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#141 in Data structures
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sqrid
sqrid provides square grid coordinates and related operations, in a crate with zero dependencies.
It's easier to explain the features of this crate in terms of the types it provides:
Pos
: position, as absolute coordinates in a grid of fixed size. The dimensions of the grid are const generics type parameters; invalid coordinates can't be created.Dir
: "movement", relative coordinates. These are the cardinal (and intercardinal) directions. Addition is implemented in the form ofPos + Dir = Option<Pos>
, which can beNone
if the result is outside the grid.Grid
: aPos
-indexed array.Gridbool
: a bitmap-backedPos
-indexed grid of booleans.Sqrid
: "factory" type that acts as an entry point to the fundamental types below and to algorithms.
We also have traits that generalize Grid
and Gridbool
:
MapPos
: trait that mapsPos
to parameterized items; it's implemented byGrid
, and someHashMap
/BTreeMap
based types.SetPos
: trait that maps eachPos
to a bool; it's implemented byGridbool
,HashSet<Pos>
andBTreeSet<Pos>
.
We then use these generalization to implement some grid algorithms:
bf
: breadth-first iteration and search.astar
: A* search that takes a destinationPos
.ucs
: uniform-cost search.
All basic types have the standard iter
, iter_mut
, extend
,
as_ref
, and conversion operations that should be expected.
Fundamental types
Pos
: absolute coordinates, position
The Pos
type represents an absolute position in a square
grid. The type itself receives the height and width of the grid as
const generic parameter.
We should usually create a type alias for the grid size we are using:
use sqrid;
type Pos = sqrid::Pos<6, 7>;
let pos = Pos::new(3, 3)?;
We can only generate Pos
instances that are inside the passed
dimensions.
Dir
: relative coordinates, direction, movement
The Dir
type represents a relative movement of one square. It
can only be one of the 8 cardinal and intercardinal directions:
Dir::N
, Dir::NE
, Dir::E
, Dir::SE
, Dir::S
,
Dir::SW
, Dir::W
, Dir::NW
.
It's a building block for paths, iterating on a Pos
neighbors,
etc. It effectively represents the edges in a graph where the
Pos
type represents nodes.
All functions that iterate on Dir
values accept a boolean const
argument that specifies whether the intercardinal directions
(NE
, SE
, SW
, NW
) should be considered.
Grid
: a Pos
-indexed array
A Grid
is a generic array that can be indexed by a Pos
.
We can create the type from a suitable Sqrid
type by using the
grid_create
macro. We can then interact with specific lines
with Grid::line
and Grid::line_mut
, or with the whole
underlying array with as_ref
(see std::convert::AsRef
) and
as_mut
(see std::convert::AsMut
).
Usage example:
type Sqrid = sqrid::sqrid_create!(3, 3, false);
type Pos = sqrid::pos_create!(Sqrid);
type Grid = sqrid::grid_create!(Sqrid, i32);
// The grid create macro above is currently equivalent to:
type Grid2 = sqrid::Grid<i32, { Sqrid::WIDTH }, { Sqrid::HEIGHT },
{ (Sqrid::WIDTH * Sqrid::HEIGHT) as usize }>;
// We can create grids from iterators via `collect`:
let mut gridnums = (0..9).collect::<Grid>();
// Iterate on their members:
for i in &gridnums {
println!("i {}", i);
}
// Change the members in a loop:
for i in &mut gridnums {
*i *= 10;
}
// Iterate on (coordinate, member) tuples:
for (pos, &i) in gridnums.iter_pos() {
println!("[{}] = {}", pos, i);
}
// And we can always use `as_ref` or `as_mut` to interact with the
// inner array directly. To reverse it, for example, with the
// [`std::slice::reverse`] function:
gridnums.as_mut().reverse();
Gridbool
: a bitmap-backed Pos
-indexed grid of booleans
The Gridbool
is a compact abstraction of a grid of booleans.
The type itself can be created with gridbool_create
macro.
It's optimized for getting and setting values at specific
coordinates, but we can also get all true
/false
coordinates
with suboptimal performance - in this case, the time is
proportional to the size of the grid and not to the quantity of
true
/false
values.
