r, int c) {
if (row[r] == 0 && col[c] == 0) return true;
return false;
}
public static void showBoard() {
for (int r = 0; r < board.length; r++) {
for (int c = 0; c < board.length; c++) {
System.out.print(board[r][c] + " ");
}
System.out.println();
}
System.out.println();
}
public static int lastY(int r) {
for (int j = 0; j < board.length; j++) {
if (board[r][j] == 1) return j;
}
return -1;
}
public static boolean solve(int r, int c) {
int last;
if (r == 0) return false;
if (r == col.length) {
found++;
/**
* When I dont include below printline statement my code
* works fine until N = 7 then gives SO error.
* But When I include this print statement in order
* to print number of results my code works fine until
* N = 6 then gives SO error
*/
//System.out.println("Found: " + found);
showBoard();
r--;
last = lastY(r);
removeRook(r, last);
c = last + 1;
}
for (int j = c; j < row.length; j++) {
if (isValid(r, j)) {
putRook(r, j);
return solve(r + 1, 0);
}
}
last = lastY(r - 1);
removeRook(r - 1, last);
return solve(r - 1, last + 1);
}
public static void main(String[] args) {
int n = Integer.parseInt(args[0]);
board = new int[n][n];
row = new int[n];
col = new int[n];
for (int i = 0; i < row.length; i++) {
boolean finished; // not important
putRook(0, i);
finished = solve(1, 0);
if (finished) System.out.println("============"); // ignore this too
}
}
}
Stackoverflow points to the lines that contain recursive calls to solve() method.
Note: I know only C like syntax of java and basic data abstraction. I wrote this code with this level of my Java.
I want to solve this problem and N queens problem myself.
Because there are so many solutions to these problems out there, both mathematically and algorithmically. And I am not interested in advanced Java data abstraction things right now.
I only want some advice about my code snippet above something like
Your backtracking algorithm is not efficient. (so straightfoward)
You need to use some Java data abstraction things to solve this problem efficiently.
You need to use another form of recursion like tail recursion (I heard about this too.)
....

The main issue why you're getting Stack Overflow error is the way your recursion is structured. The moment solve is invoked in the main method, it keeps recursing deeper and deeper; in fact, all of its invocations form a single several-thousand-calls-deep chain. For n=7, there are 3193 nested calls (I added a counter to check this). For n=8, it performs about 5k recursive calls before overflowing stack on my machine - I guess stack size is rather small by default.
Thus, to get this to work for higher values of n, you need to restructure your recursion in a way that doesn't perform all the recursive calls as a single chain. I could argue that your current solution isn't really backtracking because it never actually backtracks. Let me illustrate what backtracking means on a simpler problem. Let's say you want to print all binary strings of length n=3 ("000" through "111") programmatically, without relying on knowing the value of n. An implementation for this could be something like this:
def build_binary_string(current_prefix, chars_left):
if chars_left == 0:
print current_prefix
return
build_binary_string(current_prefix + 'a', chars_left - 1)
build_binary_string(current_prefix + 'b', chars_left - 1)
build_binary_string("", 3)
The interesting thing (backtracking!) happens at the moment when build_binary_string is invoked with arguments ("00", 1):
build_binary_string("000", 0) is invoked, prints "000" and returns immediately
we are back into build_binary_string("00", 1) function call, right about to execute build_binary_string(current_prefix + 'b', chars_left - 1)
build_binary_string("001", 0) is invoked, prints "001" and returns immediately
That point when control flow returned from build_binary_string("000", 0) to build_binary_string("00", 1) and it chose to make another function call was backtracking. Note that the depth of recursion never exceeded 3.

