| import AUXLib.Arithmetic |
| import SimpleC.SL.SeparationLogic |
|
|
| namespace Algorithms.minimal_representation.lean |
|
|
| open AUXLib |
|
|
| def MRRotation (l : List Int) (start : Int) : List Int := |
| sublist start (start + Zlength l) (l ++ l) |
|
|
| def MRValidStart (l : List Int) (start : Int) : Prop := 0 ≤ start ∧ start < Zlength l |
|
|
| def MRRotationValue (l : List Int) (start offset : Int) : Int := Znth (start + offset) (l ++ l) 0 |
|
|
| def MRRotationPrefixEq (l : List Int) (left right prefix_len : Int) : Prop := |
| ∀ offset, (0 ≤ offset ∧ offset < prefix_len) → |
| MRRotationValue l left offset = MRRotationValue l right offset |
|
|
| def MRRotationEq (l : List Int) (left right : Int) : Prop := |
| MRRotationPrefixEq l left right (Zlength l) |
|
|
| def MRRotationLt (l : List Int) (left right : Int) : Prop := |
| ∃ first_diff, (0 ≤ first_diff ∧ first_diff < Zlength l) ∧ |
| MRRotationPrefixEq l left right first_diff ∧ |
| MRRotationValue l left first_diff < MRRotationValue l right first_diff |
|
|
| def MRRotationLe (l : List Int) (left right : Int) : Prop := |
| MRRotationLt l left right ∨ MRRotationEq l left right |
|
|
| def MRMinimalRotationAt (l : List Int) (start : Int) : Prop := |
| MRValidStart l start ∧ ∀ other, MRValidStart l other → MRRotationLe l start other |
|
|
| def MRFirstMinimalRotationAt (l : List Int) (start : Int) : Prop := |
| MRMinimalRotationAt l start ∧ |
| ∀ other, MRValidStart l other → MRRotationEq l start other → start ≤ other |
|
|
| end Algorithms.minimal_representation.lean |
|
|
