The tiles are numbers from the set 1.

### How to check if an instance of 8 puzzle is solvable?

For any such board, the empty space may be legally swapped with any tile horizontally or vertically adjacent to it. In this assignment, the blank space is going to be represented with the number 0. The search space is the set of all possible states reachable from the initial state.

The cost of moving from one configuration of the board to another is the same and equal to one. Thus, the total cost of path is equal to the number of moves made from the initial state to the goal state.

The searches begin by visiting the root node of the search tree, given by the initial state. Among other book-keeping details, three major things happen in sequence in order to visit a node:. This describes the life-cycle of a visit, and is the basic order of operations for search agents in this assignmentâ€” 1 remove, 2 check, and 3 expand.

In this assignment, we will implement algorithms as described here.

### Using Uninformed & Informed Search Algorithms to Solve 8-Puzzle (n-Puzzle) in Python / Java

Suppose the program is executed for breadth-first search starting from the initial state 1,2,5,3,4,0,6,7,8 as follows:. The following algorithms are going to be implemented and taken from the lecture slides from the same course.

The following figures and animations show how the 8-puzzle was solved starting from different initial states with different algorithms. Also, the figures display the search paths from starting state to the goal node the states with red text denote the path chosen. As can be seen, with this simple example all the algorithms find the same path to the goal node from the initial state. The same problem with a little variation also appeared a programming exercise in the Coursera Course Algorithm-I By Prof.

The description of the problem taken from the assignment is shown below notice that the goal state is different in this version of the same problem :. The problem. The 8-puzzle problem is a puzzle invented and popularized by Noyes Palmer Chapman in the s. It is played on a 3-by-3 grid with 8 square blocks labeled 1 through 8 and a blank square. Your goal is to rearrange the blocks so that they are in order.GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together.

If nothing happens, download GitHub Desktop and try again. If nothing happens, download Xcode and try again. If nothing happens, download the GitHub extension for Visual Studio and try again. This is a Java implementation for the popular 8-puzzle problem using many search algorithms such as:. You need to run the App. It contains the main method. In this class, you have the ability to define your initial state.

You can also define the goal state. So, it is a very comprehensive solution. Skip to content. Dismiss Join GitHub today GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together. Sign up. A java implementation of 8-puzzle using many search algorithms. Java Branch: master. Find file. Sign in Sign up. Go back.

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It uses the sum of moves to current step and Manhattan priority function as cost function. A priority queue of search node containing number of moves, current board and previous search node is created. For each move, the search node with minimum cost is dequeued and neighboring nodes of this search node are then inserted into the priority queue.

The sequence of moves using fewest number of moves to solve the puzzle is obtained when the goal board is ultimately dequeued total number of moves is always at least its priority.

Check whether the board is solvable by simultaneously solving a twin board derived from initial board by exchanging two adjacent blocks. Test client solver is in the main function. API is shown below:. Skip to content. Dismiss Join GitHub today GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together. Sign up. Java Branch: master. Find file. Sign in Sign up. Go back.

Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. The minumum number of moves to reach solution from initial state is However, my solver, reaches goal in 17 moves. And therein lies the problem - my puzzle solver mostly solves the solvable puzzles in a correct minimum number of moves but for this particular puzzle, my solver overshoots the minimum number of moves and I think I've nailed down the problem to a miscalculation of Manhattan distance in this particular case.

At this link you can see what my solver is doing on the right and what a tried-n-tested solver is doing Brian Borowski's excellent solver, available here. In the very first move, Brian's solver immediately chooses solution that pushes element 5 up, but my solver has other ideas, and on the stacktrace given on the linkmy solver chooses solution which pushes 2 to the left since that board's Manhattan distance is lower, the board is on the front of priority queue.

I can't see what is the problem and I can't blame my Manhattan distance calculation, since it correctly solves a number of other 3x3 puzzles. I was stuck in the same place sometime back where I was solving this in 17 moves. Once you plug in this to the algorithm it works like a charm. Can be slower or faster expand more or less nodes but it returns the optimal solution.

In addition the fact that its first step it's different from the optimal one is meaningless: the algorithm can correctly performs backtrace to get the correct solution path in the future. All the open nodes are candidates for the next step, not only the child of the current node. Learn more. Asked 7 years, 6 months ago. Active 2 years, 5 months ago. Viewed 25k times. Consider these puzzles 0 element being blank space : initial 1 0 2 7 5 4 8 6 3 goal 1 2 3 4 5 6 7 8 0 The minumum number of moves to reach solution from initial state is If any additional code is needed, I'll post it right away.

Well, I've thought of that, but if you check the stacktrace, I actually think everything works as expected.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Code Review Stack Exchange is a question and answer site for peer programmer code reviews. It only takes a minute to sign up. I recently created this for a coursework assignment. I am always looking to learn and would like some feedback on my code. Is there any OO principles I'm going against or anything irritating I'm doing?

Your indentation is a little inconsistent. I don't know if that's how it looks in your IDE or is an artifact of the copy and paste. In general code is easier to read when formatted consistently. For example, your declaration of the Search class is indented more than its fields.

