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bff4ec7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 | 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
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