You release pieces one stripe at a time by randomizing within each "stripe" set. Once a "stripe" is finished, start a new stripe. choose the widths randomly based on the available remaining room. The idea is that you "stripe" the puzzle. Below are 4x4s, a 5x4, and even a 10x4 example. Choose randomly from the different configurations to fill up the width of the puzzle (samples below, but there are many, many configurations). Each of these units is composed of a set number of pieces that fit together to form squares or rectangles which are much easier to fill into a puzzle. Rather than focusing on the entire puzzle, break it into smaller, uniform units.
It's not as pure as the more complex solutions, but has the distinct advantage of being much easier to implement and works every time. Here's a technique we've used in the past to cheat a bit on more confined hardware.
All tetris blocks free#
Here are some typical outputs:įeel free to ask if you're having trouble with the implementation (I might even have a Python quick and dirty implementation lying around somewhere.) The algorithm works for any set of (convex) shapes.Īlso, an interesting aspect of a uniform random generation is that it ensures maximal diversity between consecutive generations (but you can also constrain the generation in any way you want). The key thing here is that is to start by precomputing the allowed alternatives for each state of the upper-strip, so that you no longer pay for the combinatorial explosion when you generate the regions. The idea is similar to the one described by David above, and focuses on the upper strip, placing pieces that do not create holes. D) time/space ( D being the longest dimension of an individual shape, eg 4 in the case of Tetris pieces). This article (page 11-13, disclaimer: I'm one of the authors) describes an algorithm that uses dynamic programming to uniformly generate perfectly tiled rectangular regions of width w and height h, in time which is linear in h after a preprocessing that takes about 2 ( w. => Dahlke has solved quite a few rectangles filled with identical pieces (a particularly rare tiling form) => Golomb originally coined the term "Polyomino" Or, equivalently, build a solution that favors those smaller pieces. One way to make a puzzle "easier" could be to trade bigger pieces for more smaller pieces like monominoes and dominoes, since this will leave more ways to fill in the last holes.
If a given grid/piece set doesn't meet your criteria, that is, it backtracked all the way without finishing, try a different rectangle and piece set. When you reach a state you don't like (dead end, too many small pieces, or what not) then backtrack. Perhaps check first large allowed pieces, and resort to smaller ones if necessary. Find the first open cell (numbered L-R, T-B) and try to put in your allowed pieces in their allowed orientations (8 orientations for an asymmetric piece if you allow flipping). Or rather, include some small pieces in your allowed set of pieces.Īs for solving/laying out the pieces, a typical brute force approach is to fill it from left to right, then top to bottom. Then throw in enough single-squares to fill it out, and you have guaranteed that there is at least one solution. Take a few pieces you like, and fill the puzzle however you want. However, if you're building puzzles and can control the pieces, it's the opposite, constructive problem, and easier.īuild a solution constructively. This is a known hard problem, determining what rectangles can be tiled with certain pieces.
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