I cannot test your code as I do not have some of your methods, but is the int j = c supposed to be int j = r?
for (int j = c; j < row.length; j++) {
if (isValid(row, col, r, j)) {
putRook(b, row, col, r, j);
return solve(b, row, col, r + 1, 0);
}
}
Inside of this line you are passing 0 to c then declaring j=c in the for loop conditions so j < row.length will be true every time. I do not know what your isValid() is though.
return solve(b, row, col, r + 1, 0);
EDIT: I see now the c is being declared in the if block above, but if that if block does not get executed this should be an infinite loop afterward. Maybe check to see if r == col.length is executing correctly.

Optimize Leaper Graph algorithm?

During a 45 minute technical interview with Google, I was asked a Leaper Graph problem.
I wrote working code, but later was declined the job offer because I lacked Data structure knowledge. I'm wondering what I could have done better.
The problem was as following:
"Given an N sized board, and told that a piece can jump i positions horizontally (left or right) and j positions vertically (up or down) (I.e, sort of like a horse in chess), can the leaper reach every spot on the board?"
I wrote the following algorithm. It recursively finds out if every position on the board is reachable by marking all spots on the graph that were visited. If it was not reachable, then at least one field was false and the function would return false.
static boolean reachable(int i, int j, int n) {
boolean grid[][] = new boolean[n][n];
reachableHelper(0, 0, grid, i, j, n - 1);
for (int x = 0; x < n; x++) {
for (int y = 0; y < n; y++) {
if (!grid[x][y]) {
return false;
}
}
}
return true;
}
static void reachableHelper(int x, int y, boolean[][] grid, int i, int j, int max) {
if (x > max || y > max || x < 0 || y < 0 || grid[x][y]) {
return;
}
grid[x][y] = true;
int i2 = i;
int j2 = j;
for (int a = 0; a < 2; a++) {
for (int b = 0; b < 2; b++) {
reachableHelper(x + i2, y + j2, grid, i, j, max);
reachableHelper(x + j2, y + i2, grid, i, j, max);
i2 = -i2;
}
j2 = -j2;
}
}
Now, later it was pointed out that the optimal solution would be to implement Donald Knuth's co-prime implementation:
http://arxiv.org/pdf/math/9411240v1.pdf
Is this something that one should be able to figure out on a 45 minute technical interview??
Besides the above, is there anything I could have done better?
edit:
- I enquired about starting position. I was told starting at 0,0 is fine.
edit2
Based on feedback, I wrote a while-loop with queue approach.
The recursive approach runs into a stack-overflow when n = 85.
However, the while loop with queue method below works up to ~n = 30,000. (after that it runs into heap-issues with memory exceeding GB's). If you know how to optimize further, please let me know.
static boolean isReachableLoop(int i, int j, int n) {
boolean [][] grid = new boolean [n][n];
LinkedList<Point> queue = new LinkedList<Point>();
queue.add(new Point(0,0)); // starting position.
int nodesVisited = 0;
while (queue.size() != 0) {
Point pos = queue.removeFirst();
if (pos.x >= 0 && pos.y >= 0 && pos.x < n && pos.y < n) {
if (!grid[pos.x][pos.y]) {
grid[pos.x][pos.y] = true;
nodesVisited++;
int i2 = i;
int j2 = j;
for (int a = 0; a < 2; a++) {
for (int b = 0; b < 2; b++) {
queue.add(new Point(pos.x+i2, pos.y+j2));
queue.add(new Point(pos.x+j2, pos.y+i2));
i2 = -i2;
}
j2 = -j2;
}
}
}
}
if (nodesVisited == (n * n)) {
return true;
} else {
return false;
}
}

I ask a lot of interview questions like this. I don't think you would be expected to figure out the coprime method during the interview, but I would have docked you for using O(n^2) stack space -- especially since you passed all those parameters to each recursive call instead of using an object.
I would have asked you about that, and expected you to come up with a BFS or DFS using a stack or queue on the heap. If you failed on that, I might have a complaint like "lacked data structure knowledge".
I would also have asked questions to make sure you knew what you were doing when you allocated that 2D array.
If you were really good, I would ask you if you can use the symmetry of the problem to reduce your search space. You really only have to search a J*J-sized grid (assuming J>=i).
It's important to remember that the interviewer isn't just looking at your answer. He's looking at the way you solve problems and what tools you have in your brain that you can bring to bear on a solution.
Edit: thinking about this some more, there are lots of incremental steps on the way to the coprime method that you might also come up with. Nobody will expect that, but it would be impressive!

