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Added - Add property test `biclique_complement_size` for `adjacency_list`. - Add property test `biclique_complement_size` for `adjacency_matrix`. - Add property test `complete_complement_eq_empty` for `adjacency_list`. - Add property test `complete_complement_eq_empty` for `adjacency_matrix`. - Add property test `cycle_complement_size` for `adjacency_list`. - Add property test `cycle_complement_size` for `adjacency_matrix`. - Add property test `empty_complement_eq_complete` for `adjacency_list`. - Add property test `empty_complement_eq_complete` for `adjacency_matrix`. - Add property test `star_complement_size` for `adjacency_list`. - Add property test `star_complement_size` for `adjacency_matrix`. - Add the `Complement` trait.
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,150 @@ | ||
| //! Generate the complement of a digraph. | ||
| //! | ||
| //! The complement of a digraph contains all arcs not present in the original | ||
| //! digraph. | ||
| //! | ||
| //! # Examples | ||
| //! | ||
| //! ``` | ||
| //! use graaf::{ | ||
| //! adjacency_list::Digraph, | ||
| //! gen::Cycle, | ||
| //! op::{ | ||
| //! AddArc, | ||
| //! Arcs, | ||
| //! Complement, | ||
| //! }, | ||
| //! }; | ||
| //! | ||
| //! // 0 -> {1} | ||
| //! // 1 -> {2} | ||
| //! // 2 -> {3} | ||
| //! // 3 -> {0} | ||
| //! | ||
| //! let digraph = Digraph::cycle(4); | ||
| //! | ||
| //! // 0 -> {2, 3} | ||
| //! // 1 -> {0, 3} | ||
| //! // 2 -> {0, 1} | ||
| //! // 3 -> {1, 2} | ||
| //! | ||
| //! let converse = digraph.complement(); | ||
| //! | ||
| //! assert!(converse.arcs().eq([ | ||
| //! (0, 2), | ||
| //! (0, 3), | ||
| //! (1, 0), | ||
| //! (1, 3), | ||
| //! (2, 0), | ||
| //! (2, 1), | ||
| //! (3, 1), | ||
| //! (3, 2) | ||
| //! ])); | ||
| //! ``` | ||
| use crate::gen::Empty; | ||
|
|
||
| use super::{ | ||
| AddArc, | ||
| HasArc, | ||
| Order, | ||
| }; | ||
|
|
||
| /// Generate the complement of a digraph. | ||
| /// | ||
| /// # How do I implement `Complement`? | ||
| /// | ||
| /// Provide an implementation of `complement` that returns a digraph with all | ||
| /// arcs not present in the original digraph. | ||
| /// | ||
| /// ``` | ||
| /// use { | ||
| /// graaf::op::Complement, | ||
| /// std::collections::BTreeSet, | ||
| /// }; | ||
| /// | ||
| /// struct Digraph { | ||
| /// arcs: Vec<BTreeSet<usize>>, | ||
| /// } | ||
| /// | ||
| /// impl Complement for Digraph { | ||
| /// fn complement(&self) -> Self { | ||
| /// let order = self.arcs.len(); | ||
| /// let mut arcs = vec![BTreeSet::<usize>::new(); order]; | ||
| /// | ||
| /// for u in 0..order { | ||
| /// for v in u + 1..order { | ||
| /// if !self.arcs[u].contains(&v) { | ||
| /// arcs[u].insert(v); | ||
| /// } | ||
| /// | ||
| /// if !self.arcs[v].contains(&u) { | ||
| /// arcs[v].insert(u); | ||
| /// } | ||
| /// } | ||
| /// } | ||
| /// | ||
| /// Self { arcs } | ||
| /// } | ||
| /// } | ||
| /// | ||
| /// // 0 -> {1} | ||
| /// // 1 -> {2} | ||
| /// // 2 -> {3} | ||
| /// // 3 -> {0} | ||
| /// | ||
| /// let digraph = Digraph { | ||
| /// arcs: vec![ | ||
| /// BTreeSet::from([1]), | ||
| /// BTreeSet::from([2]), | ||
| /// BTreeSet::from([3]), | ||
| /// BTreeSet::from([0]), | ||
| /// ], | ||
| /// }; | ||
| /// | ||
| /// // 0 -> {2, 3} | ||
| /// // 1 -> {0, 3} | ||
| /// // 2 -> {0, 1} | ||
| /// // 3 -> {1, 2} | ||
| /// | ||
| /// let complement = digraph.complement(); | ||
| /// | ||
| /// assert_eq!( | ||
| /// complement.arcs, | ||
| /// vec![ | ||
| /// BTreeSet::from([2, 3]), | ||
| /// BTreeSet::from([0, 3]), | ||
| /// BTreeSet::from([0, 1]), | ||
| /// BTreeSet::from([1, 2]), | ||
| /// ], | ||
| /// ); | ||
| /// ``` | ||
| pub trait Complement { | ||
| /// Generates the complement of the digraph. | ||
| #[must_use] | ||
| fn complement(&self) -> Self; | ||
| } | ||
|
|
||
| impl<D> Complement for D | ||
| where | ||
| D: AddArc + Empty + HasArc + Order, | ||
| { | ||
| fn complement(&self) -> Self { | ||
| let order = self.order(); | ||
| let mut digraph = D::empty(order); | ||
|
|
||
| for u in 0..order { | ||
| for v in u + 1..order { | ||
| if !self.has_arc(u, v) { | ||
| digraph.add_arc(u, v); | ||
| } | ||
|
|
||
| if !self.has_arc(v, u) { | ||
| digraph.add_arc(v, u); | ||
| } | ||
| } | ||
| } | ||
|
|
||
| digraph | ||
| } | ||
| } |
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