Struct Solver

pub struct Solver<T>
where
    T: Debug + PartialEq + Clone,
{ /* private fields */ }

Implements the linked lists, which are structured in the following way

i0  ⟷  i1  ⟷  i2  ⟷  i3  ⟷  i4
       ⥯      ⥯     ⥯     ⥯   s0
o1     ⦿      ⦿     ⥯     ⥯   s1
o2     ⥯      ⥯     ⦿     ⥯   s2
o3     ⥯      ⦿     ⥯     ⦿   s3
o4     ⦿      ⥯     ⥯     ⥯   s4
       ⥯      ⥯     ⥯     ⥯

where arrows denote links.

The spacers s0,…, also form a doubly circularly linked list.

i0 is the root node for the linked list of items i1,…,.i4

s0 is the root node for the spacers which link vertically to each other

⦿ denote the option elements which contain links up and down and also reference their “parent” item

We may set up and solve this problem with the following code

// Create Solver with 4 items
let mut s = Solver::new(4);
// Add options
s.add_option("o1", &[1, 2])
    .add_option("o2", &[3])
    .add_option("o3", &[2, 4])
    .add_option("o4", &[1]);

// Iterate through all solutions
if let Some(solution) = s.next() {
    assert_eq!(solution, ["o2","o3","o4"]);
    Ok(())
}
else {
    Err("No solution found".into())
    }

Implementations

impl<T: PartialEq + Debug + Clone> Solver<T>

pub fn new(n: usize) -> Self

Returns a solver with n items, all of which must be covered exactly once

pub fn new_optional(mandatory: usize, opt: usize) -> Self

Returns a solver with n mandatory items and m optional items to be covered This allows us to include items which may or may not be covered (but still may not be covered more than once)

Example, where optional elements are after |

    i1  i2  i3  i4 | i5
o1   1   0   1  0  |  0
o2   0   1   0  1  |  0
o3   1   0   0  0  |  1
o4   0   0   1  0  |  0
o5   0   0   1  0  |  1

Here we can see taking [o1,o2] works, as does [o2,o3,o4], but not [o2,o3,o5], because then i4 would be double covered

The code that does this is

let mut s = Solver::new_optional(4,1);

s.add_option("o1", &[1, 3])
    .add_option("o2", &[2, 4])
    .add_option("o3", &[1, 5])
    .add_option("o4", &[3])
    .add_option("o5", &[3, 5]);

let s1 = s.next().unwrap_or_default();
let s2 = s.next().unwrap_or_default();
let s3 = s.next();
assert_eq!(s1,["o2","o1"]);
assert_eq!(s2,["o2","o3","o4"]);
assert_eq!(s3,None);

pub fn add_option(&mut self, name: T, option: &[usize]) -> &mut Self

Adds an option which would cover items defined by option, and with name `name Specifically if our problems looks like

i0  ⟷  i1  ⟷  i2  ⟷  i3  ⟷  i4
       ⥯      ⥯     ⥯     ⥯   s0
o1     ⦿      ⦿     ⥯     ⥯   s1
o2     ⥯      ⥯     ⦿     ⥯   s2
o3     ⥯      ⦿     ⥯     ⦿   s3
o4     ⦿      ⥯     ⥯     ⥯   s4
       ⥯      ⥯     ⥯     ⥯

then add_option("o5", &[1,2]) would take it to

i0  ⟷  i1  ⟷  i2  ⟷  i3  ⟷  i4
       ⥯      ⥯     ⥯     ⥯   s0
o1     ⦿      ⦿     ⥯     ⥯   s1
o2     ⥯      ⥯     ⦿     ⥯   s2
o3     ⥯      ⦿     ⥯     ⦿   s3
o4     ⦿      ⥯     ⥯     ⥯   s4
o5     ⦿      ⦿     ⥯     ⥯   s5
       ⥯      ⥯     ⥯     ⥯

pub fn cover(&mut self, i: usize) -> Result<(), &'static str>

Covers item in column i i.e. cover(2) would transform

i0  ⟷  i1  ⟷  i2  ⟷  i3  ⟷  i4
       ⥯      ⥯     ⥯     ⥯   s0
o1     ⦿      ⦿     ⥯     ⥯   s1
o2     ⥯      ⥯     ⦿     ⥯   s2
o3     ⥯      ⦿     ⥯     ⦿   s3
o4     ⦿      ⥯     ⥯     ⥯   s4
       ⥯      ⥯     ⥯     ⥯