I'm sorry, I feel like I'm missing something.
If you can only go up or down by i and left or right by j, then a case (x,y) is reachable from a start case (a,b) if there are integers m and n so that
a + m*i = x
b + n*j = y
That is, everything is false for a square board where n > 1.
If you meant more like a knight in chess, and you can go up/down by i and left/right by j OR up/down by j and left/right by i, you can use the same technique. It just becomes 2 equations to solve:
a + m * i + n * j = x
b + o * i + p * j = y
If there are no integers m, n, o and p that satisfy those equations, you can't reach that point.

Minimax Connect 4 AI trouble

I am making connect 4 AI, except the game continues until all 42 spaces are filled.
Score is kept by every 4 in a row gets 1 point.
public int[] Max_Value(GameBoard playBoard, int depth){
GameBoard temp = new GameBoard(playBoard.playBoard);
int h = 0, tempH = 999, tempCol=0;
int myDepth = depth - 1;
int[] tempH2 = new int[2];
boolean noChildren = true;
if(myDepth != -1){
for(int i = 0; i < 7; i++){
if(temp.isValidPlay(i)){
count++;
temp.playPiece(i);
noChildren = false;
tempH2 = Min_Value(temp, myDepth);
if(tempH2[1] < tempH){
tempH=tempH2[1];
tempCol = i;
}
temp.removePiece(i);
}
}
}
int[] x = new int[2];
if(noChildren){
h = temp.getHeuristic();
}
else{
h = tempH;
x[0]=tempCol;
}
x[1]=h;
return x;
}
public int[] Min_Value(GameBoard playBoard, int depth){
GameBoard temp = new GameBoard(playBoard.playBoard);
int h = 0, tempH = -999, tempCol=0;
int myDepth = depth - 1;
int[] tempH2 = new int[2];
boolean noChildren = true;
if(myDepth != -1){
for(int i = 0; i < 7; i++){
if(temp.isValidPlay(i)){
count++;
temp.playPiece(i);
noChildren = false;
tempH2 = Max_Value(temp, myDepth);
if(tempH2[1] > tempH){
tempH=tempH2[1];
tempCol = i;
}
temp.removePiece(i);
}
}
}
int[] x = new int[2];
if(noChildren){
h = temp.getHeuristic();
}
else{
h = tempH;
x[0]=tempCol;
}
x[1]=h;
return x;
}
I feel like I just stumbled through everything, and it feels like terrible code. However, I have never attempted anything like this before, and would appreciate any input. I can't tell where I am going wrong. My evaluation function just gives 1 point for each 4 in a row it can find for any given state. The main function calls the Min_Value function to start things off with a depth of 10.
I am attempting to return the column as well as the value of the heuristic. I hope I have provided enough information. Thanks for any insight.

Allright, after implementing the methods not shown (like evaluation, playmove, remove etc.) I was able to debug this. Assuming that these functions are implemented in some correct way in your version, the mistake is that you never actually call the evaluation function if depth is -1:
You have this:
[...]if(myDepth != -1)
{/*restofthecode*/}[...]
But what you need is something like this:
[...]if(myDepth == -1)
{
return temp.getHeuristic();
}
/*restofthecode*/
[...]
That way, whenever you reach depth -1 (a leaf in your minimax tree), the board will be evaluated and the value returned (which is excactly what you need in minimax).
Do this modification in both parts (min and max) and everything shuold be allright. If there are other problems, feel free to ask.