Usually the opposite would be true. You'd normally have the left side defined by the interface rather than the implementation. That way, you can pass it to anything that expects the interface and can easily change your implementation at just a single place. It also helps remind you of what is part of the interface and what is specific to the implementation.

You can't accidentally access something specific to the implementation through an interface object. You also want to declare this as private almost always. You could also declare this as final if you never assign a new list to it.

Yes, you will still be able to clear it and add elements to the list if you declare it final. You just won't be able to assign to the variable itself. As a general rule, you don't want to do processing in your constructor. You don't show your main function, so I don't know what should change there. It could be as simple as calling searchAlgo right after calling the constructor. Note: this is a very common thing to try when first encountering objected-oriented principles.

It's just that doing this makes it harder to reuse the code in different ways. For example, you might have reasons to do something else before running the search. As a general rule, constructors should just allocate and initialize variables. They should not attempt to read input or process things. So searchAlgo seems short for search algorithm.

I tend to be against abbreviations, as they slow code reading more than they speed code writing. After school, you will find that you spend more time reading code both yours and that of others than you do writing code. But that's not actually the biggest concern that I have with that name. As a general rule, classes and objects should get noun names and methods should get verbs. This makes makes the code read more naturally. Search algorithm is an adjective followed by a noun, so I wouldn't use it as a method name.

You can then name the method either search specific to this problem or the more generic process. Since you presumably don't have a standard to which to adhere, I'd probably go with search. This isn't the optimal use case for something like process. Again, I would name this as as a verb, e.What is 8 puzzle? The objective is to place the numbers on tiles in order using the empty space. We can slide four adjacent left, right, above and below tiles into the empty space.

How to find if given state is solvable? Following are two examples, the first example can reach goal state by a series of slides.

8 Puzzle Solver

The second example cannot. Following is simple rule to check if a 8 puzzle is solvable. It is not possible to solve an instance of 8 puzzle if number of inversions is odd in the input state.

In the examples given in above figure, the first example has 10 inversions, therefore solvable. The second example has 11 inversions, therefore unsolvable. What is inversion? A pair of tiles form an inversion if the values on tiles are in reverse order of their appearance in goal state. For example, the following instance of 8 puzzle has two inversions, 8, 6 and 8, 7. Following are the implementations to check whether a given instance of 8 puzzle is solvable or not. The idea is simple, we count inversions in the given 8 puzzle.

Note that the above implementation uses simple algorithm for inversion count. It is done this way for simplicity. The code can be optimized to O nLogn using the merge sort based algorithm for inversion count. How does this work? The idea is based on the fact the parity of inversions remains same after a set of moves, i. In the goal state, there are 0 inversions.

So we can reach goal state only from a state which has even inversion count.

## Puzzle Game in Java

How parity of inversion count is invariant? When we slide a tile, we either make a row move moving a left or right tile into the blank spaceor make a column move moving a up or down tile to the blank space. See following example. Exercise: How to check if a given instance of 15 puzzle is solvable or not.

## 8 puzzle Problem using Branch And Bound

Code Review Stack Exchange is a question and answer site for peer programmer code reviews. It only takes a minute to sign up. Program consists of 2 parts:. One issue with this code is that it is painfully slow I realize that majority of methods take quadratic time, however this is way slower than the spec requires it to be.

I have commented the one with 36 required moves in Solver class's main method, cause it may consume a lot of memory and slow down your machine. Make sure you run from the command line; it perfroms poorly from Eclipse. This code is doing a lot of unnecessary work basically walking in a circles until it realizes that this was all waste and only then takes optimal path. You can see it by comparing number of expected moves vs.

My assumption was corroborated by careful debugging session and the problem is that I don't know how to circumvent this issue. Maybe insight into priority function will help: There are 2 of them, Hamming and Manhattan Manhattan is preferred, cause it converges faster Given the board below, Manhattan is calculated by subtracting deviations of tile from their positions:.

For example, tile 8 the first one is 3 tiles away from its expected position 2 rows down, 1 column to the right Tile 1 the second one is 1 tile away from its position 1 column to the left. If we consider the board as a list, then we can calculate Manhattan distance in the following way:. Each number in the top, indicates how the board should be aligned, to be deemed as solved, and numbers below, indicating how many tiles are these numbers away from their expected position.

Basically, Manhattan priority function will show us the minimum number of moves are needed to solve the puzzle. For the next neighbor node, which is dequeued, moves will equal to 1 and so on. You see, when we have two boards with the same Manhattan priorities, PriorityQueue chooses the first one even though it leads to a badI would even say catastrophic consequences and surely, as complexity of the puzzle increases, these fallacies add up the thing that is infinitely obvious to us, humans, doesn't seem to be so for computers Alternatively, algorithm checks previous Boards, that are stored in PQ with lower priority functions, due to the small number of moves and after checking them, without any result to show up, it chooses the right one.

Here comes the code for 2 classes. S Sorry for Javadocs, I couldn't complete them Board. This is incorrect. This means that you must store the number of moves used to reach a particular SearchNode in the SearchNode.

Consider a graph of nodes and edges where each edge has a non-negative cost associated with it in some cases edges can have negative costs but I won't cover it here.