into

i0  ⟷  i1  ⟷  ⟷  ⟷  i3  ⟷  i4
       ⥯            ⥯     ⥯   s0
o1     ⦿            ⥯     ⥯   s1
o2     ⥯            ⦿     ⥯   s2
o3     ⥯            ⥯     ⦿   s3
o4     ⦿            ⥯     ⥯   s4
       ⥯            ⥯     ⥯

pub fn uncover(&mut self, i: usize) -> Result<(), &'static str>

Reverse of function cover

pub fn solve(&mut self) -> Option<Vec<T>>

Implements algorithm X as a finite state machine

pub fn output(&self) -> Vec<T>

Returns a solution in a human-understandable form

The solution vector sol_vec stores each of the OptionElements which were used to cover the items in the solution. To turn this into something understandable we find the spacer to its right, and use this with a lookup table created earlier to map this to the names of options

pub fn select(&mut self, name: T) -> Result<(), &'static str>

Selects an option with the name name When setting up a general constraint solution, this is how to search for specific answers e.g. a Sudoku has all the constraints (items and options), and then the squares filled out in the specific problem need to be selected

So for the problem

   i1  i2  i3
o1  1   0   0
o2  1   0   0
o3  0   1   1

Clearly both [o1,o3] and [o2,o3] are solutions, but if we select o1, then only one solution remains

let mut s = Solver::new(3);

s.add_option("o1", &[1])
    .add_option("o2", &[1])
    .add_option("o3", &[2, 3]);

// First get all solutions
let sols: Vec<Vec<&str>> = s.clone().collect();
assert_eq!(sols.len(), 2);
assert_eq!( vec!["o3", "o1"], sols[0]);
assert_eq!( vec!["o3", "o2"], sols[1]);


// Now select o1 and get all solutions
s.select("o1");
assert_eq!( vec!["o3"], s.next().unwrap());

Trait Implementations

impl<T> Clone for Solver<T>

where T: Debug + PartialEq + Clone + Clone,

fn clone(&self) -> Solver<T>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T: Debug + PartialEq + Clone> Display for Solver<T>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T: Debug + PartialEq + Clone> Iterator for Solver<T>

fn next(&mut self) -> Option<Self::Item>

Produces next solution by following algorithm X as described in tAoCP in Fasc 5c, Dancing Links, Knuth

Returns Some containing a vector of items if a solution remains, or None when no more solutions remaining

type Item = Vec<T>

The type of the elements being iterated over.

fn next_chunk<const N: usize>( &mut self, ) -> Result<[Self::Item; N], IntoIter<Self::Item, N>>

where Self: Sized,

🔬This is a nightly-only experimental API. (iter_next_chunk)

Advances the iterator and returns an array containing the next N values.

fn size_hint(&self) -> (usize, Option<usize>)

Returns the bounds on the remaining length of the iterator.

fn count(self) -> usize

where Self: Sized,

Consumes the iterator, counting the number of iterations and returning it.

fn last(self) -> Option<Self::Item>

where Self: Sized,

Consumes the iterator, returning the last element.

fn advance_by(&mut self, n: usize) -> Result<(), NonZero<usize>>

🔬This is a nightly-only experimental API. (iter_advance_by)

Advances the iterator by n elements.

fn nth(&mut self, n: usize) -> Option<Self::Item>

Returns the nth element of the iterator.

fn step_by(self, step: usize) -> StepBy<Self>

where Self: Sized,

Creates an iterator starting at the same point, but stepping by the given amount at each iteration.

fn chain<U>(self, other: U) -> Chain<Self, <U as IntoIterator>::IntoIter>

where Self: Sized, U: IntoIterator<Item = Self::Item>,

Takes two iterators and creates a new iterator over both in sequence.

fn zip<U>(self, other: U) -> Zip<Self, <U as IntoIterator>::IntoIter>

where Self: Sized, U: IntoIterator,

‘Zips up’ two iterators into a single iterator of pairs.

fn intersperse(self, separator: Self::Item) -> Intersperse<Self>

where Self: Sized, Self::Item: Clone,

🔬This is a nightly-only experimental API. (iter_intersperse)

Creates a new iterator which places a copy of separator between adjacent items of the original iterator.

fn intersperse_with<G>(self, separator: G) -> IntersperseWith<Self, G>

where Self: Sized, G: FnMut() -> Self::Item,

🔬This is a nightly-only experimental API. (iter_intersperse)

Creates a new iterator which places an item generated by separator between adjacent items of the original iterator.

