Added new question: quantum-conveyor-belts

Author: TianLangHin

competition/quantum-conveyor-belts/.gitignore

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+/target

competition/quantum-conveyor-belts/Cargo.lock

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+[package]
+name = "quantum-conveyor-belts"
+version = "0.1.0"
+edition = "2024"
+
+[dependencies]
+rand = "0.9.1"
+rand_chacha = "0.9.0"
+regex = "1.11.1"

competition/quantum-conveyor-belts/Cargo.toml

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+---toml
+[fuzz]
+exec = ["cargo", "run", "--release", "--", "generate"]
+env = {}
+
+[judge]
+exec = ["cargo", "run", "--release", "--quiet", "--", "validate"]
+
+[problem]
+points = 20
+difficulty = 3
+---
+
+# ⚛️ Quantum Conveyor Belts?!
+
+A higher-dimensional being has dropped you into a maze of conveyor belts!
+These conveyor belts connect stations together,
+each station being marked by a unique 3-letter identifier.
+You currently find yourself situated in one such station.
+
+You notice that some conveyor belts are activated by pressing
+a key labelled with a letter, while others are always active.
+You are also told that when emerging from the end of a conveyor belt,
+you may emerge in one of several possible stations.
+*It's also possible for a key press to lead you nowhere,
+since some conveyor belts are seemingly unavailable.*
+
+While you look around trying to see if there is a way out,
+a loud echoing bout of laughter rings throughout the maze.
+"The only way out of here is to answer my question correctly," it booms.
+**"Every time you tap on a key labelled with a letter, the set of possible stations
+you could be in changes. How many such sets are impossible for you to achieve?"**
+
+Although this question sounds intimidating, you know that the higher-dimensional being
+is never directly observing you, but rather only keeping track of your key presses.
+This means that the "set of possible stations" it refers to always refers to
+every single station you *could* possibly be in, even if you know that you aren't in it.
+
+For the sake of simplicity, let's call such sets "superpositions".
+
+### Small Example
+
+Here's a small example to demonstrate the question being asked.
+Consider the following layout of conveyor belts and stations,
+where you start your journey in the `aaa` station.
+In this setup, there are only two kinds of letters that will appear: `x` and `y`.
+```
+aaa: drift(bbb); x(bbb, ccc); y(ccc)
+bbb: drift(); x(); y(ddd)
+ccc: drift(ddd); x(); y(bbb)
+ddd: drift(ccc); x(); y(ccc)
+```
+
+Before you press any key, you can take a conveyor belt for free to go to station `bbb`.
+Thus, the very first superposition you reach is the set `{aaa, bbb}`.
+
+If you are in station `aaa`, pressing the `x` key on the conveyor belt
+will either land you in station `bbb` or `ccc`.
+If you are in station `bbb`, pressing the `x` key on the conveyor belt lands you nowhere.
+
+However, `{bbb, ccc}` is *not* the superposition we end up with after pressing `x`!
+It is possible to move on a conveyor belt for free from station `ccc` to `ddd`.
+Hence, the actual superposition after pressing `x`
+from the `{aaa, bbb}` superposition is `{bbb, ccc, ddd}`.
+
+Then, from the superposition `{aaa, bbb}`, pressing the `y` key lands you in
+the station `ccc` (if starting from `aaa`), or the station `ddd` (if starting from `bbb`).
+It is possible to hop onto conveyor belts for free from those stations,
+but you only ever reach `ccc` or `ddd`.
+Hence, the superposition after pressing `x` from the `{aaa, bbb}` superposition is `{ccc, ddd}`.
+
+Note that the superposition `{ccc, ddd}` is different from `{bbb, ccc, ddd}`.
+In fact, every different combination of stations (ignoring order)
+is considered a different superposition of its own.
+
+Continuing down this line, we find that from the superposition `{ccc, ddd}`,
+if you press the `x` key, you actually end up *nowhere*!
+Funnily enough, this is still a valid superposition. Let's denote this as `{}`.
+
+Meanwhile, if you press the `y` key from the superposition `{ccc, ddd}`,
+you end up in the superposition `{bbb, ccc, ddd}`
+(`ddd` is reached by "drifting" from `ccc` after moving to it from `bbb`).
+
+Then, from the `{bbb, ccc, ddd}` superposition,
+if you press the `x` key, you reach `{}` again.
+Meanwhile, if you press the `y` key, you will go back to `{bbb, ccc, ddd}`.
+
+In this example, there are no more new superpositions that can be reached.
+Thus, the only 4 reachable superpositions are `{aaa, bbb}`, `{bbb, ccc, ddd}`, `{ccc, ddd}`, and `{}`.
+This means that the there are **12 unreachable** superpositions, as follows:
+```
+{aaa}, {bbb}, {ccc}, {ddd},
+{aaa, ccc}, {aaa, ddd}, {bbb, ccc}, {bbb, ddd},
+{aaa, bbb, ccc}, {aaa, bbb, ddd}, {aaa, ccc, ddd}, {aaa, bbb, ccc, ddd}.
+```
+
+## Input
+
+The input will be a map of all the stations and the conveyor belts connecting them,
+with each line in the input representing the outgoing conveyor belts from a single station.
+
+The first line will always be the station (not superposition) that you start your journey in.
+
+The format of each line is as follows:
+```
+<station name>: drift(<comma-separated list of stations>); <letter>(<list of stations>); ...
+```
+For example,
+```
+aju: drift(bkv); a(bkv, clw); b(clw)
+```
+means that from the station `aju`, you can move to station `bkw` for free
+(but this does not mean you can move from `bkw` to `aju` for free).
+
+If you press the `a` key in `aju`, you may end up either in `bkv` or `clw`.
+If you press the `b` key in `aju`, you will end up in `clw`.
+
+### Constraints
+* There are at most 32 stations in the map.
+* You always start in the state described by the very first line in the prompt.
+* Every line will contain exactly the same number of letter transitions.
+  (i.e., if the first line shows transitions for letters `p`, `q` and `r`,
+  all other lines are guaranteed to show the same letters.)
+
+### Example
+
+Here's another example of the question input.
+```
+aju: drift(bkv); a(bkv, clw); b(clw)
+bkv: drift(dmx); a(bkv); b(bkv)
+clw: drift(); a(eny); b(bkv)
+dmx: drift(); a(); b(eny)
+eny: drift(dmx); a(aju, dmx); b(bkv, clw)
+```
+
+Here, you start your journey in the `aju` station,
+but in fact your first reachable superposition is `{aju, bkv, dmx}`
+since you can take two conveyor belts for free to reach `bkv` and then `dmx` respectively,
+before registering a single key press.
+
+## Output
+
+The output will be a single integer, which is how many of the possible superpositions
+in the maze are *unreachable*.
+(The integer is to be given without spacing or commas in between.)
+
+In the above example, there are 6 *reachable* superpositions:
+* `{aju, bkv, dmx}`
+* `{bkv, clw, dmx}`
+* `{aju, bkv, clw, dmx}`
+* `{bkv, dmx, eny}`
+* `{aju, bkv, dmx, eny}`
+* `{bkv, clw, dmx, eny}`
+
+Therefore, in this example, there are 26 *unreachable* superpositions, and the output should be
+```
+26
+```