shared_ptr<Heap> reduce(shared_ptr<Heap> h, shared_ptr<Heap> root, Data v) {
if (v > h->val) return root;
h->val = v;
if (!h->p) return root;
if (h->val < h->p->val) {
if (h->p->l && h->p->l == h) {
h->p->l.reset();
return meld(h, root);
} else {
h->p->r.reset();
return meld(h, root);
}
} else return root;
}
void delete_min_phase_1(heap *h) {
node *min = h->root;
if (has_children(min)) {
// Orphan all children
node *first = min->child;
node *curr = min->child;
do {
curr->parent = NULL;
curr = curr->right_sibling;
} while (curr != first);
// If the root has siblings, first cut it out of its sibling list
// and then meld sibling and children lists
if (has_siblings(min)) {
node *rsib = min->right_sibling;
cut_from_sibling_list(min);
meld(first, rsib);
}
// Pick the first child as the new temporary root
h->root = first;
} else {
// Due to the early return in the top, we are guaranteed that
// if min has no children, it must have siblings, so we start
// by cutting it out of its sibling list.
node *sib = min->right_sibling;
cut_from_sibling_list(min);
// Pick a sibling (arbitrary) as the new temporary root
h->root = sib;
}
}
node* insert(heap *h, int key) {
// Create a brand new node
node *n = (node*) malloc(sizeof(node));
n->parent = NULL;
n->child = NULL;
n->left_sibling = n;
n->right_sibling = n;
n->key = key;
n->rank = 0;
n->marked = 0;
n->data = NULL;
// Meld it with the root of the heap, if it is non-null
if (h->root != NULL) {
meld(h->root, n);
if (key < h->root->key) {
h->root = n;
}
} else {
h->root = n;
}
// Remember to update the size of the heap
h->size++;
return n;
}
/* --- insert() ---
* Inserts an item $item$ with associated key $k$ into the heap.
*/
void FHeap::insert(int item, float k)
{
FHeapNode *newNode;
#if FHEAP_DUMP
printf("insert, ");
#endif
/* create an initialise the new node */
newNode = new FHeapNode;
newNode->child = NULL;
newNode->left = newNode->right = newNode;
newNode->rank = 0;
newNode->item = item;
newNode->key = k;
/* maintain a pointer to $item$'s new node in the heap */
nodes[item] = newNode;
/* meld the new node into the heap */
meld(newNode);
/* update the heaps node count */
itemCount++;
#if FHEAP_DUMP
printf("insert-exited, ");
#endif
}
node *meld(node *a, node *b) {
if (!a) return b;
if (!b) return a;
if (a->val > b->val) swap(a, b);
a->r = meld(a->r, b);
swap(a->l, a->r);
return a;
}
static int skew_merge (lua_State *L) {
heap *h1 = checkheap(L, 1);
heap *h2 = checkheap(L, 2);
lua_settop(L, 2);
if (h2 == NULL) { lua_pop(L, 1); return 1; } /* h1 */
meld(h1, h2);
return 1; /* h2 */
}
shared_ptr<Heap> meld(shared_ptr<Heap> a, shared_ptr<Heap> b) {
if (!a) return b;
if (!b) return a;
if (a->val > b->val) swap(a, b);
a->r = meld(a->r, b);
swap(a->l, a->r);
return a;
}
void Token::meld(Ref<Token> root0, Ref<Token> root1)
{
if ((!root0) || (!root1)) return;
if (!root1->firstChild()) return;
Token result_;
Ref<Token, Pointer> result = &result_;
Ref<Token, Owner> token0 = root0->firstChild();
Ref<Token, Owner> token1 = root1->firstChild();
// debug("Token::meld(): [%%: %%], [%%: %%]\n", root0->ruleName_, root0->countChildren(), root1->ruleName_, root1->countChildren());
while (true)
{
bool take0 = (token0);
bool take1 = (token1);
if (take0 && take1) {
take0 = (token0->i0_ < token1->i0_);
take1 = !take0;
}
if (take0) {
// debug("p0 [%%, %%, %%]\n", token0->ruleName_, token0->i0_, token0->i1_);
Ref<Token, Owner> next0 = token0->nextSibling();
Ref<Token> previousResult = result->lastChild();
token0->unlink();
result->insertChild(token0, previousResult);
if (previousResult)
token0->burn(previousResult->i0_, previousResult->i1_);
token0 = next0;
}
else if (take1) {
// debug("p1 [%%, %%, %%]\n", token1->ruleName_, token1->i0_, token1->i1_);
Ref<Token, Owner> next1 = token1->nextSibling();
Ref<Token> previousResult = result->lastChild();
token1->unlink();
if (previousResult) {
if ((previousResult->i0_ < token1->i0_) && (token1->i1_ < previousResult->i1_)) {
// see book 28/76: case 5
Token dummy;
dummy.appendChild(token1);
meld(previousResult, &dummy);
token1 = next1;
continue;
}
}
result->insertChild(token1, previousResult);
if (previousResult)
previousResult->burn(token1->i0_, token1->i1_);
token1 = next1;
}
else
break;
}
root0->appendAllChildrenOf(result);
}
/* --- deleteMin() ---
* Deletes and returns the minimum item from the heap.