fn map<B, F>(self, f: F) -> Map<Self, F>

where Self: Sized, F: FnMut(Self::Item) -> B,

Takes a closure and creates an iterator which calls that closure on each element.

fn for_each<F>(self, f: F)

where Self: Sized, F: FnMut(Self::Item),

Calls a closure on each element of an iterator.

fn filter<P>(self, predicate: P) -> Filter<Self, P>

where Self: Sized, P: FnMut(&Self::Item) -> bool,

Creates an iterator which uses a closure to determine if an element should be yielded.

fn filter_map<B, F>(self, f: F) -> FilterMap<Self, F>

where Self: Sized, F: FnMut(Self::Item) -> Option<B>,

Creates an iterator that both filters and maps.

fn enumerate(self) -> Enumerate<Self>

where Self: Sized,

Creates an iterator which gives the current iteration count as well as the next value.

fn peekable(self) -> Peekable<Self>

where Self: Sized,

Creates an iterator which can use the peek and peek_mut methods to look at the next element of the iterator without consuming it. See their documentation for more information.

fn skip_while<P>(self, predicate: P) -> SkipWhile<Self, P>

where Self: Sized, P: FnMut(&Self::Item) -> bool,

Creates an iterator that skips elements based on a predicate.

fn take_while<P>(self, predicate: P) -> TakeWhile<Self, P>

where Self: Sized, P: FnMut(&Self::Item) -> bool,

Creates an iterator that yields elements based on a predicate.

fn map_while<B, P>(self, predicate: P) -> MapWhile<Self, P>

where Self: Sized, P: FnMut(Self::Item) -> Option<B>,

Creates an iterator that both yields elements based on a predicate and maps.

fn skip(self, n: usize) -> Skip<Self>

where Self: Sized,

Creates an iterator that skips the first n elements.

fn take(self, n: usize) -> Take<Self>

where Self: Sized,

Creates an iterator that yields the first n elements, or fewer if the underlying iterator ends sooner.

fn scan<St, B, F>(self, initial_state: St, f: F) -> Scan<Self, St, F>

where Self: Sized, F: FnMut(&mut St, Self::Item) -> Option<B>,

An iterator adapter which, like fold, holds internal state, but unlike fold, produces a new iterator.

fn flat_map<U, F>(self, f: F) -> FlatMap<Self, U, F>

where Self: Sized, U: IntoIterator, F: FnMut(Self::Item) -> U,

Creates an iterator that works like map, but flattens nested structure.

fn flatten(self) -> Flatten<Self>

where Self: Sized, Self::Item: IntoIterator,

Creates an iterator that flattens nested structure.

fn map_windows<F, R, const N: usize>(self, f: F) -> MapWindows<Self, F, N>

where Self: Sized, F: FnMut(&[Self::Item; N]) -> R,

🔬This is a nightly-only experimental API. (iter_map_windows)

Calls the given function f for each contiguous window of size N over self and returns an iterator over the outputs of f. Like slice::windows(), the windows during mapping overlap as well.

fn fuse(self) -> Fuse<Self>

where Self: Sized,

Creates an iterator which ends after the first None.

fn inspect<F>(self, f: F) -> Inspect<Self, F>

where Self: Sized, F: FnMut(&Self::Item),

Does something with each element of an iterator, passing the value on.

fn by_ref(&mut self) -> &mut Self

where Self: Sized,

Creates a “by reference” adapter for this instance of Iterator.

fn collect<B>(self) -> B

where B: FromIterator<Self::Item>, Self: Sized,

Transforms an iterator into a collection.

fn try_collect<B>( &mut self, ) -> <<Self::Item as Try>::Residual as Residual<B>>::TryType

where Self: Sized, Self::Item: Try, <Self::Item as Try>::Residual: Residual<B>, B: FromIterator<<Self::Item as Try>::Output>,

🔬This is a nightly-only experimental API. (iterator_try_collect)

Fallibly transforms an iterator into a collection, short circuiting if a failure is encountered.

fn collect_into<E>(self, collection: &mut E) -> &mut E

where E: Extend<Self::Item>, Self: Sized,

🔬This is a nightly-only experimental API. (iter_collect_into)

Collects all the items from an iterator into a collection.

fn partition<B, F>(self, f: F) -> (B, B)

where Self: Sized, B: Default + Extend<Self::Item>, F: FnMut(&Self::Item) -> bool,

Consumes an iterator, creating two collections from it.

fn is_partitioned<P>(self, predicate: P) -> bool

where Self: Sized, P: FnMut(Self::Item) -> bool,

🔬This is a nightly-only experimental API. (iter_is_partitioned)

