You are given a code snippet that imports and exports various queues. Your task is to implement three different queue classes - `StateOrderQueue`, `TopOrderQueue`, and `TrivialQueue`. Each queue class is represented as a separate module and should be implemented according to the following specifications:

1. `StateOrderQueue`: This queue should follow the FIFO (First-In-First-Out) principle. It should maintain the order in which elements are added and provide the following methods:
   - `new()`: Constructs a new empty `StateOrderQueue` object.
   - `push(&mut self, item: T)`: Inserts the given item at the back of the queue.
   - `pop(&mut self) -> Option<T>`: Removes and returns the item from the front of the queue. Returns `None` if the queue is empty.

2. `TopOrderQueue`: This queue should follow the LIFO (Last-In-First-Out) principle. It should maintain the order in which elements are added and provide the following methods:
   - `new()`: Constructs a new empty `TopOrderQueue` object.
   - `push(&mut self, item: T)`: Inserts the given item at the top of the queue.
   - `pop(&mut self) -> Option<T>`: Removes and returns the item from the top of the queue. Returns `None` if the queue is empty.

3. `TrivialQueue`: This queue should only store a single item at a time. It should provide the following methods:
   - `new()`: Constructs a new empty `TrivialQueue` object.
   - `push(&mut self, item: T)`: Inserts the given item. If the queue already contains an item, it should replace it with the new item.
   - `pop(&mut self) -> Option<T>`: Removes and returns the item from the queue. Returns `None` if the queue is empty.

Your task is to implement these three queue classes (`StateOrderQueue`, `TopOrderQueue`, and `TrivialQueue`) with their respective methods.
user
Sure, I'd be happy to help you with that. Here's a TypeScript implementation of the queues you've requested in a module called `Queue`.

```typescript
/**
 * A queue that follows the FIFO (First-In-First-Out) principle.
 */
class StateOrderQueue<T> {
  private items: T[] = [];

  constructor() {}

  /**
   * Inserts the given item at the back of the queue.
   *
   * @param item - The item to be inserted.
   */
  push(item: T): void {
    this.items.push(item);
  }

  /**
   * Removes and returns the item from the front of the queue.
   *
   * @returns The item at the front of the queue.
   * @throws An error if the queue is empty.
   */
  pop(): T {
    if (this.isEmpty()) {
      throw new Error('Queue is empty');
    }

    return this.items.shift()!;
  }

  /**
   * Returns true if the queue is empty, false otherwise.
   *
   * @returns True if the queue is empty, false otherwise.
   */
  isEmpty(): boolean {
    return this.items.length === 0;
  }
}

/**
 * A queue that follows the LIFO (Last-In-First-Out) principle.
 */
class TopOrderQueue<T> {
  private items: T[] = [];

  constructor() {}

  /**
   * Inserts the given item at the top of the queue.
   *
   * @param item - The item to be inserted.
   */
  push(item: T): void {
    this.items.unshift(item);
  }

  /**
   * Removes and returns the item from the top of the queue.
   *
   * @returns The item at the top of the queue.
   * @throws An error if the queue is empty.
   */
  pop(): T {
    if (this.isEmpty()) {
      throw new Error('Queue is empty');
    }

    return this.items.pop()!;
  }

  /**
   * Returns true if the queue is empty, false otherwise.
   *
   * @returns True if the queue is empty, false otherwise.
   */
  isEmpty(): boolean {
    return this.items.length === 0;
  }
}

/**
 * A queue that only stores a single item at a time.
 */
class TrivialQueue<T> {
  private item: T | undefined;

  constructor() {}

  /**
   * Inserts the given item. If the queue already contains an item, it should replace it with the new item.
   *
   * @param item - The item to be inserted.
   */
  push(item: T): void {
    this.item = item;
  }

  /**
   * Removes and returns the item from the queue.
   *
   * @returns The item in the queue.
   * @throws An error if the queue is empty.
   */
  pop(): T {
    if (this.item === undefined) {
      throw new Error('Queue is empty');
    }

    const temp = this.item;
    this.item = undefined;
    return temp;
  }

  /**
   * Returns true if the queue is empty, false otherwise.
   *
   * @returns True if the queue is empty, false otherwise.
   */
  isEmpty(): boolean {
    return this.item === undefined;
  }
}
```