*/
int FHeap::deleteMin()
{
FHeapNode *minNode, *child, *next;
float k, k2;
int r, v, item;
#if FHEAP_DUMP
printf("deleteMin, ");
#endif
/* First we determine the maximum rank in the heap. */
v = treeSum;
r = -1;
while(v) {
v = v >> 1;
r++;
};
/* Now determine which root node is the minimum. */
minNode = trees[r];
k = minNode->key;
while(r > 0) {
r--;
next = trees[r];
if(next) {
if((k2 = next->key) < k) {
k = k2;
minNode = next;
}
compCount++;
}
}
/* We remove the minimum node from the heap but keep a pointer to it. */
r = minNode->rank;
trees[r] = NULL;
treeSum -= (1 << r);
child = minNode->child;
if(child) meld(child);
/* Record the vertex no of the old minimum node before deleting it. */
item = minNode->item;
nodes[item] = NULL;
delete minNode;
itemCount--;
#if FHEAP_DUMP
printf("deleteMin-exited, ");
#endif
return item;
}
shared_ptr<Heap> meld(
shared_ptr<Heap> a, shared_ptr<Heap> b, shared_ptr<Heap> p = nullptr) {
if (!a) {
if (b) b->p = p;
return b;
}
if (!b) {
if (a) a->p = p;
return a;
}
if (a->val > b->val) swap(a, b);
a->p = p;
a->r = meld(a->r, b, a);
swap(a->l, a->r);
return a;
}
void insert_item(item* i, heap* h) {
heap* new_h = make_heap();
node* n = (node*)malloc(sizeof(node));
n->key = i->key;
n->rank = 0;
n->marked = 0;
n->item = i;
n->parent = NULL;
n->child = NULL;
n->left_sibling = n;
n->right_sibling = n;
new_h->min_node = n;
i->n = n;
meld(h, new_h);
}
void decrease_key_cut(heap *h, node *n) {
// Cut is only relevant on non-roots
if (n->parent != NULL) {
// Remember the parent
node *parent = n->parent;
// Then cut out the subtree, and insert as a new root
cut_subtree(n);
meld(h->root, n);
// If the parent was marked, cut recursively
if (parent->marked) {
parent->marked = 0;
decrease_key_cut(h, parent);
} else {
parent->marked = 1;
}
}
// Update the heap minimum
h->root = (n->key < h->root->key) ? n : h->root;
}
shared_ptr<Heap> push(shared_ptr<Heap> h, Data v) {
return meld(h, make_shared<Heap>(v));
}
/* --- decreaseKey() ---
* Decreases the key used for item $item$ to the value newValue. It is left
* for the user to ensure that newValue is in-fact less than the current value
*/
void FHeap::decreaseKey(int item, float newValue)
{
FHeapNode *cutNode, *parent, *newRoots, *r, *l;
int prevRank;
#if FHEAP_DUMP
printf("decreaseKey on vn = %d, ", item);
#endif
/* Obtain a pointer to the decreased node and its parent then decrease the
* nodes key.
*/
cutNode = nodes[item];
parent = cutNode->parent;
cutNode->key = newValue;
/* No reinsertion occurs if the node changed was a root. */
if(!parent) {
#if FHEAP_DUMP
printf("decreaseKey-exited, ");
#endif
return;
}
/* Update the left and right pointers of cutNode and its two neighbouring
* nodes.
