| import AUXLib.Arithmetic |
| import SimpleC.SL.SeparationLogic |
| import AUXLib.ListLib.LengthCompat |
| import AUXLib.ListLib.Arithmetic |
| import MaxMinLib.Interface |
|
|
| namespace Algorithms.huffman_encoding.lean |
|
|
| open AUXLib MaxMinLib |
|
|
| inductive HuffmanTree : Type |
| | HuffmanLeaf : Int → HuffmanTree |
| | HuffmanNode : HuffmanTree → HuffmanTree → HuffmanTree |
|
|
| export HuffmanTree (HuffmanLeaf HuffmanNode) |
|
|
| def HuffmanLeaves : HuffmanTree → List Int |
| | .HuffmanLeaf weight => [weight] |
| | .HuffmanNode left_tree right_tree => HuffmanLeaves left_tree ++ HuffmanLeaves right_tree |
|
|
| def HuffmanTreeWeight : HuffmanTree → Int |
| | .HuffmanLeaf weight => weight |
| | .HuffmanNode left_tree right_tree => HuffmanTreeWeight left_tree + HuffmanTreeWeight right_tree |
|
|
| def HuffmanWeightedPathLength : HuffmanTree → Int |
| | .HuffmanLeaf _ => 0 |
| | .HuffmanNode left_tree right_tree => |
| HuffmanWeightedPathLength left_tree + HuffmanWeightedPathLength right_tree + |
| HuffmanTreeWeight left_tree + HuffmanTreeWeight right_tree |
|
|
| def HuffmanTreeFeasible (weights : List Int) (tree : HuffmanTree) : Prop := |
| List.Perm weights (HuffmanLeaves tree) |
|
|
| def HuffmanOptimalCost (weights : List Int) (answer : Int) : Prop := |
| min_value_of_subset (· ≤ ·) (HuffmanTreeFeasible weights) HuffmanWeightedPathLength answer |
|
|
| def HuffmanInputBounded (weights : List Int) : Prop := |
| ∀ i, (0 ≤ i ∧ i < Zlength weights) → (1 ≤ Znth i weights 0 ∧ Znth i weights 0 ≤ 1000) |
|
|
| def HuffmanScratchFinal (weights scratch : List Int) : Prop := Znth 0 scratch 0 = sum weights |
|
|
| end Algorithms.huffman_encoding.lean |
|
|
