Griddler Creator. Supervisor: Linda Brackenbury. Temitope Otudeko 04/05

Transcription

1 Griddler Creator Supervisor: Linda Brackenbury Temitope Otudeko 04/05

2 TABLE OF CONTENTS Introduction... 3 Griddler puzzle Puzzles... 3 Rules and Techniques for solving griddler puzzles... 3 History of Griddler puzzles... 5 Project... 5 Background and Literature survey... 6 Design... 8 Requirements... 8 Development... 9 User Interface Implementation User Interface Back- End Features RESULTS, Testing and Evaluation Conclusions References

3 CHAPTER 1 INTRODUCTION In this section I intend to inform you about griddler puzzles and give you an overview of my project. At the end of this chapter you will know what griddler puzzles are, their history, other relevant information about griddler puzzles and how they relate to my project, the aim of my project and how I intend to carry out my project. GRIDDLER PUZZLE PUZZLES Griddler puzzles are picture logic puzzles. The aim of the puzzle is to fill or leave blank, cells of the grid with the help of the clues on the side of the grid to reveal a picture. For example a clue for a row could be "3 2 5", this would mean that the row contains a set of 3, 2 and 5 filled in squares respectively with at least one blank square between each successive group. FIGURE 1: A SOLVED LINE OF A GRIDDLER PUZZLE Griddler puzzle puzzles can range from very easy to challenging to solve depending on the size of the grid and the clues. For instance clues that have a lot of ones are generally quite difficult to solve and the bigger the grid the more time consuming and difficult it will probably be to solve. FIGURE 2: EXAMPLE OF AN UNSOLVED PUZZLE FIGURE 3: EXAMPLE OF THE A SOLVED PUZZLE RULES AND TECHNIQUES FOR SOLVING GRIDDLER PUZZLES There are a number of techniques and rules used to solve griddler puzzle puzzles. The following are some of the different techniques, rules and tips used to solve griddler puzzle puzzles. A helpful technique that most puzzle solvers start with is the overlap rule; it is mainly helpful with large clues for example the clue 14 on row 10 or 8 6 on row 11 of the reindeer puzzle i.e. figure3. It is the only rule that can be used when solving a griddler puzzle in which no square s state has been determined. To apply the overlap rule, the row is filled in from the left starting 3

4 with the first clue with a blank square between each clue then from the right starting with the last clue and if any of the filled in squares overlap for the same clue then the square is filled in. FIGURE 4: EXAMPLES OF THE OVERLAP TECHNIQUE Another helpful technique in solving griddler puzzle puzzles is determining spaces and it is used on partially solved lines. An instance where it could be used to determine spaces is let us say a row had clues 3 1 and the 3 part of the clue had one square filled in for it. If the amount of spaces up to the filled in square is not enough to contain 3 filled in squares and an empty square then it is determined the filled in square is part of the cluster for the first clue which is 3. Another way to determine it is part of the 3 cluster is if the 1 clue has been determined. One square is filled in so the cluster of 3 filled in squares is made up of either the two squares to the left of the filled in square, the two squares to the right or one on either side but since the one has been filled in and there are no other clues to be filled in but the 3 it is best to leave the maximum amount to either side undetermined to leave all possibilities open. Since the two to either side of the filled in square have been accounted for and all other filled in squares have been determined it means all undetermined squares on the row must be spaces. FIGURE 5: EXAMPLE OF THE DETERMINING SPACE TECHNIQUE Another technique that can be applied to partially solved lines is forcing. If a row contains two squares that have been determined as spaces and the amount of squares between the spaces is for instance one and the smallest clue is two then the square between the spaces must be a space as it is too small to fit a cluster of two filled in squares in there. FIGURE 6: EXAMPLE OF THE FORCING TECHNIQUE A technique used to determine filled in squares is glue in the sense that the squares are glued on at the end of a determined squares. For instance let us say a row has clue 5 and the distance between the first filled in square and the start of the row is two undetermined squares. What can be determined from this is that if the cluster of five filled in squares was to start from the beginning the two squares after the filled in square would be filled in or if the cluster was to start from the filled in square the two squares after it would also be filled in therefore it can be said that the two squares after the filled in squares are filled in. The same logic can be used in the middle of a row with the closest determined space used as the beginning of the row. FIGURE 7: EXAMPLE OF THE GLUE TECHNIQUE 4

