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Rubik’s Cube solution analyzer using R-tool

Rubik’s Cube solution analyzer using R-tool

                                                    Ms, K.BHUVANA MEENAKSHI
        UG Scholar, Department of Computer Science and Engineering,
           Dhirajlal Gandhi College of Technology, Salem, Tamil Nadu, India – 636309
                                                           bhuvanameenakshi@outlook.com
Abstract- The scrambled puzzle is to be captured in the form photograph (initially we are working with 2-d but later could be modified to 3-d) and is uploaded in the app. The app analyse the picture captured and gives the appropriate answer. For this initially we will make a study of all possible solutions using R-tool and pre-store it in the app and then the captured picture will be matched with pre-stored analysis. The appropriate steps needed to unscramble the Rubik’s cube will be displayed to the user. Thus we created an app that gives instant solution to the Rubik’s cube by analyzing the puzzle using R-tool.

Keywords— Puzzle, 3-d, 2-d, R-tool, IDA- Iterative Deepening Algorithm

1. INTRODUCTION

1.1 Rubik’s Cube
Rubik's Cube is a 3-D mix riddle designed in 1974 by Hungarian stone carver and teacher of engineering Ernő Rubik. Initially called the Magic Cube,the riddle was authorized by Rubik to be sold by Ideal Toy Corp. in 1980 by means of businessperson TiborLaczi and Seven Towns organizer Tom Kremer,and won the German Game of the Year extraordinary grant for Best Puzzle that year. As of January 2009, 350 million 3D shapes had been sold overall making it the world's top-offering riddle amusement. It is broadly thought to be the world's top rated toy.
In a great Rubik's Cube, each of the six appearances is secured by nine stickers, each of one of six strong hues: white, red, blue, orange, green, and yellow. In right now sold models, white is inverse yellow, blue is inverse green, and orange is inverse red, and the red, white and blue are organized in a specific order in a clockwise game plan. On ahead of schedule shapes, the position of the hues fluctuated from 3D shape to solid shape. An inside turn system empowers every face to turn freely, in this way stirring up the hues. For the riddle to be settled, every face must be come back to have one and only shading. Comparable riddles have now been delivered with different quantities of sides, measurements, and stickers, not every one of them by Rubik.
Despite the fact that the Rubik's Cube achieved its stature of standard notoriety in the 1980s, it is still generally known and utilized. Numerous pace cubers keep on honing it and other twisty riddles and vie for the quickest times in different classes. Following 2003, The World Cube Association, the Rubik's Cube's global administering body, has composed rivalries worldwide and kept the official world records.


2. Solutions for 3x3 cube

There are numerous calculations to settle mixed Rubik's Cubes. The most extreme number of face swings expected to fathom any case of the Rubik's Cube is 20,and the greatest number of quarter turns is 26. These numbers are additionally the widths of the relating Cayley charts of the Rubik's Cube bunch. A calculation that illuminates a block in the base number of moves is known as God's calculation.
There are two basic approaches to quantify the length of an answer. The first is to check the quantity of quarter turns. The second is to tally the quantity of face turns. A move like F2 (a half turn of the front face) would be included as 2 moves the quarter turn metric and as just 1 turn in the face metric.








Fig1: A computer graphic of a scrambled Rubik's Cube

2.1 Move notation

To mean a grouping of proceeds onward the 3×3×3 Rubik's Cube, this article utilizes "Singmasternotation",which was created by David Singmaster.
The letters L,R,F,B,U,D show a quarter clockwise turn of the left, right, front, back, all over face individually. Half turns are demonstrated by attaching a 2. A quarter counterclockwise turn is shown by attaching a prime image ( ′ ).


