Maze/Labyrinth Generation


About this tutorial

This tutorial is free and open source, and all code uses the MIT license - so you are free to do with it as you like. My hope is that you will enjoy the tutorial, and make great games!

If you enjoy this and would like me to keep writing, please consider supporting my Patreon.


A mainstay of dungeon crawl games is the good old-fashioned labyrinth, often featuring a Minotaur. Dungeon Crawl: Stone Soup has a literal minotaur labyrinth, Tome 4 has sand-worm mazes, One Knight has an elven hedge maze. These levels can be annoying for the player, and should be used sparingly: a lot of players don't really enjoy the tedium of exploring to find an exit. This chapter will show you how to make a labyrinth!

Scaffolding

Once again, we'll use the previous chapter as scaffolding - and set our "random" builder to use the new design. In map_builders/maze.rs, place the following code:


#![allow(unused_variables)]
fn main() {
use super::{MapBuilder, Map,  
    TileType, Position, spawner, SHOW_MAPGEN_VISUALIZER,
    remove_unreachable_areas_returning_most_distant, generate_voronoi_spawn_regions};
use rltk::RandomNumberGenerator;
use specs::prelude::*;
use std::collections::HashMap;

pub struct MazeBuilder {
    map : Map,
    starting_position : Position,
    depth: i32,
    history: Vec<Map>,
    noise_areas : HashMap<i32, Vec<usize>>
}

impl MapBuilder for MazeBuilder {
    fn get_map(&self) -> Map {
        self.map.clone()
    }

    fn get_starting_position(&self) -> Position {
        self.starting_position.clone()
    }

    fn get_snapshot_history(&self) -> Vec<Map> {
        self.history.clone()
    }

    fn build_map(&mut self)  {
        self.build();
    }

    fn spawn_entities(&mut self, ecs : &mut World) {
        for area in self.noise_areas.iter() {
            spawner::spawn_region(ecs, area.1, self.depth);
        }
    }

    fn take_snapshot(&mut self) {
        if SHOW_MAPGEN_VISUALIZER {
            let mut snapshot = self.map.clone();
            for v in snapshot.revealed_tiles.iter_mut() {
                *v = true;
            }
            self.history.push(snapshot);
        }
    }
}

impl MazeBuilder {
    pub fn new(new_depth : i32) -> MazeBuilder {
        MazeBuilder{
            map : Map::new(new_depth),
            starting_position : Position{ x: 0, y : 0 },
            depth : new_depth,
            history: Vec::new(),
            noise_areas : HashMap::new()
        }
    }

    #[allow(clippy::map_entry)]
    fn build(&mut self) {
        let mut rng = RandomNumberGenerator::new();        

        // Find a starting point; start at the middle and walk left until we find an open tile
        self.starting_position = Position{ x: self.map.width / 2, y : self.map.height / 2 };
        let mut start_idx = self.map.xy_idx(self.starting_position.x, self.starting_position.y);
        while self.map.tiles[start_idx] != TileType::Floor {
            self.starting_position.x -= 1;
            start_idx = self.map.xy_idx(self.starting_position.x, self.starting_position.y);
        }
        self.take_snapshot();

        // Find all tiles we can reach from the starting point
        let exit_tile = remove_unreachable_areas_returning_most_distant(&mut self.map, start_idx);
        self.take_snapshot();

        // Place the stairs
        self.map.tiles[exit_tile] = TileType::DownStairs;
        self.take_snapshot();

        // Now we build a noise map for use in spawning entities later
        self.noise_areas = generate_voronoi_spawn_regions(&self.map, &mut rng);
    }
}
}

And in random_builder (map_builders/mod.rs):


#![allow(unused_variables)]
fn main() {
pub fn random_builder(new_depth: i32) -> Box<dyn MapBuilder> {
    /*let mut rng = rltk::RandomNumberGenerator::new();
    let builder = rng.roll_dice(1, 7);
    match builder {
        1 => Box::new(BspDungeonBuilder::new(new_depth)),
        2 => Box::new(BspInteriorBuilder::new(new_depth)),
        3 => Box::new(CellularAutomataBuilder::new(new_depth)),
        4 => Box::new(DrunkardsWalkBuilder::open_area(new_depth)),
        5 => Box::new(DrunkardsWalkBuilder::open_halls(new_depth)),
        6 => Box::new(DrunkardsWalkBuilder::winding_passages(new_depth)),
        _ => Box::new(SimpleMapBuilder::new(new_depth))
    }*/
    Box::new(MazeBuilder::new(new_depth))
}
}

