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A water sort solver needs more than a way to shuffle colors: it must represent tube contents, enforce the game’s pour rules, and search the resulting board states. In Kang Wang’s tutorial, a roughly 300-line, single-file JavaScript solver uses a heuristic-guided search first and a breadth-first fallback when it cannot find a solution. The heuristic can help prioritize states, but it does not guarantee the shortest solution. The fallback can establish that a level is impossible only if it exhausts every reachable state before reaching its 300,000-state cap.
How the solver represents a board
The board is a shelf: an array of tubes, with each tube represented as an array of color indexes. The final element in a tube array is its top layer. That convention makes the basic operations intuitive: removing the last element takes liquid from the top, and adding an element puts liquid on top.
For example, a tube represented as [0, 1, 1] has color 0 at the bottom and a two-layer run of color 1 at the top. A pour can remove that contiguous top run and add it to another tube, rather than moving only one layer. This is the move semantics indicated by the tutorial’s topRun and pourBlock code; other water sort games may define pours differently.
Which pours are legal?
Search should only consider moves allowed by the game. For a block pour, the solver must identify the contiguous run of the top color, then check the destination before changing either tube. The destination must have enough free capacity for the run, and its top color must match the poured color unless the destination is empty.
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- Source: It must contain liquid to pour.
- Destination: It must not be the source itself, must have free capacity for the block, and must be empty or have the same color at its top.
- Completed tube: A tube already filled with one color is complete; treating it explicitly avoids wasting moves by disturbing a solved tube.
- Empty tube: It can accept a block if it has room, subject to the game’s rules and the solver’s handling of symmetry between empty tubes.
These checks define the state graph. Each valid board is a state, and every legal pour is an edge to another state. Accurate rules matter: a search result only applies to the modeled rules, not necessarily to a game whose pour behavior differs.
How heuristic-guided search works
The solver estimates how disordered a board is by counting color boundaries within tubes and counting how many extra tubes contain each color. A tube such as [0, 1, 1] has one internal boundary, between 0 and 1. If a color is spread across several tubes, consolidating it also contributes to the estimate.
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The estimate guides the search toward states that appear closer to sorted. It is not admissible: one pour can remove more than one boundary or reduce the spread of a color at once, so the estimate can overstate the remaining work. Consequently, a solution found by this search is not guaranteed to use the fewest pours.
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What the breadth-first fallback can prove
The fallback breadth-first search explores reachable states in increasing order of pour count. If it finds a sorted board, that path has the fewest pours among the states the search considers, because BFS visits shallower states first. If it exhausts the queue without finding a sorted board, then no solution exists under the modeled rules and entered starting position.
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The fallback is limited to 300,000 states. That figure is a configured search cap, not a speed test, a puzzle-difficulty rating, or a guarantee that any particular level will finish. If the search reaches the cap before it finds a solution or empties the queue, the correct result is unknown, not “impossible.” A complete impossibility result also depends on entering the level accurately; a mistyped board can make a solvable game appear unsolvable.
How A* and BFS differ
Other implementations illustrate different trade-offs rather than proving that one approach is always faster. The Octo Go solver describes an A* heuristic based on color transitions and bottom-color distribution, and says its A* search returns optimal solutions. A browser-based solver describes BFS as exploring by pour depth to find a fewest-pour solution. These are project descriptions, not controlled performance comparisons.
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| Approach | Shortest-path guarantee | What a limit or pruning means | Practical trade-off |
|---|---|---|---|
| Heuristic-guided search in Wang’s tutorial | No guarantee: its heuristic is not admissible. | The tutorial’s BFS fallback has a 300,000-state cap; hitting it leaves the result unknown. | Uses an estimate of color breaks and color distribution to direct search. |
| Breadth-first search | Finds a fewest-pour path if it finds a goal, since states are visited by increasing depth. | Impossibility is established only when the queue is exhausted; a state cap reached first leaves the result unknown. | Conceptually straightforward, but may need to retain many reachable states. |
| A* as described by the Octo Go project | The project says its A* solver returns optimal solutions. | Optimality depends on the algorithm’s assumptions and any pruning or limits; project descriptions alone do not establish performance for other puzzles. | Uses a heuristic involving color transitions and bottom-color distribution. |
Memory use and explored-state counts depend on the puzzle and implementation. The available project descriptions do not provide a controlled benchmark that would support a universal speed ranking. Pruning also deserves scrutiny: removing duplicate states can avoid repeated work, but any pruning rule that discards potentially useful states can affect completeness or optimality.
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Kang Wang’s article presents the solver as a dependency-free, one-file JavaScript program under the MIT license that runs in a browser or Node. Those are claims made by the tutorial; its current repository contents and compatibility are not independently established here. The stated size of about 300 lines describes the project’s scale, not its performance.
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