Jigsaw Puzzle Solver [duplicate] - java

Ok, so I have a 3 x 3 jig saw puzzle game that I am writing and I am stuck on the solution method.
public Piece[][] solve(int r, int c) {
if (isSolved())
return board;
board[r][c] = null;
for (Piece p : pieces) {
if (tryInsert(p, r, c)) {
pieces.remove(p);
break;
}
}
if (getPieceAt(r, c) != null)
return solve(nextLoc(r, c).x, nextLoc(r, c).y);
else {
pieces.add(getPieceAt(prevLoc(r, c).x, prevLoc(r, c).y));
return solve(prevLoc(r, c).x, prevLoc(r, c).y);
}
}
I know I haven't provided much info on the puzzle, but my algorithm should work regardless of the specifics. I've tested all helper methods, pieces is a List of all the unused Pieces, tryInsert attempts to insert the piece in all possible orientations, and if the piece can be inserted, it will be. Unfortunately, when I test it, I get StackOverflow Error.

Your DFS-style solution algorithm never re-adds Piece objects to the pieces variable. This is not sound, and can easily lead to infinite recursion.
Suppose, for example, that you have a simple 2-piece puzzle, a 2x1 grid, where the only valid arrangement of pieces is [2, 1]. This is what your algorithm does:
1) Put piece 1 in slot 1
2) It fits! Remove this piece, pieces now = {2}. Solve on nextLoc()
3) Now try to fit piece 2 in slot 2... doesn't work
4) Solve on prevLoc()
5) Put piece 2 in slot 1
6) It fits! Remove this piece, pieces is now empty. Solve on nextLoc()
7) No pieces to try, so we fail. Solve on prevLoc()
8) No pieces to try, so we fail. Solve on prevLoc()
9) No pieces to try, so we fail. Solve on prevLoc()
Repeat ad infinitum...
As commenters have mentioned, though, this may only be part of the issue. A lot of critical code is missing from your post, and their may be errors there as well.

I think you need to structure your recursion differently. I'm also not sure adding and removing pieces from different places of the list is safe; much as I'd rather avoid allocation in the recursion it might be safest to create a list copy, or scan the board
so far for instances of the same piece to avoid re-use.
public Piece[][] solve(int r, int c, List<Piece> piecesLeft) {
// Note that this check is equivalent to
// 'have r and c gone past the last square on the board?'
// or 'are there no pieces left?'
if (isSolved())
return board;
// Try each remaining piece in this square
for (Piece p : piecesLeft) {
// in each rotation
for(int orientation = 0; orientation < 4; ++orientation) {
if (tryInsert(p, r, c, orientation)) {
// It fits: recurse to try the next square
// Create the new list of pieces left
List<Piece> piecesLeft2 = new ArrayList<Piece>(piecesLeft);
piecesLeft2.remove(p);
// (can stop here and return success if piecesLeft2 is empty)
// Find the next point
Point next = nextLoc(r, c);
// (could also stop here if this is past end of board)
// Recurse to try next square
Piece[][] solution = solve(next.x, next.y, piecesLeft2);
if (solution != null) {
// This sequence worked - success!
return solution;
}
}
}
}
// no solution with this piece
return null;
}

StackOverflowError with recursive functions means that you're either lacking a valid recursion stop condition or you're trying to solve too big problem and should try an iterated algorithm instead. Puzzle containing 9 pieces isn't too big problem so the first thing must be the case.
The condition for ending recursion is board completion. You're only trying to insert a piece in the for loop, so the problem is probably either that the tryInsert() method doesn't insert the piece or it doesn't get invoked. As you're sure that this method works fine, I'd suggest removing break; from
if (p.equals(prev[r][c]))
{
System.out.println("Hello");
break;
}
because it's the only thing that may prevent the piece from being inserted. I'm still unsure if I understand the prev role though.

Related

Minmax algorithm doesn't return direct child of root (returns illegal move)