*/
l = cutNode->left;
r = cutNode->right;
l->right = r;
r->left = l;
cutNode->left = cutNode->right = cutNode;
/* Initially the list of new roots contains only one node. */
newRoots = cutNode;
/* While there is a parent node that is marked a cascading cut occurs. */
while(parent && parent->marked) {
/* Decrease the rank of cutNode's parent and update its child pointer.
*/
parent->rank--;
if(parent->rank) {
if(parent->child == cutNode) parent->child = r;
}
else {
parent->child = NULL;
}
/* Update the cutNode and parent pointers to the parent. */
cutNode = parent;
parent = cutNode->parent;
/* Update the left and right pointers of cutNodes two neighbouring
* nodes.
*/
l = cutNode->left;
r = cutNode->right;
l->right = r;
r->left = l;
/* Add cutNode to the list of nodes to be reinserted as new roots. */
l = newRoots->left;
newRoots->left = l->right = cutNode;
cutNode->left = l;
cutNode->right = newRoots;
newRoots = cutNode;
}
/* If the root node is being relocated then update the trees[] array.
* Otherwise mark the parent of the last node cut.
*/
if(!parent) {
prevRank = cutNode->rank + 1;
trees[prevRank] = NULL;
treeSum -= (1 << prevRank);
}
else {
/* Decrease the rank of cutNode's parent an update its child pointer.
*/
parent->rank--;
if(parent->rank) {
if(parent->child == cutNode) parent->child = r;
}
else {
parent->child = NULL;
}
parent->marked = 1;
}
/* Meld the new roots into the heap. */
meld(newRoots);
#if FHEAP_DUMP
printf("decreaseKey-exited, ");
#endif
}
void delete_min_phase_2(heap *h) {
int max_rank = (int) ceil(2 * (log(h->size + 1) / log(2.0)));
node *ranks[max_rank];
for (int i = 0; i < max_rank; i++) {
ranks[i] = NULL;
}
// The chain of root nodes is modified in the linking step, so to make
// absolutely sure we go through all the root nodes, we store pointers
// to them in an array, and iterate the array instead of depending on
// the possibly shifty sibling list.
int n = root_count(h);
node **roots = (node**) malloc(n * sizeof(node*));
// Populate the array
node *current = h->root;
for (int i = 0; i < n; i++) {
roots[i] = current;
current = current->right_sibling;
}
// Go through each node in the array
for (int i = 0; i < n; i++) {
node *curr = roots[i];
// If there are pre-existing array entries, start linking
while (ranks[curr->rank] != NULL) {
// Determine winner and loser
node *winner = (curr->key < ranks[curr->rank]->key ? curr : ranks[curr->rank]);
node *loser = (curr->key < ranks[curr->rank]->key ? ranks[curr->rank] : curr);
// Null the array entry right away
ranks[curr->rank] = NULL;
// Update loser's parent pointer and promote winner
loser->parent = winner;
winner->rank += 1;
// Cut loser out of its sibling list, and meld with the
// children list of the winner (if any, otherwise just
// set the loser as the only child of the winner).
cut_from_sibling_list(loser);
if (has_children(winner)) {
meld(winner->child, loser);
} else {
winner->child = loser;
}
// Update current to be the winner
curr = winner;
}
// Otherwise/finally, insert current into its place in the
// array, and make it the temporary heap root.
ranks[curr->rank] = curr;
h->root = curr;
}
// Free the possibly HUGE array
free(roots);
}
pair<shared_ptr<Heap>, shared_ptr<Heap>> push(shared_ptr<Heap> h, Data v) {
auto n = make_shared<Heap>(v);
return make_pair(meld(h, n), n);
}
shared_ptr<Heap> pop(shared_ptr<Heap> h) {
return meld(h->l, h->r);
}
void pop() {
node *t = root;
root = meld(t->l, t->r);
t.l = t.r = NULL;
delete t;
}
void push(const T& val) { root = meld(root, new node(val)); }
void meld(const meldable_heap<T>&& t) { root = meld(root, t.root); }
shared_ptr<Heap> pop(shared_ptr<Heap> h) {
if (h->l) h->l->p.reset();
if (h->r) h->r->p.reset();
return meld(h->l, h->r);
}