5 An extra technique that is useful in determining spaces and filled in squares is splitting and joining. An instance of where this technique can be used is when a row has clues and has small clusters of filled in squares on the row like the diagram below. The filled in squares at the end of the row have a space between then and if it was filled in would make a cluster of three which is invalid for this row as none of the clue numbers is a three so therefore it must be a space. This determines that the two clusters of two filled in squares at the beginning of the row must be linked with the one clue and the length of the clue is five and so it must be filled in between the cluster to create the bigger cluster of five. FIGURE 8: EXAMPLE OF THE SPLITTING AND JOINING TECHNIQUE Another technique used to determine spaces is punctuation. This is putting a space before or after or both when the filled in squares of a clue has been determined. These are the main techniques used when solving griddler puzzle puzzles manually and I shall inform you about the development and increased popularity of griddler puzzle puzzles over the years. HISTORY OF GRIDDLER PUZZLES The aim of this section is to briefly inform you about the history of griddler puzzles i.e. how it started and where it is at today. The concept of griddler puzzle puzzles has been around since 1987 when Non Ishida, a Japanese graphics editor, won a competition in Tokyo designing pictures. Non Ishida s picture entailed using skyscraper lights, which were turned on or off. The following year, Non Ishida published three picture grid puzzles in Japan under the name of "Window Art Puzzles" coincidentally around the same time and with no connection, a professional Japanese puzzler named Tetsuya Nishio invented the same type of puzzle. In 1990, James Dalgety in the UK invented the name Nonograms after Non Ishida and Dia gram. James persuaded The Sunday Telegraph to publish the puzzle weekly for a trial period, after a successful trial period they were continued. In 1993, First book of Nonograms was published by Non Ishida in Japan and later on that year The Sunday Telegraph Book of Nonograms was published in the UK. Nonograms were also published in Sweden, United States, South Africa and other countries. Pan Books were published the 4 th Sunday Telegraph Book of Nonograms in 1995 and because Non Ishida wanted to exclusively use the name "Nonogram" for her puzzles in Japan, her collaboration with James Dalgety ended in In the summer of 1998, The Sunday Telegraph ran a competition to find a replacement name for their puzzles and Griddler puzzle was the winning name chosen by its readers. Today, magazines with griddler puzzle puzzles are published in the USA, UK, Germany, Netherlands, Italy, Hungary, Finland and many other countries and have started appearing on hand held electronic toys such as Nintendo products and on other plastic puzzle toys. PROJECT This is section gives an overview of my research and the aim of my project; I shall expand on my research in the next chapter. The aim of my project is to create a program that allows users to create griddler puzzle puzzles as there are loads of griddler puzzle solvers out there but only a handful of creators. A griddler puzzle creator will be used by puzzle enthusiasts who wish to create their own griddler puzzle puzzles for entertainment or puzzle makers specialising in 5