2.2 Lower bounds

It can be demonstrated by tallying contentions that there exist positions requiring no less than 18 moves to tackle. To demonstrate this, first check the quantity of shape positions that exist altogether, and afterward tally the quantity of positions achievable utilizing at most 17 moves. Things being what they are the last number is littler.
This contention was not enhanced for a long time. Likewise, it is not a helpful verification: it doesn't show a solid position that needs this numerous moves. It was guessed that the supposed superflip would be a position that is exceptionally troublesome. A Rubik's Cube is in the superflip design when every corner piece is in the right position, yet every edge piece is inaccurately arranged. In 1992, an answer for the superflip with 20 face turns was found by Dik T. Winter, of which the negligibility was appeared in 1995 by Michael Reid, giving another lower bound to the width of the shape bunch. Additionally in 1995, an answer for superflip in 24 quarter turns was found by Michael Reid, with its insignificance demonstrated by Jerry Bryan. In 1998, another position requiring more than 24 quarter swings to comprehend was found. The position, which was known as a 'superflip created with four spot' needs 26 quarter turns.


2.3 Upper bounds

The principal upper limits depended on the "human" calculations. By joining the most pessimistic scenario situations for every part of these calculations, the run of the mill upper bound was observed to associate with 100.
Maybe the principal solid worth for an upper bound was the 277 moves specified by David Singmaster in mid 1979. He essentially checked the greatest number of moves required by his 3D shape explaining calculation. Later, Singmaster reported that ElwynBerlekamp, John Conway, and Richard Guy had concocted an alternate calculation that took at most 160 moves. Before long, Conway's Cambridge Cubists reported that the solid shape could be restored in at most 94 moves.


2.4 Thistlethwaite's algorithm

The achievement was found by Morwen Thistlethwaite; points of interest of Thistlethwaite's calculation were distributed in Scientific American in 1981 by Douglas Hofstadter. The ways to deal with the shape that prompt calculations with not very many moves depend on gathering hypothesis and on broad PC seeks. Thistlethwaite's thought was to separate the issue into sub issues. Where calculations up to that point separated the issue by taking a gander at the parts of the solid shape that ought to stay altered, he partitioned it by limiting the sort of moves you could execute. Specifically he isolated the 3D shape bunch into the accompanying chain of subgroups:

G0 = (L, R, F, B, U, D)
G1= (L, R, F, B, U2, D2)
G2 = (L, R, F2, B2, U2, D2)
G3 = (L2, R2, F2, B2, U2, D2)
G4= {1}

Next he arranged tables for each of the right storeroom spaces Gi+1\ Gi . For every component he found a succession of moves that took it to the following littler gathering. After these arrangements he functioned as takes after G0. An arbitrary 3D shape is in the general 3D square gathering. Next he found this component in the right storage room space G1\G0. He connected the comparing procedure to the 3D square. This took it to a block in   G1. Next he gazed upward a procedure that takes the 3D square to G2, G3 alongside lastly to  G4
Despite the fact that the entire solid shape gathering G0 is huge (~4.3×1019), the privilege closet spaces   G1\G0, G2\G1, G3\G2 and G3 are much littler. The wardrobe space  G2\G1 is the biggest and contains just 1082565 components. The quantity of moves required by this calculation is the entirety of the biggest procedure in every stride.

At first, Thistlethwaite demonstrated that any setup could be fathomed in at most 85 moves. In January 1980 he enhanced his system to yield a greatest of 80 moves. Later that same year, he decreased the number to 63, and after that again to 52. By comprehensively seeking the closet spaces it was later found that the most ideal number of moves for every stage was 7, 10, 13, and 15 giving an aggregate of 45 moves at most.

2.5 Kociemba's algorithm

Thistlethwaite's calculation was enhanced by Herbert Kociemba in 1992. He diminished the quantity of middle of the road gatherings to just two:

G0= (U, D, L, R, F, B)
G1= (U, D, L2, R2, F2, B2)
G2= {1}

Likewise with Thistlethwaite's Algorithm, he would look through the privilege closet space G1\G0 to take the 3D shape to assemble. Next he hunt the ideal arrangement down gathering G1. The pursuits in G1\G0 and  G1 were both finished with a strategy equal to IDA. The hunt in G1\G0 necessities at most 12 moves and the pursuit in G1 at most 18 moves, as Michael Reid appeared in 1995. By producing additionally imperfect arrangements that take the shape to gathering and searching for short arrangements in  G1, you typically get much shorter general arrangements. Utilizing this calculation arrangements are regularly found of less than 21 moves, however there is no evidence that it will dependably do as such.

