Struct dlx_rs::solver::Solver

source · [−]
pub struct Solver { /* private fields */ }
Expand description

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

// Iterate through all solutions
assert_eq!(s.next().unwrap(), ["o2","o3","o4"]);

Implementations

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

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

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

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
       ⥯      ⥯     ⥯     ⥯

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
       ⥯            ⥯     ⥯

Reverse of function cover

Implements algorithm X as a finite state machine

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

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

// First get all solutions
let sols: Vec<Vec<String>> = 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

Returns a copy of the value. Read more

Performs copy-assignment from source. Read more

Formats the value using the given formatter. Read more

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

The type of the elements being iterated over.

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

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

Returns the bounds on the remaining length of the iterator. Read more

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

Consumes the iterator, returning the last element. Read more

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

Advances the iterator by n elements. Read more

Returns the nth element of the iterator. Read more

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

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

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

🔬 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. Read more

🔬 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. Read more

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

Calls a closure on each element of an iterator. Read more

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

Creates an iterator that both filters and maps. Read more

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

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. Read more

Creates an iterator that skips elements based on a predicate. Read more

Creates an iterator that yields elements based on a predicate. Read more

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

Creates an iterator that skips the first n elements. Read more

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

An iterator adapter similar to fold that holds internal state and produces a new iterator. Read more

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

Creates an iterator that flattens nested structure. Read more

Creates an iterator which ends after the first None. Read more

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

Borrows an iterator, rather than consuming it. Read more

Transforms an iterator into a collection. Read more

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

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

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

Collects all the items from an iterator into a collection. Read more

Consumes an iterator, creating two collections from it. Read more

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

Reorders the elements of this iterator in-place according to the given predicate, such that all those that return true precede all those that return false. Returns the number of true elements found. Read more

🔬 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. Read more

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

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

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

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

🔬 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. Read more

Tests if every element of the iterator matches a predicate. Read more

Tests if any element of the iterator matches a predicate. Read more

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

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

🔬 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. Read more

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

Searches for an element in an iterator from the right, returning its index. Read more

Returns the maximum element of an iterator. Read more

Returns the minimum element of an iterator. Read more

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

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

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

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

Reverses an iterator’s direction. Read more

Converts an iterator of pairs into a pair of containers. Read more

Creates an iterator which copies all of its elements. Read more

Creates an iterator which clones all of its elements. Read more

Repeats an iterator endlessly. Read more

Sums the elements of an iterator. Read more

Iterates over the entire iterator, multiplying all the elements Read more

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

🔬 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. Read more

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

🔬 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. Read more

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

🔬 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. Read more

Determines if the elements of this Iterator are unequal to those of another. Read more

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

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

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

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

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

Checks if the elements of this iterator are sorted. Read more

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

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

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

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

Auto Trait Implementations

Blanket Implementations

Gets the TypeId of self. Read more

Immutably borrows from an owned value. Read more

Mutably borrows from an owned value. Read more

Returns the argument unchanged.

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

The type of the elements being iterated over.

Which kind of iterator are we turning this into?

Creates an iterator from a value. Read more

The resulting type after obtaining ownership.

Creates owned data from borrowed data, usually by cloning. Read more

Uses borrowed data to replace owned data, usually by cloning. Read more

Converts the given value to a String. Read more

The type returned in the event of a conversion error.

Performs the conversion.

The type returned in the event of a conversion error.

Performs the conversion.