6 griddler puzzle puzzles. The program will show a grid of a specified size (i.e. 5x5, 10x10, etc.) determined by the user, which they can draw the image on and this will be transformed into a puzzle. The transformation process entails validating the puzzle, if the puzzle is not valid informing the user accordingly and if it is valid generating clues for it. Griddler puzzle puzzles are not the easiest of puzzles to create as not every picture can be a puzzle; this is because not all pictures when converted to griddler puzzle puzzles will have a unique solution meaning some puzzles can have more than one solution. Another difficulty with setting griddler puzzle puzzles is not every puzzle is solvable using logic meaning some puzzles might require some guesswork in order to be solved. This is not ideal so I will give guidelines on how to create unique puzzles and solvable puzzles to the users to prevent the need for guesswork or if not possible at least reduce the amount of it needed. The next chapter explains my research on griddler puzzle creators and solvers available, the difficulties in solving griddler puzzle puzzles and setting them, what makes them unique and explains why my project went in the direction it did. CHAPTER 2 BACKGROUND AND LITERATURE SURVEY This chapter contains the details of my research and gives an insight into why I came to certain conclusions about the direction of my project. I shall explain the complications involved in solving griddler puzzle puzzles and its implications on my project. My research mainly took place online because information about griddler puzzle puzzles is not easily obtainable in libraries or bookstores. During the course of my research, I discovered a number of dedicated griddler puzzle websites, for example griddler puzzle.net, puzzlemuseum.com and Steve Simpson s nonogram website comp.lancs.ac.uk/~ss/nonogram, some of them with online communities. Common features of these websites were pages describing griddler puzzle puzzles and solution techniques and links to online solvers or an online solver incorporated on the website. I found a small number of website that allowed its user to create griddler puzzle puzzles online and via a program that had to be downloaded first namely comp.lancs.ac.uk/~ss/nonogram, griddler puzzle.net, yarivh.com/cryptopics, and so on. The different methods available to the user of the creator programs I discovered to create puzzles were either drawing the image in manually on a grid of a specified size by filling in certain square or by importing an image. The latter method is the easier method for inputting a picture but depending on the application it might get a bit complex as it requires a large amount of constraint to be met with regards to the colour of the image, the size of the image and the format of the image which might be quite complicated for the users if they are not familiar with computer graphics. A griddler puzzle editor I have found that simplifies the use of this feature is Griddler puzzles Deluxe From my experiments using these various applications to create a puzzle, on the outside, what it seemed to be doing was scanning each line of the grid and counting the clues and the end product was a list of clues. These creators also had a way of testing that when the grid is solved the picture produced would be the one inputted. This made me wonder if a different picture could be produced even if the griddler puzzle was solved correctly and on further investigation I found out that it was possible, not all griddler puzzle puzzles have one solution. 6

7 The information stated in the previous paragraph steered my research towards what makes griddler puzzle puzzles unique and how I could ensure that when I create my program only unique puzzles shall be outputted. During the course of my validation research I discovered puzzle makers mostly validate their puzzles, i.e. prove that their puzzle has a unique solution, by trying to solve them which guided my research towards the direction of solvers. My research involved finding out how the various griddler puzzle editors tested their puzzles. I discovered that the solution of griddler puzzle puzzles is actually a complex combinatorial problem which is why it is sometimes difficult to solve or why it might not always have a unique solution. I also discovered that it is an NP complete problem which explains why the problem of finding a solution to a griddler puzzle is more time consuming to solve the larger it is. The largest solvable griddler puzzle created is a 500 x 500 was introduced in 2005 and was first solved in The griddler.net s griddler puzzle creator has modified to be able to validate it so this creator has the capacity to validate puzzles up to the 500 x 500. There are a number of griddler puzzle solvers available online and they are written in numerous languages namely C, C++, C#, CGI, Eclipse, Java, JavaScript, PalmPilot, Perl, PROLOG, Python, Scheme, VBA, Windows and so on. The method these solver uses to solve the griddler puzzle is broken down into three stages. The first stage is the line selector; all solvers need a method by which it selects a line to be solved otherwise it would have no sensible way of keeping track of what it is doing. A basic line selector is one that puts the lines of the grid in a queue so it can iterate through the grid either rows then columns or columns then rows. The other type of line selector is a heuristic line selector; this computes a score equivalent to how much information can be obtained from each line based on the line s clues and sorts the lines based on this score. The next stage is the line solver; this I believe is a vital part of the application as it determines how good the solver is. The better and faster the line solver is, determines how advanced the puzzles that can quickly be solved using the application are. The line solver receives lines from the line selector to solve and these lines could range from unsolved lines to partially solved lines. The different methods used by the griddler puzzle solvers that I researched were depth first search algorithm, the fast algorithm, the complete algorithm and the fcomp algorithm. Depth first search involves looking at all the possibilities of the solution to each row and combining all the rows possible solutions to find. This is similar to the complete algorithm except it does not try to combine row possibilities instead it tries to find out where the possibilities overlap. These are algorithms that look extensively at all the solutions to the problem therefore they are not fast. The fast algorithm does the same thing as the complete algorithm but faster because it does not exhaustively look at the solution it streamlines the possibilities so it only has to consider essential ones and find out where the possibilities of overlap exist between them. The refinement process is acceptable but a few solutions might not be spotted due to its lack of thoroughness. The fcomp algorithm is a fusion of the concept of the complete and the fast algorithm. It is faster than the complete algorithm but more thorough than the fast algorithm although I do not fully comprehend how it works so I will have to ask you to refer to Steve Simpson of the University of Lancashire s website for more detail on how it works; the relevant information is in my references. The third part of the solver is the guesser. After the lines solver has been exhaustively on the griddler puzzle and no more information can be obtained from the puzzle and it is still unsolved the guesser is the next direction to turn. I came across two types of guessers during my research and the first one picks a square at random and guesses a state for it i.e. decides whether it will be filled in or a space and continues to try and solve the puzzle using the line selector and line solver from that piece of information. The solver stores information about its guess and the information determined from it because if the guess is wrong the solver will get to a 7