I am trying to create "AI" for Nine Men's Morris but I got hardstuck on minMax algorithm. Summing up, I was trying to find the issue for over 10h but didn't manage to. (debugging this recursion is nasty or I am doing it badly or both)
Since I started doubting everything I wrote I decided to post my issue so someone can find anything wrong in my version of minMax. I realise it is really hard task without the whole application so any suggestions where I should triple check my code are also very welcome.
Here is link to the video, explaining minMax, on which I based my implementation: https://www.youtube.com/watch?v=l-hh51ncgDI (First video that pops up on yt after searching for minmax - just in case you want to watch the video and don't want to click the link)
My minMax without alpha-beta pruning:
//turn - tells which player is going to move
//gameStage - what action can be done in this move, where possible actions are: put pawn, move pawn, take opponent's pawn
//depth - tells how far down the game tree should minMax go
//spots - game board
private int minMax(int depth, Turn turn, GameStage gameStage, Spot[] spots){
if(depth==0){
return evaluateBoard(spots);
}
//in my scenario I am playing as WHITE and "AI" is playing as BLACK
//since heuristic (evaluateBoard) returns number equal to black pawns - white pawns
//I have decided that in my minMax algorithm every white turn will try to minimize and black turn will try to maximize
//I dont know if this is correct approach but It seems logical to me so let me know if this is wrong
boolean isMaximizing = turn.equals(Turn.BLACK);
//get all possible (legal) actions based on circumstances
ArrayList<Action> children = gameManager.getAllPossibleActions(spots,turn,gameStage);
//this object will hold information about game circumstances after applying child move
//and this information will be passed in recursive call
ActionResult result;
//placeholder for value returned by minMax()
int eval;
//scenario for maximizing player
if(isMaximizing){
int maxEval = NEGATIVE_INF;
for (Action child : children){
//aplying possible action (child) and passing its result to recursive call
result = gameManager.applyMove(child,turn,spots);
//evaluate child move
eval = minMax(depth-1,result.getTurn(),result.getGameStage(),result.getSpots());
//resets board (which is array of Spots) so that board is not changed after minMax algorithm
//because I am working on the original board to avoid time consuming copies
gameManager.unapplyMove(child,turn,spots,result);
if(maxEval<eval){
maxEval = eval;
//assign child with the biggest value to global static reference
Instances.theBestAction = child;
}
}
return maxEval;
}
//scenario for minimizing player - the same logic as for maximizing player but for minimizing
else{
int minEval = POSITIVE_INF;
for (Action child : children){
result = engine.getGameManager().applyMove(child,turn,spots);
eval = minMax(depth-1,result.getTurn(),result.getGameStage(),result.getSpots());
engine.getGameManager().unapplyMove(child,turn,spots,result);
if(minEval>eval){
minEval=eval;
Instances.theBestAction = child;
}
}
return minEval;
}
}
Simple heuristic for evaluation:
//calculates the difference between black pawns on board
//and white pawns on board
public int evaluateBoard(Spot[] spots) {
int value = 0;
for (Spot spot : spots) {
if (spot.getTurn().equals(Turn.BLACK)) {
value++;
}else if(spot.getTurn().equals(Turn.WHITE)){
value--;
}
}
return value;
}
My issue:
//the same parameters as in minMax() function
public void checkMove(GameStage gameStage, Turn turn, Spot[] spots) {
//one of these must be returned by minMax() function
//because these are the only legal actions that can be done in this turn
ArrayList<Action> possibleActions = gameManager.getAllPossibleActions(spots,turn,gameStage);
//I ignore int returned by minMax() because,
//after execution of this function, action choosed by minMax() is assigned
//to global static reference
minMax(1,turn,gameStage,spots);
//getting action choosed by minMax() from global
//static reference
Action aiAction = Instances.theBestAction;
//flag to check if aiAction is in possibleActions
boolean wasFound = false;
//find the same action returned by minMax() in possibleActions
//change the flag upon finding one
for(Action possibleAction : possibleActions){
if(possibleAction.getStartSpotId() == aiAction.getStartSpotId() &&
possibleAction.getEndSpotId() == aiAction.getEndSpotId() &&
possibleAction.getActionType().equals(aiAction.getActionType())){
wasFound = true;
break;
}
}
//when depth is equal to 1 it always is true
//because there is no other choice, but
//when depth>1 it really soon is false
//so direct child of root is not chosen
System.out.println("wasFound?: "+wasFound);
}
Is the idea behind my implementation of minMax algorithm correct?
I think the error might exist in that you are updating Instances.theBestAction even while evaluating child moves.
For example, lets say 'Move 4' is the true best move that will eventually be returned, but while evaluating 'Move 5', theBestAction is set to the best child action of 'Move 5'. From this point on, you won't update the original theBestAction back to 'Move 4'.
Perhaps just a simple condition that only sets theBestAction when depth == originalDepth?
Rather than using a global, you could also consider returning a struct/object that contains both the best score AND the move that earned the score.