Actually building a maze

There are lots of good maze building algorithms out there, all guaranteed to give you a perfectly solvable maze. In One Knight in the Dungeon, I based my maze building code off of a relatively standard implementation - Cyucelen's mazeGenerator. It's an interesting algorithm because - like a lot of maze algorithms - it assumes that walls are part of the tile grid, rather than having separate wall entities. That isn't going to work for the type of tile map we are using, so we generate the grid at half the resolution of the actual map, and generate walls based upon wall adjacency information in the grid.

The algorithm started as C++ code with pointers everywhere, and took a bit of time to port. The most basic structure in the algorithm: the Cell. Cells are tiles on the map:


#![allow(unused_variables)]
fn main() {
const TOP : usize = 0;
const RIGHT : usize = 1;
const BOTTOM : usize = 2;
const LEFT : usize = 3;

#[derive(Copy, Clone)]
struct Cell {
    row: i32,
    column: i32,
    walls: [bool; 4],
    visited: bool,
}
}

We define four constants: TOP, RIGHT, BOTTOM and LEFT and assign them to the numbers 0..3. We use these whenever the algorithm wants to refer to a direction. Looking at Cell, it is relatively simple:

  • row and column define where the cell is on the map.
  • walls is an array, with a bool for each of the directions we've defined. Rust arrays (static, you can't resize them like a vector) are defined with the syntax [TYPE ; NUMBER_OF_ELEMENTS]. Most of the time we just use vectors because we like the dynamic sizing; in this case, the number of elements is known ahead of time, so using the lower-overhead type makes sense.
  • visited - a bool indicating whether we've previously looked at the cell.

Cell also defines some methods. The first is its constructor:


#![allow(unused_variables)]
fn main() {
impl Cell {
    fn new(row: i32, column: i32) -> Cell {
        Cell{
            row,
            column,
            walls: [true, true, true, true],
            visited: false
        }
    }
    ...
}

This is a simple constructor: it makes a cell with walls in each direction, and not previously visited. Cells also define a function called remove_walls:


#![allow(unused_variables)]
fn main() {
fn remove_walls(&mut self, next : &mut Cell) {
    let x = self.column - next.column;
    let y = self.row - next.row;

    if x == 1 {
        self.walls[LEFT] = false;
        next.walls[RIGHT] = false;
    }
    else if x == -1 {
        self.walls[RIGHT] = false;
        next.walls[LEFT] = false;
    }
    else if y == 1 {
        self.walls[TOP] = false;
        next.walls[BOTTOM] = false;
    }
    else if y == -1 {
        self.walls[BOTTOM] = false;
        next.walls[TOP] = false;
    }
}
}

Uh oh, there's some new stuff here:

  • We set x to be our column value, minus the column value of the next cell.
  • We do the same with y - but with row values.
  • If x is equal to 1, then the next's column must be greater than our column value. In other words, the next cell is to the right of our current location. So we remove the wall to the right.
  • Likewise, if x is -1, then we must be going left - so we remove the wall to the left.
  • Once again, if y is 1, we must be going up. So we remove the walls to the top.
  • Finally, if y is -1, we must be going down - so we remove the walls below us.