8 contradiction and then the decision to fill in or leave the square empty will be reversed and all the moves after that reversed as well and the opposite of the decision is accepted as the right decision. This is because there are only two decisions that can be made so if it is not one, it is the other. The solver goes on to either solve the problem or might keeps requiring guesses. The other guesser I came across was called probing. It does a similar thing to the previous guesser with a different spin to the method; for one, it does not pick the square to fill in or leaves blank at random but instead probes. It probes the grid at levels instead so the first level of probing would be the neighbouring cells of the cell selected in the last iteration, then the neighbouring cells of cells that were changed, i.e. their value was determined "black" or "white", in the last iteration, then cells which have two or more known neighbours with known meaning the colour of the cell has already been determined, then finally cells which have one known neighbour. The process of the probing is described like this We go over the cells in each level looking for contradictions. If a contradiction is found we stop, and set the cell s colour. Once we finished probing cells in a level, we go to the next. If we haven t found a contradiction in any level, we guess the cell according to the following heuristic: We choose that cell that, when we guessed its colour an employed the line solver, determined the most cells to be black or white. For example: We start with an empty board. We guess the colour of cell (1,1) to be black, and employ the line solver. After the line solver was employed, the colour of 4 more cells is determined so the score of (1,1) is 4. We use a tree- based search in to keep track of our guesses, and backtrack whenever we hit a contradiction. Our search method can find all possible solutions to a board (unless we explicitly set a solution limit to stop after) The next chapter shall build on my research; in other words the information gathered from my research, which I have stated in this chapter, is what determined the design choices I made for my puzzle editor. CHAPTER 3 DESIGN In this chapter, I shall go through the requirements and design of my program and explain the reason for my choices. I would delve deeper into the details of creating a puzzle editor and explaining what happens behind the scenes by explaining how I plan to implement my puzzle editor. REQUIREMENTS There are certain features required by my puzzle editor, which are firstly allowing the user to specify the size of the grid. This is important because the size of a griddler puzzle is not fixed, it ranges from 1x1 to 500x500 and the user needs to be able to create whatever size puzzle they want. I have thought of the various ways I could implement this and I decided on a dialog box at the start of a program would be ideal because it is not needed once the grid size has been determined so it is a good method of keeping it out of sight and out of the way. Another feature of my editor is a grid in which the squares can be filled in and a filled in square can be changed to a blank square that way the user can easily correct their mistake. The editor should also be able to validate puzzles that way after the user has finished creating the puzzle they can find out if it has a unique solution or not. 8