How do I write an efficient/optimized loop for comparing several conditions at once? Badugi cardgame method

Say, I'm making a simple badugi card game where the Hand is represented by 10 characters in a string. E.g:
2s3h5dQs - 2 of spades, 3 of hearts, 5 of diamonds, Queen of spades
Now, in this badugi card game I want to create two loops where the first loop checks if all the ranks are different(none of them can be the same) and the other loop checks if all the suits are different. If both of these conditions return as true where they all have different ranks and suits, the hand has drawn a badugi(please excuse my lack of terminology where necessary.)
Now, how can I create an efficient loop for such a situation? I was thinking that I could create several if statements as such:
if (hand.charAt(0) != hand.charAt(2) && hand.charAt(0) != hand.charAt(4) && hand.charAt(0) != hand.charAt(6))
if (hand.charAt(2) != hand.charAt(0) && hand.charAt(2) != hand.charAt(4) && hand.charAt(2) != hand.charAt(6))
... and so forth comparing every single index to one another. But this gets tedious and seems very unprofessional. So my question is, how do I write an efficient loop for this scenario? How can I compare/check if there are no matches at these specific index points to one another?
If I haven't explained properly then please let me know.
Please keep in mind, I am not allowed freedom of how to formulate a hand. It has to be in the format above
You are putting your energy into the wrong place.
You do not need to worry about efficiency at all.
Instead, you should worry about creating a clean design (based on reasonable abstractions) and then write code that is super-easy to read and understand.
And your current approach fails both of those ideas; unfortunately completely.
In other words: you do not represent hands and values as characters within a String.
You create a class that abstracts a Card (with its value and face).
And then a "hand" becomes a List / array of such Card objects. And then you can use concepts such as Comparator to compare card values, or you can make use of equals() ...
And even when you wish to keep your (actually over-complex) naive, simple approach of using chars within a string; then you should at least use some kind of looping so that you don't compare charAt(0) against charAt(2); but maybe charAt(i) against charAt(j).
And following your edit and the excellent comment by jsheeran: even when you are forced to deal with this kind of "string notation"; you could still write reasonable code ... that takes such string as input, but transforms them into something that makes more sense.
For example, the Card class constructor could take two chars for suite/value.
But to get you going with your actual question; you could something like:
public boolean isCardDistinctFromAllOtherCards(int indexToCheck) {
for (int i=0; i<cardString.length-1; i+=2) {
if (i == indexToCheck) {
continue;
}
if (cardString.charAt(indexToCheck) == cardString.charAt(i)) {
return false;
}
}
return true;
}
( the above is just an idea how to write down a method that checks that all chars at 0, 2, 4, ... are not matching some index x).
You should really think about your design, like creating Card class etc., but back to the question now, since it's not gonna solve it.
I suggest adding all 4 values to a Set and then checking if size of the Set is 4. You can even shortcut it and while adding this yourSet.add(element) return false then it means there is already that element in the set and they are not unique. That hardly matters here since you only need to add 4 elements, but it may be useful in the future if you work with more elements.
I would advice creating an array with these chars you are referencing just to clean up the fact you are using indices. i.e create a vals array and a suits array.
This would be my suggestion by using a return or break the loop will stop this means when a match is found it wont have to loop through the rest of the elements .. Hope this helps !
private static int check(char[] vals, char[] suits){
int flag;
for(int i=0; i<=vals.length-2;i++){
for(int k=vals.length-1; k<=0;k++){
if(vals[i]==vals[k]){
flag=-1;
return flag;
}
if(suits[i]==suits[k]){
flag=1;
return flag;
}
}
}
return 0;
}
Why not simply iterate over your string and check for same ranks or suits:
public class NewClass {
public static void main(String[] args) {
System.out.println(checkRanks("2s3h5dQs"));
System.out.println(checkSuits("2s3h5dQs"));
}
public static boolean checkRanks(String hand){
List<Character> list = new ArrayList<>();
for (int i = 0; i< hand.length(); i+=2){
if (!list.contains(hand.charAt(i))){
list.add(hand.charAt(i));
}
else{
return false;
}
}
return true;
}
public static boolean checkSuits(String hand){
List<Character> list = new ArrayList<>();
for (int i = 1; i< hand.length(); i+=2){
if (!list.contains(hand.charAt(i))){
list.add(hand.charAt(i));
}
else{
return false;
}
}
return true;
}
}

