Rewrite presentation draft to essay

I wrote a presentation draft and I need it to translate to a professionally essay. I’ve attached my presentation draft and the slides I used in presentation. Also the original reference I used named《a simple and rapid lights-up solver》are also provided. My draft is basically summarized from that and I need a more academically paper. It is better to rewrite my draft by reading and summarized the original reference and combine them together.a solver that mix pattern matching method with elimination search to solve Lights-up puzzles. First, the pattern matching method is used to solve some parts of puzzle in a very short time. Then, the elimination search method is applied to solve the part in which the former method cannot be applied. This algorithm can correctly solve Lights-up problems of 25*25 fast and efficient.

 

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Pattern matching is basically finding the tricks and rules. And use the rules to set up the lights.Each pattern can be used several times until there is no new places. The white cells are temporarynotlighten, and the yellow cells are the cells already lights up. The yellow cells are not allow to put any light on it.

 

Pattern 1 is telling us theblackcellswithnumberonitshould equal tothenumberofbulbsneed toplacearoundit.(ifthenumberis0,nolightbulbsallow). For example. This 7*7 puzzle has black cells with 3 on the top left, it means we have to place 3 bulbs around it and fortunately we only got 3 white to place. And for the two black cells with 0, let’s put “X” around them. (next slide)Then we can see for the black 2 and black 1 on the bottom left corner can easily place their bulbs, Same to the black 2 on the top right. After that we notice pattern 1 can give no more help.

 

(next slide) now its pattern 2, it shows ifonewhitecell”y”canonlybelightenbyanotherwhitecell”z”.“z”mustplaceabulb (” z”canbeyitself). In this case, we are aware that only this white cell can light up the cell on its right. And for this, the cell can only be lightened with put a blub on itself. (next slide) and for the following we do the same things.

 

(next slide)pattern 3 means IfonewhitecellAcannotplaceabulbitself,and its diagonalarealsonotallowabulb. And in this situation, we can see cell A is Definity can’t light itself and only cell B&C can light it up. So, if we put a light bulb in position D, both B&C can be lightened. Hence, we can make sure there is no bulb in D.

 

(next slide)nowwe have pattern 4, it shows us iftheblackcellsareinthecorner,itsdiagonalcannotplacebulb.Allfourdiagonalsforcellswithnumber3&4can’thavebulbs. In figure one, we know only B&C can put light bulb in it. Then position D cannothave bulb, from this rule, we can get all the diagonals for cell with number 3 and 4 are not allow any bulbs. For this case, after we use two times of pattern 4, we figure out the place which cannot have blubs.

The use of all these four patterns is with no restriction and order. We can use it again and again until no more clues we can have.

 

(next slide)About elimination search, it should be more appropriate to call it an assumption. After we use all the patterns but still not lighten all the cells. Then we are going to assume one of the white cells can place with blub and after that we are keep using patterns until paradox exist. If there this no paradox, then we are done.

Let’s see, if position m has bulbs, then we can get light all the cells up for the bottom left area. If we choose n as the place with bulb, we can see this cell will never be lightened.

 

 

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