Even though it isn't stated in the question, I think you are not getting good moves from your search, right?
Without looking through your while code, I can already say that your program will only work during the last 10 moves of the game (last 10 empty fields or forced win in 10). Otherwise, your program will return either the last or the first move it evaluated. That is because of your evaluation function, where you only handle a win (respectively 4 in a row), but not 2 in a row, traps, 3 in a row, etc.). It will think of all moves as equal if it can't force a win.
This is a problem, because starting with an empty field, a win can only be forced by the starting player, and just with the 2nd last piece to be placed on the board. (In your version 4 in a row forced).
And since your searchdepth (10) is smaller than the maximum game moves (42), your program will always play its first move.
If the rest of your algorithm is correctly implemented, you can fix this by simply improve your evaluation function, so that it can differ between "good" and "bad" game positions.

how to improve this code?

I have developed a code for expressing the number in terms of the power of the 2 and I am attaching the same code below.
But the problem is that the expressed output should of minimum length.
I am getting output as 3^2+1^2+1^2+1^2 which is not minimum length.
I need to output in this format:
package com.algo;
import java.util.Scanner;
public class GetInputFromUser {
public static void main(String[] args) {
// TODO Auto-generated method stub
int n;
Scanner in = new Scanner(System.in);
System.out.println("Enter an integer");
n = in.nextInt();
System.out.println("The result is:");
algofunction(n);
}
public static int algofunction(int n1)
{
int r1 = 0;
int r2 = 0;
int r3 = 0;
//System.out.println("n1: "+n1);
r1 = (int) Math.sqrt(n1);
r2 = (int) Math.pow(r1, 2);
// System.out.println("r1: "+r1);
//System.out.println("r2: "+r2);
System.out.print(r1+"^2");
r3 = n1-r2;
//System.out.println("r3: "+r3);
if (r3 == 0)
return 1;
if(r3 == 1)
{
System.out.print("+1^2");
return 1;
}
else {
System.out.print("+");
algofunction(r3);
return 1;
}
}
}