Converting a recursive method into a non-recursive method using loop in java

So I'm currently making a game where the instructions are to move left or right within an array using the integer stored at a marked index (circle in this case) until we can get the circle to the last index of the array. The last integer of the array is always 0.
For example,
[4] 1 2 3 1 0, here we start at the circle 0 (index)
We move 4 to the right, 4 1 2 3 [1] 0
Then 1 time to the right, 4 1 2 3 1 [0]. Here the game stops and we win.
My code is as follows for a recursive method:
public static boolean rightWing (int circle, int[] game, List<Integer> checkerList){
int last = game.length-1;
if (circle == last){ // base case for recursion
return true;
}
if (circle < 0){ // if we go out of bounds on the left
return false;
}
if (circle > last){ // if we go out of bounds on the right
return false;
}
if (checkerList.contains(circle)){ // check for the impossible case
return false;
}
checkerList.add(circle); // adds the circle value for the last check to checkerList so we can check for the impossible case
int moveRight = circle + game[circle]; // these two integers help the game move according to the value of the int at circle
int moveLeft = circle - game[circle];
return rightWing( moveRight, game, checkerList) || rightWing(moveLeft, game,checkerList);
}
This works great, but the only problem is it's recursive and slow. I'm trying to redesign it using loops and stacks/queues to make it more efficient, but I'm stuck after writing this (in pseudo):
Boolean rightWing (int circle, List<int> game, List<int> checkerList)
Int lastPlace = game.size() - 1
For int i <- 0 to game.size() - 1 do
If i equals lastPlace then // returns true when i is at the last position of the game
Return true
Any input on how to go forward would be appreciated!
The most important bit: when debugging app for the slowness, you should collect some performance data first to identify where your app is spending the most of its time. Otherwise fixing performance is inefficient. You can use jvisualvm it's bundled with jdk.
Data structures rule the world of performance
One thing why it can be slow is because of this:
if (checkerList.contains(circle)){ // check for the impossible case
return false;
}
The more items you have in the list, the slower it becomes. List has linear complexity for the contains method. You can make it constant complexity if you'll use HashSet. E.g. if you have list with 100 elements, this part will be around slower 100 times with List than with HashSet.
Another thing which might be taking some time is boxing/unboxing: each time you put element to the list, int is being wrapped into new Integer object - this is called boxing. You might want to use IntSet to avoid boxing/unboxing and save on the GC time.
Converting to the iterative form
I won't expect this to affect your application speed, but just for the sake of completeness of the answer.
Converting recursive app to iterative form is pretty simple: each of the method parameters under the cover is stored on a hidden stack on each call of your (or others function). During conversion you just create your own stack and manage it manually
public static boolean rightWingRecursive(int circle, int[] game) {
Set<Integer> checkerList = new HashSet<Integer>();
Deque<Integer> statesToExplore = new LinkedList<>();
int last = game.length - 1;
statesToExplore.push(circle);
while (!statesToExplore.isEmpty()) {
int circleState = statesToExplore.pop();
if (circleState == last) { // base case for recursion
return true;
}
if (circleState < 0) { // if we go out of bounds on the left
continue;
}
if (circleState > last) { // if we go out of bounds on the right
continue;
}
if (checkerList.contains(circle)) { // check for the impossible case
continue;
}
checkerList.add(circle); // adds the circle value for the last check to
// checkerList so we can check for the
// impossible case
int moveRight = circle + game[circle]; // these two integers help the
// game move according to the
// value of the int at circle
int moveLeft = circle - game[circle];
statesToExplore.push(moveRight);
statesToExplore.push(moveLeft);
}
return false;
}

How to hard-code legal moves for fast lookup?

