File size: 2,025 Bytes
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 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 | /*@ Import Lean
import Algorithms.huffman_encoding.lean.spec_lib
open scoped SimpleC
*/
/*
* Huffman encoding: minimum weighted path length of a binary prefix code.
*
* Repeatedly merging the two smallest live weights constructs a Huffman tree.
* The sum of all merge weights is that tree's weighted path length and is
* minimum among all full binary prefix-code trees over the input frequencies.
*
* This verification-oriented implementation uses a fresh selection scan for
* each of the two minima. Removing a selected item is done by moving the last
* live item into its slot, so only the prefix work[0..active) is live.
*/
/*@ Extern Coq
(HuffmanInputBounded : list Z -> Prop)
(HuffmanOptimalCost : list Z -> Z -> Prop)
(HuffmanScratchFinal : list Z -> list Z -> Prop)
*/
int huffman_cost(int *weights, int n, int *work)
/*@ With (weights_l : list Z)
Require
1 <= n && n <= 8 &&
Zlength(weights_l) == n &&
HuffmanInputBounded(weights_l) &&
IntArray::full(weights, n, weights_l) *
IntArray::undef_full(work, n)
Ensure
exists work_l,
Zlength(work_l) == n &&
HuffmanOptimalCost(weights_l, __return) &&
HuffmanScratchFinal(weights_l, work_l) &&
0 <= __return && __return <= 56000 &&
IntArray::full(weights, n, weights_l) *
IntArray::full(work, n, work_l)
*/
{
for (int i = 0; i < n; ++i) {
work[i] = weights[i];
}
int active = n;
int total = 0;
while (active > 1) {
int first = 0;
for (int i = 1; i < active; ++i) {
if (work[i] < work[first]) {
first = i;
}
}
int x = work[first];
--active;
work[first] = work[active];
int second = 0;
for (int i = 1; i < active; ++i) {
if (work[i] < work[second]) {
second = i;
}
}
int y = work[second];
--active;
work[second] = work[active];
int merged = x + y;
total += merged;
work[active] = merged;
++active;
}
return total;
}
|