| import AUXLib.Arithmetic | |
| import SimpleC.SL.SeparationLogic | |
| import AUXLib.ListLib.LengthCompat | |
| import AUXLib.ListLib.Arithmetic | |
| import MaxMinLib.Interface | |
| namespace Algorithms.house_robber.lean | |
| open AUXLib MaxMinLib | |
| def NonAdjacentIndexList (limit : Int) (picks : List Int) : Prop := | |
| 0 ≤ limit ∧ NoDup picks ∧ Forall (fun i => 0 ≤ i ∧ i < limit) picks ∧ | |
| ∀ i j : Int, i ∈ picks → j ∈ picks → i ≠ j → 2 ≤ Z.abs (i - j) | |
| def RobPlanValue (l picks : List Int) : Int := sum (picks.map (fun i => Znth i l 0)) | |
| def RobPrefixValue (l : List Int) (len value : Int) : Prop := | |
| ∃ picks, (0 ≤ len ∧ len ≤ Zlength l) ∧ NonAdjacentIndexList len picks ∧ | |
| value = RobPlanValue l picks | |
| def HouseRobberAnswer (l : List Int) (answer : Int) : Prop := | |
| MaxMinLib.max_value_of_subset (· ≤ ·) (fun value => RobPrefixValue l (Zlength l) value) | |
| (fun value => value) answer | |
| end Algorithms.house_robber.lean | |