I have created a gameboard (5x5) and I now want to decide when a move is legal as fast as possible. For example a piece at (0,0) wants to go to (1,1), is that legal? First I tried to find this out with computations but that seemed bothersome. I would like to hard-code the possible moves based on a position on the board and then iterate through all the possible moves to see if they match the destinations of the piece. I have problems getting this on paper. This is what I would like:
//game piece is at 0,0 now, decide if 1,1 is legal
Point destination = new Point(1,1);
destination.findIn(legalMoves[0][0]);
The first problem I face is that I don't know how to put a list of possible moves in an array at for example index [0][0]. This must be fairly obvious but I am stuck at this for some time. I would like to create an array in which there is a list of Point objects. So in semi-code: legalMoves[0][0] = {Point(1,1),Point(0,1),Point(1,0)}
I am not sure if this is efficient but it makes logically move sense than maybe [[1,1],[0,1],[1,0]] but I am not sold on this.
The second problem I have is that instead of creating the object at every start of the game with an instance variable legalMoves, I would rather have it read from disk. I think that it should be quicker this way? Is the serializable class the way to go?
My 3rd small problem is that for the 25 positions the legal moves are unbalanced. Some have 8 possible legal moves, others have 3. Maybe this is not a problem at all.
You are looking for a structure that will give you the candidate for a given point, i.e. Point -> List<Point>.
Typically, I would go for a Map<Point, List<Point>>.
You can initialise this structure statically at program start or dynamically when needing. For instance, here I use 2 helpers arrays that contains the possible translations from a point, and these will yield the neighbours of the point.
// (-1 1) (0 1) (1 1)
// (-1 0) (----) (1 0)
// (-1 -1) (0 -1) (1 -1)
// from (1 0) anti-clockwise:
static int[] xOffset = {1,1,0,-1,-1,-1,0,1};
static int[] yOffset = {0,1,1,1,0,-1,-1,-1};
The following Map contains the actual neighbours for a Point with a function that compute, store and return these neighbours. You can choose to initialise all neighbours in one pass, but given the small numbers, I would not think this a problem performance wise.
static Map<Point, List<Point>> neighbours = new HashMap<>();
static List<Point> getNeighbours(Point a) {
List<Point> nb = neighbours.get(a);
if (nb == null) {
nb = new ArrayList<>(xOffset.length); // size the list
for (int i=0; i < xOffset.length; i++) {
int x = a.getX() + xOffset[i];
int y = a.getY() + yOffset[i];
if (x>=0 && y>=0 && x < 5 && y < 5) {
nb.add(new Point(x, y));
}
}
neighbours.put(a, nb);
}
return nb;
}
Now checking a legal move is a matter of finding the point in the neighbours:
static boolean isLegalMove(Point from, Point to) {
boolean legal = false;
for (Point p : getNeighbours(from)) {
if (p.equals(to)) {
legal = true;
break;
}
}
return legal;
}
Note: the class Point must define equals() and hashCode() for the map to behave as expected.
The first problem I face is that I don't know how to put a list of possible moves in an array at for example index [0][0]
Since the board is 2D, and the number of legal moves could generally be more than one, you would end up with a 3D data structure:
Point legalMoves[][][] = new legalMoves[5][5][];
legalMoves[0][0] = new Point[] {Point(1,1),Point(0,1),Point(1,0)};
instead of creating the object at every start of the game with an instance variable legalMoves, I would rather have it read from disk. I think that it should be quicker this way? Is the serializable class the way to go?
This cannot be answered without profiling. I cannot imagine that computing legal moves of any kind for a 5x5 board could be so intense computationally as to justify any kind of additional I/O operation.
for the 25 positions the legal moves are unbalanced. Some have 8 possible legal moves, others have 3. Maybe this is not a problem at all.
This can be handled nicely with a 3D "jagged array" described above, so it is not a problem at all.

different for loops java

I'm having some difficulties with the following problem:
I'm making a little game where you're at a specific spot and each spot has each some possible directions.
The available directions are N(ord),E(ast),S,W . I use the function getPosDirections to get the possible directions of that spot. The function returns the directions into an ArrayList<String> e.g. for spot J3: [E,W]
Now the game goes like this: 2 dice will be rolled so you get a number between 2 and 12, this number represents the number of steps you can make.
What I want is an ArrayList of all the possible routes
clarification of all the possible routes:
When I'm at the current position I check what the possibilities are from there. Let's say that's go East and go West. So we get 2 new positions and from there on we need to check for the next possibilities again for both positions (until we took x directions)
(x equals the number thrown by the dice).
e.g.: I throw 3 and I'm currently at spot J3:
[[E,N,E],[E,N,S],[E,S,E],[E,S,S],[W,N,E],[W,N,S],[W,S,E],[W,S,S]]
How would obtain the last mentioned Array(list)?
First, you might wish to think about your approach some more. In the worst case (a 12 is rolled, and all 4 directions are possible at every location), there will be 4^12 ~= 160 million routes. Is it really necessary to iterate over them all? And is it necessary to fill about 1 GB of memory to store that list?
Next, it is probably a good idea to represent directions in a type-safe manner, for instance using an enum.
That being said, recursion is your friend:
private void iteratePaths(Location currentLoc, List<Direction> currentPath, List<List<Direction>> allPaths, int pathLength) {
if (currentPath.size() >= pathLength) {
allPaths.add(new ArrayList<Direction>(currentPath));
return;
}
for (Direction d : currentLoc.getPosDirections()) {
currentPath.add(d);
Location newLoc = currentLoc.walk(d);
iteratePaths(newLoc, currentPath, allPaths, pathLength);
currentPath.remove(currentPath.size() - 1);
}
}
public void List<List<Direction>> getAllPaths(Location loc, int length) {
List<List<Direction>> allPaths = new ArrayList<List<Direction>>();
List<Direction> currentPath = new ArrayList<Direction>();
iteratePaths(loc, currentPath, allPaths, length);
return allPaths;
}
You can assume that your field of spots is a complete graph. Then you need to implement BFS or DFS with saving pathes.
You can implement all logic in any of these algorithms (like getting a list of possible directions from a certain node).

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