Whew! Cell is done. Now to actually use it. In our maze algorithm, Cell is part of Grid. Here's the basic Grid definition:


#![allow(unused_variables)]
fn main() {
struct Grid<'a> {
    width: i32,
    height: i32,
    cells: Vec<Cell>,
    backtrace: Vec<usize>,
    current: usize,
    rng : &'a mut RandomNumberGenerator
}
}

Some commentary on Grid:

  • The <'a> is a lifetime specifier. We have to specify one so that Rust's borrow checker can ensure that the Grid will not expire before we delete the RandomNumberGenerator. Because we're passing a mutable reference to the caller's RNG, Rust needs this to ensure that the RNG doesn't go away before we're finished with it. This type of bug often affects C/C++ users, so Rust made it really hard to mess up. Unfortunately, the price of making it hard to get wrong is some ugly syntax!
  • We have a width and height defining the size of the maze.
  • Cells are just a Vector of the Cell type we defined earlier.
  • backtrace is used by the algorithm for recursively back-tracking to ensure that every cell has been processed. It's just a vector of cell indices - the index into the cells vector.
  • current is used by the algorithm to tell which Cell we're currently working with.
  • rng is the reason for the ugly lifetime stuff; we want to use the random number generator built in the build function, so we store a reference to it here. Because obtaining a random number changes the content of the variable, we have to store a mutable reference. The really ugly &'a mut indicates that it is a reference, with the lifetime 'a (defined above) and is mutable/changeable.

Grid implements quite a few methods. First up, the constructor:


#![allow(unused_variables)]
fn main() {
impl<'a> Grid<'a> {
    fn new(width: i32, height:i32, rng: &mut RandomNumberGenerator) -> Grid {
        let mut grid = Grid{
            width,
            height,
            cells: Vec::new(),
            backtrace: Vec::new(),
            current: 0,
            rng
        };

        for row in 0..height {
            for column in 0..width {
                grid.cells.push(Cell::new(row, column));
            }
        }

        grid
    }
    ...
}

Notice that once again we had to use some ugly syntax for the lifetime! The constructor itself is quite simple: it makes a new Grid structure with the specified width and height, a new vector of cells, a new (empty) backtrace vector, sets current to 0 and stores the random number generator reference. Then it iterates the rows and columns of the grid, pushing new Cell structures to the cells vector, numbered by their location.

The Grid also implements calculate_index:


#![allow(unused_variables)]
fn main() {
fn calculate_index(&self, row: i32, column: i32) -> i32 {
    if row < 0 || column < 0 || column > self.width-1 || row > self.height-1 {
        -1
    } else {
        column + (row * self.width)
    }
}
}

This is very similar to our map's xy_idx function: it takes a row and column coordinate, and returns the array index at which one can find the cell. It also does some bounds checking, and returns -1 if the coordinates are invalid. Next, we provide get_available_neighbors:


#![allow(unused_variables)]
fn main() {
fn get_available_neighbors(&self) -> Vec<usize> {
    let mut neighbors : Vec<usize> = Vec::new();

    let current_row = self.cells[self.current].row;
    let current_column = self.cells[self.current].column;

    let neighbor_indices : [i32; 4] = [
        self.calculate_index(current_row -1, current_column),
        self.calculate_index(current_row, current_column + 1),
        self.calculate_index(current_row + 1, current_column),
        self.calculate_index(current_row, current_column - 1)
    ];

    for i in neighbor_indices.iter() {
        if *i != -1 && !self.cells[*i as usize].visited {
            neighbors.push(*i as usize);
        }
    }

    neighbors
}
}

This function provides the available exits from the current cell. It works by obtaining the row and column coordinates of the current cell, and then puts a call to calculate_index into an array (corresponding to the directions we defined with Cell). It finally iterates the array, and if the values are valid (greater than -1), and we haven't been there before (the visited check) it pushes them into the neighbors list. It then returns neighbors. A call to this for any cell address will return a vector listing all of the adjacent cells to which we can travel (ignoring walls). We first use this in find_next_cell:


#![allow(unused_variables)]
fn main() {
fn find_next_cell(&mut self) -> Option<usize> {
    let neighbors = self.get_available_neighbors();
    if !neighbors.is_empty() {
        if neighbors.len() == 1 {
            return Some(neighbors[0]);
        } else {
            return Some(neighbors[(self.rng.roll_dice(1, neighbors.len() as i32)-1) as usize]);
        }
    }
    None
}
}

This function is interesting in that it returns an Option. It's possible that there is nowhere to go from the current cell - in which case it returns None. Otherwise, it returns Some with the array index of the next destination. It works by:

  • Obtain a list of neighbors for the current cell.
  • If there are neighbors:
    • If there is only one neighbor, return it.
    • If there are multiple neighbors, pick one and random and return it.
  • If there are no neighbors, return None.