In 1995 Michael Reid demonstrated that utilizing these two gatherings each position can be explained in at most 29 face turns, or in 42 quarter turns. This outcome was enhanced by SilviuRadu in 2005 to 40.

2.6 Korf's algorithm

Utilizing these gathering arrangements consolidated with PC inquiries will by and large rapidly give short arrangements. Be that as it may, these arrangements don't generally accompany a certification of their negligible. To hunt particularly down negligible arrangements another methodology was needed. In 1997 Richard Korf reported a calculation with which he had ideally unravelled irregular occasions of the shape. Of the ten arbitrary 3D shapes he did, none required more than 18 face turns. The technique he utilized is called IDA and is portrayed in his paper "Finding Optimal Solutions to Rubik's Cube Using Pattern Databases". Korf portrays this technique as takes after
IDA is a profundity first scan that searches for progressively more arrangements in a progression of emphases, utilizing a lower-bound heuristic to prune branches once a lower bound on their length surpasses the ebb and flow cycles bound.
It works generally as takes after. In the first place he distinguished various sub issues that are sufficiently little to be unravelled ideally. He utilized:
The solid shape limited to just the corners, not taking a gander at the edges
The solid shape limited to just 6 edges, not taking a gander at the corners nor at alternate edges.
The solid shape limited to the next 6 edges.
Plainly the quantity of moves required to take care of any of these sub issues is a lower headed for the quantity of moves you should tackle the whole 3D shape.
Given an irregular block C, it is understood as iterative developing. To start with all 3D shapes are produced that are the after-effect of applying 1 move to them. That is C * F, C * U, … Next, from this rundown, all 3D shapes are created that are the after-effect of applying two moves. At that point three moves etcetera. On the off chance that anytime a solid shape is found that needs an excess of moves in light of the upper limits to still be ideal it can be dispensed with from the rundown.
Despite the fact that this calculation will dependably discover ideal arrangements, there is no most pessimistic scenario examination. It is not known what number of moves this calculation may require. An execution of this calculation can be found here.


3. PROPOSED DIAGRAM

3.1 A  Schematic  Diagram  On  structure of the analyzer




3.2 Requirements
·         Data on prediction of 2-D picture
·         Data on history of all possible solution algorithms


3.3 Techniques used
·         Data Mining
·         R-Tool
·         Big data analytic


3.4 Description of the block diagram:

Step 1: The scrambled 3-D cube required for the puzzle is taken.

Step 2: A picture in 2-D is captured through any of the smart phones or tablets.

Step 3: The picture is uploaded to the “Rubik’s Cube solution analyzer”.

The analyzer analyses the possible solutions using R-tool.

Step 4: The “Step by step solution” is provided to the end users.

3.4 ALGORITHM USED

                                

The approach to solve the puzzle is to generate all possible descendants of the goal state in the form of a tree. For 3x3 puzzles we have 9! Permutations. Each configuration has exactly 9! /2 solutions.




4. CONCLUSION
       In conclusion we believe that out solution analyzer will be of great help to all the curious players of the Rubik’s cube. And also this has been of great help to learn more on the subject of R-tool.

5. REFERENCES



Bibliography



Ms. K. Bhuvana Meenakshi, UG scholar in Dhirajlal Gandhi College of Technology, Salem, Tamil Nadu, India. She has infinite curiosity in computer programming. Her major area of interests are Cloud Computing, Big data, Virtual Reality and Augmentation Reality. On the other hand hardware and system designing has also fascinated her. She has done many paper works and won “Best Paper Awards”.Besides these she is a state level awardee in Bharathanatyam (classical dance of Tamil Nadu ),holding a grade certificate degree from Annamalai University in the field of Bharatanatyam. She is a district level player in chess. And equally interested in writing poems and short stories.















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