Checks if the elements of this iterator are partitioned according to the given predicate, such that all those that return true precede all those that return false.

fn try_fold<B, F, R>(&mut self, init: B, f: F) -> R

where Self: Sized, F: FnMut(B, Self::Item) -> R, R: Try<Output = B>,

An iterator method that applies a function as long as it returns successfully, producing a single, final value.

fn try_for_each<F, R>(&mut self, f: F) -> R

where Self: Sized, F: FnMut(Self::Item) -> R, R: Try<Output = ()>,

An iterator method that applies a fallible function to each item in the iterator, stopping at the first error and returning that error.

fn fold<B, F>(self, init: B, f: F) -> B

where Self: Sized, F: FnMut(B, Self::Item) -> B,

Folds every element into an accumulator by applying an operation, returning the final result.

fn reduce<F>(self, f: F) -> Option<Self::Item>

where Self: Sized, F: FnMut(Self::Item, Self::Item) -> Self::Item,

Reduces the elements to a single one, by repeatedly applying a reducing operation.

fn try_reduce<R>( &mut self, f: impl FnMut(Self::Item, Self::Item) -> R, ) -> <<R as Try>::Residual as Residual<Option<<R as Try>::Output>>>::TryType

where Self: Sized, R: Try<Output = Self::Item>, <R as Try>::Residual: Residual<Option<Self::Item>>,

🔬This is a nightly-only experimental API. (iterator_try_reduce)

Reduces the elements to a single one by repeatedly applying a reducing operation. If the closure returns a failure, the failure is propagated back to the caller immediately.

fn all<F>(&mut self, f: F) -> bool

where Self: Sized, F: FnMut(Self::Item) -> bool,

Tests if every element of the iterator matches a predicate.

fn any<F>(&mut self, f: F) -> bool

where Self: Sized, F: FnMut(Self::Item) -> bool,

Tests if any element of the iterator matches a predicate.

fn find<P>(&mut self, predicate: P) -> Option<Self::Item>

where Self: Sized, P: FnMut(&Self::Item) -> bool,

Searches for an element of an iterator that satisfies a predicate.

fn find_map<B, F>(&mut self, f: F) -> Option<B>

where Self: Sized, F: FnMut(Self::Item) -> Option<B>,

Applies function to the elements of iterator and returns the first non-none result.

fn try_find<R>( &mut self, f: impl FnMut(&Self::Item) -> R, ) -> <<R as Try>::Residual as Residual<Option<Self::Item>>>::TryType

where Self: Sized, R: Try<Output = bool>, <R as Try>::Residual: Residual<Option<Self::Item>>,

🔬This is a nightly-only experimental API. (try_find)

Applies function to the elements of iterator and returns the first true result or the first error.

fn position<P>(&mut self, predicate: P) -> Option<usize>

where Self: Sized, P: FnMut(Self::Item) -> bool,

Searches for an element in an iterator, returning its index.

fn max(self) -> Option<Self::Item>

where Self: Sized, Self::Item: Ord,

Returns the maximum element of an iterator.

fn min(self) -> Option<Self::Item>

where Self: Sized, Self::Item: Ord,

Returns the minimum element of an iterator.

fn max_by_key<B, F>(self, f: F) -> Option<Self::Item>

where B: Ord, Self: Sized, F: FnMut(&Self::Item) -> B,

Returns the element that gives the maximum value from the specified function.

fn max_by<F>(self, compare: F) -> Option<Self::Item>

where Self: Sized, F: FnMut(&Self::Item, &Self::Item) -> Ordering,

Returns the element that gives the maximum value with respect to the specified comparison function.

fn min_by_key<B, F>(self, f: F) -> Option<Self::Item>

where B: Ord, Self: Sized, F: FnMut(&Self::Item) -> B,

Returns the element that gives the minimum value from the specified function.

fn min_by<F>(self, compare: F) -> Option<Self::Item>

where Self: Sized, F: FnMut(&Self::Item, &Self::Item) -> Ordering,

Returns the element that gives the minimum value with respect to the specified comparison function.

fn unzip<A, B, FromA, FromB>(self) -> (FromA, FromB)

where FromA: Default + Extend<A>, FromB: Default + Extend<B>, Self: Sized + Iterator<Item = (A, B)>,

Converts an iterator of pairs into a pair of containers.

fn copied<'a, T>(self) -> Copied<Self>

where T: Copy + 'a, Self: Sized + Iterator<Item = &'a T>,

Creates an iterator which copies all of its elements.

