In dynamic programming, you find some sort of "step" that takes you possibly closer to your solution, and keep track of the results of each step in a big matrix. To get a faster solution than exhaustive search, I think what you want is probably dynamic programming. Note that the speed of your search is going to greatly depend on how tight your Upper Bound is and how tight your Lower Bound is. Once you have these two functions you can apply standard Bound and Branch search. You can do this several times taking the highest lower bound that you get. When your calculating U(S) for a given S it should go quicker if you choose higher K (the conditions are relaxed) so choosing the value of K will be a trade of for quickness of finding U(S) and quality (how tight an upper bound U(S) is.)įor the L(S) function calculate the score that you would get if you simply randomly kept click until you got to a state that could not be solved any further. You need two functions U(S) and L(S) that compute a lower and upper bound respectively of a given state S.įor the U(S) function I'm thinking calculate the score that you would get if you were able to freely shuffle K bubbles in the board (each move) and arrange the blocks in such a way that would result in the highest score, where K is a value you choose yourself. Given a state of the game S, you branch on S by breaking it up in m sets Si where each Si is the state after taking a legal move of all m legal moves given the state S I'm thinking you could try a branch and bound search with the following idea: Thanks to David Locke for posting the paper link which talks above a window solver which uses a constant-depth lookahead heuristic. But trending towards larger and larger bubbles groups seems to be one approach I don't seen any obvious way to divide and conquer. What other approaches could yield high scores besides the exhaustive search? Memoization table grows to 5,692,482 boards, and hits 6,713,566 times. The solver rate is ~3k-4k boards/sec and gradually decreases as the memoization search takes longer. A (3,15,5) board takes 12,384,726 boards in 50 minutes on a server. I create a prototype in python which shows a (2,15,5) board takes 8859 boards to solve in about 3 seconds. Once a board is solved we store the board and the best score in a memoization table. Some of the ideas I am using include normalized memoization. Once the bubble group is picked, we create a new board and try to solve that board, recursively descending down The first algorithm is a simple exhaustive recursive algorithm which explores going through the board row by row and column by column picking bubble groups. A bubble group score = n * (n - 1) where n is the number of bubbles in the bubble group.When a group is picked, the bubbles disappear, any holes are filled with bubbles from above first, ie shift down, then any holes are filled by shifting right. ![]() A bubble group is 2 or more bubbles of the same color that are adjacent to each other in either x or y direction.The goal is to get the highest score by picking the sequence of bubble groups that ultimately leads to the highest score.The random (N,M,C) board consists N rows x M columns with C colors.If you’d like to find out more about the studio you can read our interview here.For a mental exercise I decided to try and solve the bubble breaker game found on many cell phones as well as an example here: Bubble Break Game The hobbyist games developers formerly served in the Israeli army before turning their passion into their work in 2013. The origin of the team behind Ilyon is atypical. "While we will celebrate reaching 50 million downloads, our focus continues to remain on creating engaging, fun and exciting games for our users." "The popularity of Bubble Shooter has been so exciting for our team to see and we are extremely grateful to all of our fans," said Ilyon CEO Yonatan Erez. ![]() The title currently features over 2,000 levels along with a colourblind mode and daily rewards. ![]() Ilyon’s Bubble shooter takes influences from the popular 90s arcade video game of the same name and plays like a classic shooter with the added twist that players need to match at least three bubbles of the same colour to pop them. The Israel-based mobile games developer originally acquired the IP from online games company Absolutist in 2015, which had initially launched the game on Flash websites in 2002. Ilyon Dynamics’ free-to-play puzzle game Bubble shooter has surpassed the 50 million download mark on Android and iOS collectively.
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