We use this from generate_maze:


#![allow(unused_variables)]
fn main() {
fn generate_maze(&mut self, generator : &mut MazeBuilder) {
    loop {
        self.cells[self.current].visited = true;
        let next = self.find_next_cell();

        match next {
            Some(next) => {
                self.cells[next].visited = true;
                self.backtrace.push(self.current);
                //   __lower_part__      __higher_part_
                //   /            \      /            \
                // --------cell1------ | cell2-----------
                let (lower_part, higher_part) =
                    self.cells.split_at_mut(std::cmp::max(self.current, next));
                let cell1 = &mut lower_part[std::cmp::min(self.current, next)];
                let cell2 = &mut higher_part[0];
                cell1.remove_walls(cell2);
                self.current = next;
            }
            None => {
                if !self.backtrace.is_empty() {
                    self.current = self.backtrace[0];
                    self.backtrace.remove(0);
                } else {
                    break;
                }
            }
        }

        self.copy_to_map(&mut generator.map);
        generator.take_snapshot();    
    }
}
}

So now we're onto the actual algorithm! Lets step through it to understand how it works:

  1. We start with a loop. We haven't used one of these before (you can read about them here). Basically, a loop runs forever - until it hits a break statement.
  2. We set the value of visited in the current cell to true.
  3. We add the current cell to the beginning of the backtrace list.
  4. We call find_next_cell and set its index in the variable next. If this is our first run, we'll get a random direction from the starting cell. Otherwise, we get an exit from the current cell we're visiting.
  5. If next has a value, then:
    1. Split cells to two mutable references. We will need two mutable references to the same slice, Rust normally doesn't allow this, but we can split our slice to two non-overlapping parts. This is a common use case and Rust provides a safe function to do exactly that.
    2. Get mutable reference to the cell with lower index from first part and to the second from start of second part.
    3. We call remove_walls on the cell1 cell, referencing the cell2 cell.
  6. If next does not have a value (it's equal to None), we:
    1. If backtrace isn't empty, we set current to the first value in the backtrace list.
    2. If backtrace is empty, we've finished - so we break out of the loop.
  7. Finally, we call copy_to_map - which copies the maze to the map (more on that below), and take a snapshot for the iterative map generation renderer.

So why does that work?

  • The first few iterations will get a non-visited neighbor, carving a clear path through the maze. Each step along the way, the cell we've visited is added to backtrace. This is effectively a drunken walk through the maze, but ensuring that we cannot return to a cell.
  • When we hit a point at which we have no neighbors (we've hit the end of the maze), the algorithm will change current to the first entry in our backtrace list. It will then randomly walk from there, filling in more cells.
  • If that point can't go anywhere, it works back up the backtrace list.
  • This repeats until every cell has been visited, meaning that backtrace and neighbors are both empty. We're done!

The best way to understand this is to watch it in action:

Screenshot.

Finally, there's the copy_to_map function:


#![allow(unused_variables)]
fn main() {
fn copy_to_map(&self, map : &mut Map) {
    // Clear the map
    for i in map.tiles.iter_mut() { *i = TileType::Wall; }

    for cell in self.cells.iter() {
        let x = cell.column + 1;
        let y = cell.row + 1;
        let idx = map.xy_idx(x * 2, y * 2);

        map.tiles[idx] = TileType::Floor;
        if !cell.walls[TOP] { map.tiles[idx - map.width as usize] = TileType::Floor }
        if !cell.walls[RIGHT] { map.tiles[idx + 1] = TileType::Floor }
        if !cell.walls[BOTTOM] { map.tiles[idx + map.width as usize] = TileType::Floor }
        if !cell.walls[LEFT] { map.tiles[idx - 1] = TileType::Floor }
    }
}
}

This is where the mismatch between Grid/Cell and our map format is resolved: each Cell in the maze structure can have walls in any of the four major directions. Our map doesn't work that way: walls aren't part of a tile, they are a tile. So we double the size of the Grid, and write carve floors where walls aren't present. Lets walk through this function:

  1. We set all cells in the map to be a solid wall.
  2. For each cell in the grid, we:
    1. Calculate x as the cell's column value, plus one.
    2. Calculate y as the cell's row value, plus one.
    3. Set idx to map.xy_idx of DOUBLE the x and y values: so spread each cell out.
    4. We set the map tile at idx to be a floor.
    5. If the Cell we're referencing does not have a TOP wall, we set the map tile above our idx tile to be a floor.
    6. We repeat that for the other directions.