9 DEVELOPMENT This section shall be used to explain why I decided on a particular language and how I intend to organize and carryout my development of the program. I chose to write my program in java because it is the language I am more proficient in therefore I believe it would be less challenging than C or any other language I could write the program in. I plan to create multiple version of my program but each one building on the previous one for example I would start with the basics like building the user interface with no functionality and the second version of the program would provide some functionality for the grid and the third version of the program would let a button perform an action and so on. This is an advantageous technique to use in the development of applications as it allows the modification of the program without crippling the development progress if it all goes pear shaped, as previous versions of the program are available. Another advantage of this process is if the programmer wants to modify certain features jeopardizing the progress on current and future versions. I drew the flow diagram (figure 9) to give me a visual of the process that will be going on behind the scenes of the editor to validate puzzle. I shall start the validation by putting the rows and columns into a queue. Rows first then columns I'm not sure if the order it is inputted into the priority queue matters that is if the column were put into the priority queue before the row and the puzzle was not unique if it would yield a different solution. The queue shall be the method I use to implement my line selector. The line at the top of the queue shall be solved if it is fully solved then the state of the line shall be changed to solved to prevent unnecessary work being carried out on it and it is removed from the queue. If it is partially solved, the state of the line is modified to reflect that, it is put at the back of the queue, the adjacent column is moved up the queue and the next line is selected. If no solution was found for the line it is also put to the back of the queue and then the next line is selected. If the queue is empty when the next line is about to be selected, it means that the puzzle is solved because lines are only removed from the queue when the puzzle is solved. If the queue is not empty when the next line is to be selected, the process of trying to solve the line and changing states and the process of returning or removing the line from the queue is repeated till the queue is not empty and the solver is stuck. When the solver is stuck, probing starts, the solver makes a random guess on whether the square is filled on or not and solves the lines in the queue based on that information. The solver carries on its original path before the probing stage and tries to solve the puzzle if it gets a contradiction then it reverses all its decisions after the guess and changes the guess to the opposite if it does not meet a contradiction but if it gets stuck again then it randomly guesses another square and repeats the process again. These processes will goon till every line has been removed from the queue. 9

10 FIGURE 9: FLOW DIAGRAM OF THE VALIDATION PROCESS USER INTERFACE FIGURE 10: SKETCH OF THE USER INTERFACE Student ID:

11 The user interface will have to be a Graphical User Interface (GUI) because it is the only way to allow the user to draw their puzzle using the program. The dialog box which I have decided to go with a simple and easy to use user interface that will contain the grid in the centre, buttons at the bottom of the interface and instructions on the side. I want the grid at the centre of the interface as this is the main feature and it would allow the user colour in a square or reverse the operation by simply clicking on the desired square. I would like a buttons at the bottom of the page for convenience as it is standard on most applications and so that is the first place the user would search for it. I would like two buttons on my interface; one to generate clues and another to validate the puzzle. I decided there would be two different buttons for the processes one because although they are linked they are separate processes and because of the how I intended to organise my development of the program so that I can write the code for the buttons. The next chapter is about how I implemented my design and explains my reason for the implementation choices I made. CHAPTER 4 IMPLEMENTATION In this chapter I shall discuss how I implemented the design of my project, the reasons for choosing certain methods of implementation, the difficulties I encountered during implementation and how I solved them. USER INTERFACE This section explains how I implemented the front end of my program, i.e. the user interface, and the reason for some of implementation features and methods. I decided to use components of the swing package to implement my GUI because it has more features and I would have more at my disposal which I believe would make implementation easier for me. The first version of my griddler puzzle editor contained the implementation of the main GUI. I decided to create a Griddler puzzle class which extended the JFrame class rather than create it in the main method because it would give me the option of running multiple instances of the griddler puzzle object if I needed to. I encountered a minor setback with my user interface which was determining how I would colour in the grid. After researching the methods available, I thought it might be a good option to use JLabel as a wide variety of methods are available permitting me to perform various manipulations on the object. The JLabel object allows me to create an empty instance of it which is what I needed for my grid, change the background colour and can listen for various events which were the manipulations I needed to perform. In order to implement my grid I created a JPanel with a combination of border layout and grid layout. The centre of the border layout contained a JPanel with a grid layout and I wrote a loop to place an empty opaque JLabel in every grid of the panel as well as storing the labels in two dimensional array of type JLabel. I created the two JButtons and placed them in the south section of the panel. The second version of the program made changes to the user interface as it allowed the input of the grid size by the user. In order to achieve this, I extended my main method to allow it possess the properties of a JFrame component then I modified it to display a dialog box with two text fields in which the size of the grid could be inputted and a JButton to create an instance of the griddler puzzle class with the sizes passed as arguments to the class. 11