fn cloned<'a, T>(self) -> Cloned<Self>

where T: Clone + 'a, Self: Sized + Iterator<Item = &'a T>,

Creates an iterator which clones all of its elements.

fn cycle(self) -> Cycle<Self>

where Self: Sized + Clone,

Repeats an iterator endlessly.

fn array_chunks<const N: usize>(self) -> ArrayChunks<Self, N>

where Self: Sized,

🔬This is a nightly-only experimental API. (iter_array_chunks)

Returns an iterator over N elements of the iterator at a time.

fn sum<S>(self) -> S

where Self: Sized, S: Sum<Self::Item>,

Sums the elements of an iterator.

fn product<P>(self) -> P

where Self: Sized, P: Product<Self::Item>,

Iterates over the entire iterator, multiplying all the elements

fn cmp<I>(self, other: I) -> Ordering

where I: IntoIterator<Item = Self::Item>, Self::Item: Ord, Self: Sized,

Lexicographically compares the elements of this Iterator with those of another.

fn cmp_by<I, F>(self, other: I, cmp: F) -> Ordering

where Self: Sized, I: IntoIterator, F: FnMut(Self::Item, <I as IntoIterator>::Item) -> Ordering,

🔬This is a nightly-only experimental API. (iter_order_by)

Lexicographically compares the elements of this Iterator with those of another with respect to the specified comparison function.

fn partial_cmp<I>(self, other: I) -> Option<Ordering>

where I: IntoIterator, Self::Item: PartialOrd<<I as IntoIterator>::Item>, Self: Sized,

Lexicographically compares the PartialOrd elements of this Iterator with those of another. The comparison works like short-circuit evaluation, returning a result without comparing the remaining elements. As soon as an order can be determined, the evaluation stops and a result is returned.

fn partial_cmp_by<I, F>(self, other: I, partial_cmp: F) -> Option<Ordering>

where Self: Sized, I: IntoIterator, F: FnMut(Self::Item, <I as IntoIterator>::Item) -> Option<Ordering>,

🔬This is a nightly-only experimental API. (iter_order_by)

Lexicographically compares the elements of this Iterator with those of another with respect to the specified comparison function.

fn eq<I>(self, other: I) -> bool

where I: IntoIterator, Self::Item: PartialEq<<I as IntoIterator>::Item>, Self: Sized,

Determines if the elements of this Iterator are equal to those of another.

fn eq_by<I, F>(self, other: I, eq: F) -> bool

where Self: Sized, I: IntoIterator, F: FnMut(Self::Item, <I as IntoIterator>::Item) -> bool,

🔬This is a nightly-only experimental API. (iter_order_by)

Determines if the elements of this Iterator are equal to those of another with respect to the specified equality function.

fn ne<I>(self, other: I) -> bool

where I: IntoIterator, Self::Item: PartialEq<<I as IntoIterator>::Item>, Self: Sized,

Determines if the elements of this Iterator are not equal to those of another.

fn lt<I>(self, other: I) -> bool

where I: IntoIterator, Self::Item: PartialOrd<<I as IntoIterator>::Item>, Self: Sized,

Determines if the elements of this Iterator are lexicographically less than those of another.

fn le<I>(self, other: I) -> bool

where I: IntoIterator, Self::Item: PartialOrd<<I as IntoIterator>::Item>, Self: Sized,

Determines if the elements of this Iterator are lexicographically less or equal to those of another.

fn gt<I>(self, other: I) -> bool

where I: IntoIterator, Self::Item: PartialOrd<<I as IntoIterator>::Item>, Self: Sized,

Determines if the elements of this Iterator are lexicographically greater than those of another.

fn ge<I>(self, other: I) -> bool

where I: IntoIterator, Self::Item: PartialOrd<<I as IntoIterator>::Item>, Self: Sized,

Determines if the elements of this Iterator are lexicographically greater than or equal to those of another.

fn is_sorted(self) -> bool

where Self: Sized, Self::Item: PartialOrd,

Checks if the elements of this iterator are sorted.

fn is_sorted_by<F>(self, compare: F) -> bool

where Self: Sized, F: FnMut(&Self::Item, &Self::Item) -> bool,

Checks if the elements of this iterator are sorted using the given comparator function.

fn is_sorted_by_key<F, K>(self, f: F) -> bool

where Self: Sized, F: FnMut(Self::Item) -> K, K: PartialOrd,

Checks if the elements of this iterator are sorted using the given key extraction function.