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docs: fix grammatical errors
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README.md

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<p align="center"><img src="./docs/assets/auto_crate_push.gif" width=50%></p>
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- [**Level management**](docs/level_management.md):
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Levels and solutions are stored in a database.
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Levels and solutions are stored in the database.
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- [**Customizing**](docs/customizing.md):
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Options can be customized via configuration file.
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Supports moving and zooming the map. When switching levels, the zoom will be automatically adjusted to fit the window size.
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- **Player character animation**:
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Player character have smooth movement and movement animations in different directions.
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Player character has smooth movement and movement animations in different directions.
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- **Front-end and back-end separation**:
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Backend code (such as solvers) does not depend on frontend (such as Bevy).
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### Mouse
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| Key | Action |
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|---------------------------------------|------------------------------------------|
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| ------------------------------------- | ---------------------------------------- |
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| Click `Left` on player reachable area | Move the character to this position |
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| Click `Left` on a crate | Show the pushable area of the crate |
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| Click `Left` on crate pushable area | Push the selected crate to this position |
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| Hold `Right` and drag | Adjust viewport |
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| Click `Button 4` | Undo last push |
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| Click `Button 5` | Redo last push |
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| Click `Button 4` | Undo the last push |
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| Click `Button 5` | Redo the last push |
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| Scroll `Middle` | Zoom in/out |
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### Keyboard
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| Arrow keys | Move the character |
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| `[`/`]` | Switch to the previous/next level |
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| `Ctrl` + `[`/`Ctrl` + `]` | Switch to the previous/next unsolved level |
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| `Ctrl` + `Z` | Undo last push |
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| `Ctrl` + `Shift` + `Z` | Redo last push |
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| `Ctrl` + `Z` | Undo the last push |
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| `Ctrl` + `Shift` + `Z` | Redo the last push |
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| `Esc` | Reset current level |
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| `-`/`=` | Zoom in/out |
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| `Ctrl` + `V` | Import levels from clipboard |
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### Keyboard (Vim)
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| Key | Action |
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|-----------------|-----------------------------------|
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| `H`/`J`/`K`/`L` | Move the character |
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| `U` | Undo last push |
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| `Ctrl` + `R` | Redo last push |
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| Key | Action |
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| --------------- | ------------------ |
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| `H`/`J`/`K`/`L` | Move the character |
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| `U` | Undo the last push |
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| `Ctrl` + `R` | Redo the last push |
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### Controller
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| Key | Action |
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| -------------- | --------------------------------- |
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| D-Pad | Move the character |
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| `LB`/`RB` | Switch to the previous/next level |
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| `B`/`Circle` | Undo last push |
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| `A`/`Cross` | Redo last push |
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| `B`/`Circle` | Undo the last push |
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| `A`/`Cross` | Redo the last push |
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| `LT`/`RT` | Zoom in/out |
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| Right stick | Adjust viewport |
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| `X`/`Square` | Toggle instant move[^1] |

docs/auto_move.md

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<p align="center"><img src="assets/auto_crate_push.gif" width=70%></p>
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This feature can provide good assistance when users play larger levels.
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At the same time, it also retains the traditional control method.
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This feature can significantly assist users when playing larger levels.
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At the same time, it also maintains the traditional control method.
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Clicking on a crate will display all the points that the crate can reach (without moving other crates).
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Clicking on one of the points will automatically push the selected crate to that position.
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In this case, user can click on the target, and the character will automatically push the selected crate to the target to complete the level.
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In this case, the user can click on the target, and the character will automatically push the selected crate to the target to complete the level.
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Some areas where the crates are reachable do not display points. This is because pushing the crate to those positions will lead to a deadlock and the player will be unable to continue completing the level.
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## Controversial
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This feature is a bit controversial, with some people saying it's akin to cheating.
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This feature is a bit controversial, with some users saying it's akin to cheating.
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For simple levels, this does significantly reduce the level difficulty. An extreme example is a level with only a single crate and target, which means the player can complete it without having to do any reasoning.
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But for complex levels, the difficulty mainly lies in the complex pushing relationship between multiple crates, rather than the pushing of a single crate. This feature allows players to focus on more complex reasoning instead of repeating the simple work of pushing a single crate.
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But for challenging levels, the difficulty mainly lies in the intricate pushing relationship between multiple crates, rather than the pushing of a single crate. This feature allows players to focus on more complex reasoning instead of repeating the simple work of pushing a single crate.
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In addition, this feature is **optional**. Users can still use the traditional control methods.

docs/customizing.md

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## Configuration
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User can configure settings by editing `config.toml` in the same directory. If the file does not exist, a default configuration file will be automatically generated when the program is run.
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The user can configure settings by editing `config.toml` in the same directory. If the file does not exist, a default configuration file will be automatically generated when the program is run.
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```toml
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# Player movement animation speed, seconds per step.
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## Keymap
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User can configure keymap by editing `keymap.toml` in the same directory. If the file does not exist, a default keymap configuration file will be automatically generated when the program is run.
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The user can configure keymap by editing `keymap.toml` in the same directory. If the file does not exist, a default keymap configuration file will be automatically generated when the program is run.

docs/level_management.md

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Supports importing levels in XSB format (support run-length encoding) from files or system clipboard:
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- Import from file: User can drag single or multiple level files in XSB format into the window.
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- Import from clipboard: If the level in XSB format is already in the clipboard, it can be imported by input action.
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- Import from files: The user can drag single or multiple level files in XSB format into the window.
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- Import from clipboard: If some levels in XSB format is already in the clipboard, it can be imported using the input action.
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The levels will be standardized first to prevent repeated import of the same or similar levels. The standardized levels are only used for deduplication, and the final imported levels are not standardized.
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The levels will first be standardized to prevent repeated import of the same or similar levels. The standardized levels are only used for deduplication, and the final imported levels are not standardized.
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Levels that meet the following conditions are considered similar:
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docs/solver.md

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<p align="center"><img src="assets/auto_solve.gif" width=70%></p>
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The solver can automatically solve simple levels.
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The solver can automatically solve levels of moderate complexity.
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## Strategy
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## Lower bound calculation method
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- `MinimumPush`: Minimum push count to nearest target.
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- `MinimumMove`: Minimum move count to nearest target. (Slow, especially on maps with many crates or large areas)
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- `ManhattanDistance`: Manhattan distance to nearest target. (Fast, suitable for maps with many crates or large areas)
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- `MinimumMove`: Minimum move count to nearest target. (This method is slow, especially on maps with many crates or large areas)
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- `ManhattanDistance`: Manhattan distance to nearest target. (This method is fast, suitable for maps with many crates or large areas)
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## Optimization
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- Deadlocks detection.
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- Dead square deadlocks.
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- Freeze deadlocks.
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- Detects dead square deadlocks.
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- Detects freeze deadlocks.
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- Tunnels detection.
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## Statistics
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CPU : 13th Gen Intel(R) Core(TM) i9-13900HX (Base speed: 2.20 GHz).
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Threads : 1.
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Time limit: 10 sec.
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Time limit: 10 seconds.
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| Collection | Total | Solved |
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| ------------------- | ----- | ------ |
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## Visualization
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Supports visualization of the automatic solution process. This feature can be used to intuitively view the working status of the solver.
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Supports visualizing the automatic solution process. This feature can be used to intuitively view the working status of the solver.
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- Displays the optimal state obtained by the current solver.
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- Display the lower bound as a heat map.

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