12 The next section shall explain back end functionality and how I implemented it and what motivated me to choose the methods I decided on eventually to implement the back end of the program. BACK- END FEATURES This section explains how I implemented the functionality behind the buttons and the grid. The third version of my program is where functionality to the grid was applied. A JLabel listener was created for and registered to every JLabel in the grid and it listened for the click action on the squares. I created a JLabel listener class that extended the mouse action event with the JLabel source as it argument because it was easier using this method to identify the label that triggered the event and change it background colour. In the fourth version of my program, the generate clue JButton performs actions. In order to implement this I had to create a button listener class for the JButton to keep the amount of code in the griddler puzzle class to a reasonable level to make it easier to read and maintain. Therefore I would have chunks of code that would be easier to manage and maintain and it was also an efficient way of implementing the action. My button listener object listens for clicks to either of the buttons i.e. the generate clue button or the validate button. The generate clue button s functionality is added in this version of the program to generate clues from the grid. It was implemented by scanning through each row or column and counting the amount of labels with their background colour set to black and stores the amount in as a list when it reaches a white label or the end of the row or column, then it stores the list in a two dimensional array. The first column of the array is where the clue lists for the rows are stored and the second column of the array is where the clue lists for the columns are stored. The fifth version of the editor is adding functionality to the validate button by creating clue object from the clue list array and creating a linked lists. I am using a clue object as this can contain all the information about a clue needed i.e. the row number, the clue list, the line state i.e. solved, partially solved and unsolved and other relevant information. I decided to implement my queue using a linked list as there are loads of features available to me in java to easily implement it and I was implementing a basic queue. I progressed as far as the implementation of logic rules i.e. the overlap rule and identifying spaces. The next chapter shall contain information about the results my program produced when run, its speed and performance and the tests I carried out on it and where I rate it in terms of my requirements. CHAPTER 5 RESULTS, TESTING AND EVALUATION In this section I shall try to explain how I tested my program and state the results of the test i.e. how it performed when valid data was inputted how it performed when erroneous data was inputted and if it met the user requirements stated in the design section. 12

13 FIGURE 11: SCREENSHOT OF MY DIALOG BOX AND THE GRIDDLER OBJECT PRODUCED FIGURE 12: SCREENSHOT OF MY EDITOR GENERATING CLUES The front end of my system could be easily tested as I had a visual of the outcome of the code and could swiftly spot when I was not getting the expected result. For the back end, I created dialog boxes to output results to make sure the right parameters and results were obtained. For instance while I was generating the clues I had a dialog box return the resulting clue of every line of to confirm the code was generating the right clues. With the validation process it was a bit tricky because although I could see the output of the code it was hard to identify what cause what. If the column were put into the priority queue before the row and the puzzle was not unique would it yield a different solution to if the rows are put before the column. CHAPTER 6 CONCLUSIONS During the course of this project, I have learnt a great deal about griddler puzzles, gained more experience programming in java and learnt more about large scale projects which I did not realise. I learnt more about the swing and action event classes in java throughout the project and I believe it has made me a more proficient java programmer as I have proven to myself I can learn a great deal of new concepts on my own and implement them. With regards to the success of my project, I have not reached my goal. I have produced a program that griddler puzzle 13

14 puzzles of any size can be created on but unfortunately I cannot confidently say it validates griddler puzzle puzzles created on it. Further activity I would propose for my project would be to improve the solver as it is the backbone of the validation process which is a weak part of my project. 14

15 REFERENCES puzzle/gridhist.htm Page name: Griddler history Date accessed: October Page name: All pages Date accessed: October puzzles.net/ Page name: Griddler workshop Date accessed: November Page name: Home page Date accessed: November column- new.pdf Authors names: Jessica Benton, Rion Snow, Nolan Wallach Title: A combinatorial problem associated with nonograms Year of publication: March 21, Page name: nonogram page Date accessed: October Page name: homepage Date accessed: December Intelligent_Interaction/2004_01_C_W.A.Wiggers- A_comparison_of_a_genetic_algorithm_and_a_depth_first_search_algorithm_applied_to_Japanese _nonograms.pdf Author s name: Wouter Wiggers, Faculty of EECMS, University of Twente w.a.wiggers@student.utwente.nl Title: A comparison of a genetic algorithm and a depth first search algorithm applied to Japanese nonograms 15