Speeding up the generator

We're wasting a lot of time by snapshotting at every iteration - we're building a huge list of snapshot maps. That was great for learning the algorithm, but simply takes too long when playing the game. We'll modify our generate_maze function to count iterations, and only log every 10th:


#![allow(unused_variables)]
fn main() {
fn generate_maze(&mut self, generator : &mut MazeBuilder) {
    let mut i = 0;
    loop {
        self.cells[self.current].visited = true;
        let next = self.find_next_cell();

        match next {
            Some(next) => {
                self.cells[next].visited = true;
                self.backtrace.push(self.current);
                unsafe {
                    let next_cell : *mut Cell = &mut self.cells[next];
                    let current_cell = &mut self.cells[self.current];
                    current_cell.remove_walls(next_cell);
                }
                self.current = next;
            }
            None => {
                if !self.backtrace.is_empty() {
                    self.current = self.backtrace[0];
                    self.backtrace.remove(0);
                } else {
                    break;
                }
            }
        }

        if i % 50 == 0 {
            self.copy_to_map(&mut generator.map);
            generator.take_snapshot();    
        }
        i += 1;
    }
}
}

This brings the generator up to a reasonable speed, and you can still watch the maze develop.

Finding the exit

Fortunately, our current algorithm will start you at Cell (1,1) - which corresponds to map location (2,2). So in build, we can easily specify a starting point:


#![allow(unused_variables)]
fn main() {
self.starting_position = Position{ x: 2, y : 2 };
let start_idx = self.map.xy_idx(self.starting_position.x, self.starting_position.y);
self.take_snapshot();
}

We can then use the same code we've used in the last two examples to find an exit:


#![allow(unused_variables)]
fn main() {
// Find all tiles we can reach from the starting point
let exit_tile = remove_unreachable_areas_returning_most_distant(&mut self.map, start_idx);
self.take_snapshot();

// Place the stairs
self.map.tiles[exit_tile] = TileType::DownStairs;
self.take_snapshot();

// Now we build a noise map for use in spawning entities later
self.noise_areas = generate_voronoi_spawn_regions(&self.map, &mut rng);
}

This is also a great test of the library's Dijkstra map code. It can solve a maze very quickly!

Restoring the randomness

Once again, we should restore random_builder to be random:


#![allow(unused_variables)]
fn main() {
pub fn random_builder(new_depth: i32) -> Box<dyn MapBuilder> {
    let mut rng = rltk::RandomNumberGenerator::new();
    let builder = rng.roll_dice(1, 8);
    match builder {
        1 => Box::new(BspDungeonBuilder::new(new_depth)),
        2 => Box::new(BspInteriorBuilder::new(new_depth)),
        3 => Box::new(CellularAutomataBuilder::new(new_depth)),
        4 => Box::new(DrunkardsWalkBuilder::open_area(new_depth)),
        5 => Box::new(DrunkardsWalkBuilder::open_halls(new_depth)),
        6 => Box::new(DrunkardsWalkBuilder::winding_passages(new_depth)),
        7 => Box::new(MazeBuilder::new(new_depth)),
        _ => Box::new(SimpleMapBuilder::new(new_depth))
    }    
}
}

Wrap-Up

In this chapter, we've built a maze. It's a guaranteed solvable maze, so there's no risk of a level that you can't beat. You still have to use this type of map with caution: they make good one-off maps, and can really annoy players!

The source code for this chapter may be found here

Run this chapter's example with web assembly, in your browser (WebGL2 required)

Copyright (C) 2019, Herbert Wolverson.