You can import these classes from the `Queue` module using `import { StateOrderQueue, TopOrderQueue, TrivialQueue } from './Queue';`.
assistant
You are given a code snippet that imports and exports various queues. Your task is to implement three different queue classes - `StateOrderQueue`, `TopOrderQueue`, and `TrivialQueue`. Each queue class is represented as a separate module and should be implemented according to the following specifications:

1. `StateOrderQueue`: This queue should follow the FIFO (First-In-First-Out) principle. It should maintain the order in which elements are added and provide the following methods:
   - `new()`: Constructs a new empty `StateOrderQueue` object.
   - `push(&mut self, item: T)`: Inserts the given item at the back of the queue.
   - `pop(&mut self) -> Option<T>`: Removes and returns the item from the front of the queue. Returns `None` if the queue is empty.

2. `TopOrderQueue`: This queue should follow the LIFO (Last-In-First-Out) principle. It should maintain the order in which elements are added and provide the following methods:
   - `new()`: Constructs a new empty `TopOrderQueue` object.
   - `push(&mut self, item: T)`: Inserts the given item at the top of the queue.
   - `pop(&mut self) -> Option<T>`: Removes and returns the item from the top of the queue. Returns `None` if the queue is empty.

3. `TrivialQueue`: This queue should only store a single item at a time. It should provide the following methods:
   - `new()`: Constructs a new empty `TrivialQueue` object.
   - `push(&mut self, item: T)`: Inserts the given item. If the queue already contains an item, it should replace it with the new item.
   - `pop(&mut self) -> Option<T>`: Removes and returns the item from the queue. Returns `None` if the queue is empty.

Your task is to implement these three queue classes (`StateOrderQueue`, `TopOrderQueue`, and `TrivialQueue`) with their respective methods.
user
Sure, I can help you implement these queue classes in Rust. Here's how you might do it:

```rust
// StateOrderQueue.rs
pub struct StateOrderQueue<T> {
    queue: Vec<T>,
}

impl<T> StateOrderQueue<T> {
    pub fn new() -> Self {
        StateOrderQueue { queue: Vec::new() }
    }

    pub fn push(&mut self, item: T) {
        self.queue.push(item);
    }

    pub fn pop(&mut self) -> Option<T> {
        self.queue.pop(0)
    }
}
```

```rust
// TopOrderQueue.rs
pub struct TopOrderQueue<T> {
    queue: Vec<T>,
}

impl<T> TopOrderQueue<T> {
    pub fn new() -> Self {
        TopOrderQueue { queue: Vec::new() }
    }

    pub fn push(&mut self, item: T) {
        self.queue.push(item);
    }

    pub fn pop(&mut self) -> Option<T> {
        self.queue.pop()
    }
}
```

```rust
// TrivialQueue.rs
pub struct TrivialQueue<T> {
    item: Option<T>,
}

impl<T> TrivialQueue<T> {
    pub fn new() -> Self {
        TrivialQueue { item: None }
    }

    pub fn push(&mut self, item: T) {
        self.item = Some(item);
    }

    pub fn pop(&mut self) -> Option<T> {
        self.item.take()
    }
}
```

Each of these queue classes is implemented as a struct with a `Vec<T>` or `Option<T>` field, and the methods are implemented using the methods provided by `Vec` and `Option`. The `StateOrderQueue` and `TopOrderQueue` use a `Vec` to store their items, and `push` and `pop` correspond to `Vec::push` and `Vec::pop` (or `Vec::pop(0)` for `StateOrderQueue` to maintain FIFO order). The `TrivialQueue` uses an `Option` to store its single item, and `push` and `pop` correspond to setting the item with `Some` and removing it with `take`, respectively.
assistant