File size: 3,758 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 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 | /*@ Extern Coq (multiset :: * => *) */
/*@ Extern Coq
(heap_capacity : Z)
(mlist : {A} -> multiset A -> list A)
(list_to_multiset : {A} -> list A -> multiset A)
(multiset_size : {A} -> multiset A -> Z)
(multiset_equiv : {A} -> multiset A -> multiset A -> Prop)
(multiset_insert : {A} -> multiset A -> A -> multiset A)
(multiset_remove :
{A} -> multiset A -> A -> multiset A)
(multiset_max : multiset Z -> Z)
(multiset_maximum : multiset Z -> Z -> Prop)
(store_heap : Z -> multiset Z -> Z -> Assertion)
(heap_retired_cell : Z -> Z -> Z -> Assertion)
(heap_representation :
multiset Z -> list Z -> Z -> Prop)
(PrefixMaximum : list Z -> Z -> Z -> Prop)
(PushSource : list Z -> multiset Z -> Z -> Z -> Prop)
(PushLoopState : list Z -> list Z -> Z -> Z -> Z -> Prop)
(PushResult : multiset Z -> list Z -> Z -> Z -> Prop)
(BuildPrefixState : multiset Z -> list Z -> Z -> Prop)
(heap_parent : Z -> Z)
(PopLoopState : list Z -> list Z -> Z -> Z -> Prop)
(PopSelectedChild : list Z -> Z -> Z -> Z -> Prop)
(PopReadyState : list Z -> list Z -> Z -> Z -> Prop)
(PopResult :
multiset Z -> list Z -> list Z -> Z -> Z -> Prop)
(HeapSortState :
list Z -> multiset Z -> list Z -> Prop)
(Permutation : list Z -> list Z -> Prop)
(increasing : list Z -> Prop)
*/
/*@ Import Coq Require Import PVbench.Data_structures.priority_queue.rocq.spec_lib */
void push(int *heap, int n, int x)
/*@ With (S_before : multiset Z)
Require
n < heap_capacity &&
store_heap(heap, S_before, n) *
IntArray::undef_seg(heap, n, n + 1)
Ensure
store_heap(
heap, multiset_insert(S_before, x), n + 1
)
*/
{
heap[n] = x;
int child = n;
while (child > 0) {
int parent = (child - 1) / 2;
if (heap[parent] >= heap[child]) {
break;
}
int tmp = heap[parent];
heap[parent] = heap[child];
heap[child] = tmp;
child = parent;
}
}
void build(int *heap, int n)
/*@ With (input : list Z)
Require
0 <= n &&
n <= heap_capacity &&
Zlength(input) == n &&
IntArray::full(heap, n, input)
Ensure
store_heap(heap, list_to_multiset(input), n)
*/
{
for (int i = 1; i < n; ++i) {
int x = heap[i];
push(heap, i, x);
}
}
int pop(int *heap, int n)
/*@ With (S_before : multiset Z)
Require
1 <= n &&
store_heap(heap, S_before, n)
Ensure
__return == multiset_max(S_before) &&
multiset_maximum(S_before, __return) &&
store_heap(
heap,
multiset_remove(S_before, multiset_max(S_before)),
n - 1
) *
IntArray::undef_seg(heap, n - 1, n)
*/
{
int ret = heap[0];
if (n == 1) {
return ret;
}
heap[0] = heap[n - 1];
int idx = 0;
while (idx * 2 + 1 < n - 1) {
int left = idx * 2 + 1;
int right = left + 1;
int largest = left;
if (right < n - 1 && heap[left] < heap[right]) {
largest = right;
}
if (heap[idx] >= heap[largest]) {
break;
}
int tmp = heap[idx];
heap[idx] = heap[largest];
heap[largest] = tmp;
idx = largest;
}
return ret;
}
void heap_sort(int *heap, int n)
/*@ With (input : list Z)
Require
0 <= n &&
n <= heap_capacity &&
Zlength(input) == n &&
IntArray::full(heap, n, input)
Ensure
exists output,
Zlength(output) == n &&
Permutation(input, output) &&
increasing(output) &&
IntArray::full(heap, n, output)
*/
{
build(heap, n);
int i = n;
while (i > 0) {
int extracted = pop(heap, i);
heap[i - 1] = extracted;
--i;
}
}
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