Usage example:
type Sqrid = sqrid::sqrid_create!(3, 3, false);
type Pos = sqrid::pos_create!(Sqrid);
type Gridbool = sqrid::gridbool_create!(Sqrid);
// We can create a gridbool from a Pos iterator via `collect`:
let mut gb = Pos::iter().filter(|pos| pos.is_corner()).collect::<Gridbool>();
// We can also set values from an iterator:
gb.set_iter_t(Pos::iter().filter(|pos| pos.is_side()));
// Iterate on the true/false values:
for b in gb.iter() {
println!("{}", b);
}
// Iterate on the true coordinates:
for pos in gb.iter_t() {
assert!(pos.is_side());
}
// Iterate on (coordinate, bool):
for (pos, b) in gb.iter_pos() {
println!("[{}] = {}", pos, b);
}
Sqrid
: entry point for algorithms
The Pos
type and some methods on the Dir
type require const
generic arguments that usually don't change inside an application.
Both Grid
and Gridbool
also require further arguments that
can actually be derived from the width and height of the grid, but
that have to be explicitly specified due to some Rust limitations.
To make the creation of these types easier, we provide the
Sqrid
type, which acumulates all const generic parameters and
can be used to create the other types via macros.
Example usage:
type Sqrid = sqrid::sqrid_create!(4, 4, false);
type Pos = sqrid::pos_create!(Sqrid);
type Grid = sqrid::grid_create!(Sqrid, i32);
type Gridbool = sqrid::gridbool_create!(Sqrid);
Algorithms
Breadth-first traversal
The Sqrid::bf_iter
function instantiates an iterator struct
(bf::BfIterator
) that can be used to iterate coordinates in
breadth-first order, from a given origin, using a provided
function to evaluate a given Pos
position + Dir
direction
into the next Pos
position.
Example usage:
type Sqrid = sqrid::sqrid_create!(3, 3, false);
type Pos = sqrid::pos_create!(Sqrid);
for (pos, dir) in Sqrid::bf_iter(sqrid::mov_eval, &Pos::CENTER)
.flatten() {
println!("breadth-first pos {} from {}", pos, dir);
}
Breadth-first search
Sqrid::bfs_path
takes an origin, a movement function and a
goal function, and figures out the shortest path to a goal by
using a breadth-first iteration.
The function returns the Pos
that fulfills the goal and a
path in the form of a Vec<Dir>
.
Example usage:
type Sqrid = sqrid::sqrid_create!(3, 3, false);
type Pos = sqrid::pos_create!(Sqrid);
// Generate the grid of "came from" directions from bottom-right to
// top-left:
if let Ok((goal, path)) = Sqrid::bfs_path(
sqrid::mov_eval, &Pos::TOP_LEFT,
|pos| pos == Pos::BOTTOM_RIGHT) {
println!("goal: {}, path: {:?}", goal, path);
}
A* search
Sqrid::astar_path
takes a movement function, an origin and a
destination, and figures out the shortest path by using A*.
The function returns path in the form of a Vec<Dir>
.
Example usage:
type Sqrid = sqrid::sqrid_create!(3, 3, false);
type Pos = sqrid::pos_create!(Sqrid);
// Generate the grid of "came from" directions from bottom-right to
// top-left:
if let Ok(path) = Sqrid::astar_path(sqrid::mov_eval, &Pos::TOP_LEFT,
&Pos::BOTTOM_RIGHT) {
println!("path: {:?}", path);
}
Uniform-cost search
Sqrid::ucs_path
takes a movement-cost function, an origin and a
destination, and figures out the path with the lowest cost by using
uniform-cost search, which is essentially a variation of
Dijkstra.
The function returns path in the form of a Vec<Dir>
.
Example usage:
type Sqrid = sqrid::sqrid_create!(3, 3, false);
type Pos = sqrid::pos_create!(Sqrid);
fn traverse(position: Pos, direction: sqrid::Dir) -> Option<(Pos, usize)> {
let next_position = (position + direction).ok()?;
let cost = 1;
Some((next_position, cost))
}
// Generate the grid of "came from" directions from bottom-right to
// top-left:
if let Ok(path) = Sqrid::ucs_path(traverse, &Pos::TOP_LEFT,
&Pos::BOTTOM_RIGHT) {
println!("path: {:?}", path);
}