Dynamic programming is all about defining the problem in such a way that if you knew the answer to a smaller version of the original, you could use that to answer the main problem more quickly/directly. It's like applied mathematical induction.
In your particular problem, we can define MinLen(n) as the minimum length representation of n. Next, say, since we want to solve MinLen(12), suppose we already knew the answer to MinLen(1), MinLen(2), MinLen(3), ..., MinLen(11). How could we use the answer to those smaller problems to figure out MinLen(12)? This is the other half of dynamic programming - figuring out how to use the smaller problems to solve the bigger one. It doesn't help you if you come up with some smaller problem, but have no way of combining them back together.
For this problem, we can make the simple statement, "For 12, it's minimum length representation DEFINITELY has either 1^2, 2^2, or 3^2 in it." And in general, the minimum length representation of n will have some square less than or equal to n as a part of it. There is probably a better statement you can make, which would improve the runtime, but I'll say that it is good enough for now.
This statement means that MinLen(12) = 1^2 + MinLen(11), OR 2^2 + MinLen(8), OR 3^2 + MinLen(3). You check all of them and select the best one, and now you save that as MinLen(12). Now, if you want to solve MinLen(13), you can do that too.
Advice when solo:
The way I would test this kind of program myself is to plug in 1, 2, 3, 4, 5, etc, and see the first time it goes wrong. Additionally, any assumptions I happen to have thought were a good idea, I question: "Is it really true that the largest square number less than n will be in the representation of MinLen(n)?"
Your code:
r1 = (int) Math.sqrt(n1);
r2 = (int) Math.pow(r1, 2);
embodies that assumption (a greedy assumption), but it is wrong, as you've clearly seen with the answer for MinLen(12).
Instead you want something more like this:
public ArrayList<Integer> minLen(int n)
{
// base case of recursion
if (n == 0)
return new ArrayList<Integer>();
ArrayList<Integer> best = null;
int bestInt = -1;
for (int i = 1; i*i <= n; ++i)
{
// Check what happens if we use i^2 as part of our representation
ArrayList<Integer> guess = minLen(n - i*i);
// If we haven't selected a 'best' yet (best == null)
// or if our new guess is better than the current choice (guess.size() < best.size())
// update our choice of best
if (best == null || guess.size() < best.size())
{
best = guess;
bestInt = i;
}
}
best.add(bestInt);
return best;
}
Then, once you have your list, you can sort it (no guarantees that it came in sorted order), and print it out the way you want.
Lastly, you may notice that for larger values of n (1000 may be too large) that you plug in to the above recursion, it will start going very slow. This is because we are constantly recalculating all the small subproblems - for example, we figure out MinLen(3) when we call MinLen(4), because 4 - 1^2 = 3. But we figure it out twice for MinLen(7) -> 3 = 7 - 2^2, but 3 also is 7 - 1^2 - 1^2 - 1^2 - 1^2. And it gets much worse the larger you go.
The solution to this, which lets you solve up to n = 1,000,000 or more, very quickly, is to use a technique called Memoization. This means that once we figure out MinLen(3), we save it somewhere, let's say a global location to make it easy. Then, whenever we would try to recalculate it, we check the global cache first to see if we already did it. If so, then we just use that, instead of redoing all the work.
import java.util.*;
class SquareRepresentation
{
private static HashMap<Integer, ArrayList<Integer>> cachedSolutions;
public static void main(String[] args)
{
cachedSolutions = new HashMap<Integer, ArrayList<Integer>>();
for (int j = 100000; j < 100001; ++j)
{
ArrayList<Integer> answer = minLen(j);
Collections.sort(answer);
Collections.reverse(answer);
for (int i = 0; i < answer.size(); ++i)
{
if (i != 0)
System.out.printf("+");
System.out.printf("%d^2", answer.get(i));
}
System.out.println();
}
}
public static ArrayList<Integer> minLen(int n)
{
// base case of recursion
if (n == 0)
return new ArrayList<Integer>();
// new base case: problem already solved once before
if (cachedSolutions.containsKey(n))
{
// It is a bit tricky though, because we need to be careful!
// See how below that we are modifying the 'guess' array we get in?
// That means we would modify our previous solutions! No good!
// So here we need to return a copy
ArrayList<Integer> ans = cachedSolutions.get(n);
ArrayList<Integer> copy = new ArrayList<Integer>();
for (int i: ans) copy.add(i);
return copy;
}
ArrayList<Integer> best = null;
int bestInt = -1;
// THIS IS WRONG, can you figure out why it doesn't work?:
// for (int i = 1; i*i <= n; ++i)
for (int i = (int)Math.sqrt(n); i >= 1; --i)
{
// Check what happens if we use i^2 as part of our representation
ArrayList<Integer> guess = minLen(n - i*i);
// If we haven't selected a 'best' yet (best == null)
// or if our new guess is better than the current choice (guess.size() < best.size())
// update our choice of best
if (best == null || guess.size() < best.size())
{
best = guess;
bestInt = i;
}
}
best.add(bestInt);
// check... not needed unless you coded wrong
int sum = 0;
for (int i = 0; i < best.size(); ++i)
{
sum += best.get(i) * best.get(i);
}
if (sum != n)
{
throw new RuntimeException(String.format("n = %d, sum=%d, arr=%s\n", n, sum, best));
}
// New step: Save the solution to the global cache
cachedSolutions.put(n, best);
// Same deal as before... if you don't return a copy, you end up modifying your previous solutions
//
ArrayList<Integer> copy = new ArrayList<Integer>();
for (int i: best) copy.add(i);
return copy;
}
}
It took my program around ~5s to run for n = 100,000. Clearly there is more to be done if we want it to be faster, and to solve for larger n. The main issue now is that in storing the entire list of results of previous answers, we use up a lot of memory. And all of that copying! There is more you can do, like storing only an integer and a pointer to the subproblem, but I'll let you do that.
And by the by, 1000 = 30^2 + 10^2.

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