| import AUXLib.Arithmetic | |
| import SimpleC.SL.SeparationLogic | |
| namespace Algorithms.lcs_n.lean | |
| open AUXLib | |
| def LCSNCellIndex (n row col : Int) : Int := row * (n + 1) + col | |
| def LCSNCellRecurrence (xs ys table : List Int) (n row col : Int) : Prop := | |
| ((row = 0 ∨ col = 0) ∧ Znth (LCSNCellIndex n row col) table 0 = 0) ∨ | |
| (0 < row ∧ 0 < col ∧ | |
| ((Znth (row - 1) xs 0 = Znth (col - 1) ys 0 ∧ | |
| Znth (LCSNCellIndex n row col) table 0 = | |
| Znth (LCSNCellIndex n (row - 1) (col - 1)) table 0 + 1) ∨ | |
| (Znth (row - 1) xs 0 ≠ Znth (col - 1) ys 0 ∧ | |
| Znth (LCSNCellIndex n row col) table 0 = | |
| max (Znth (LCSNCellIndex n (row - 1) col) table 0) | |
| (Znth (LCSNCellIndex n row (col - 1)) table 0)))) | |
| def LCSNTableResult (xs ys : List Int) (n : Int) (table : List Int) : Prop := | |
| Zlength table = (n + 1) * (n + 1) ∧ ∀ row col, | |
| (0 ≤ row ∧ row ≤ n) → (0 ≤ col ∧ col ≤ n) → | |
| LCSNCellRecurrence xs ys table n row col | |
| end Algorithms.lcs_n.lean | |