/**
* Recurses up the tree to make a series of cascading cuts. Cuts each
* node that has lost two children from its parent.
*
* @param queue Queue to which node belongs
* @param node Node to cut
*/
static void cut_from_parent( fibonacci_heap *queue, fibonacci_node *node )
{
fibonacci_node *next, *prev;
if ( node->parent != NULL ) {
next = node->next_sibling;
prev = node->prev_sibling;
next->prev_sibling = node->prev_sibling;
prev->next_sibling = node->next_sibling;
node->next_sibling = node;
node->prev_sibling = node;
node->parent->rank--;
if ( node->parent->first_child == node )
{
if ( node->parent->rank == 0 )
node->parent->first_child = NULL;
else
node->parent->first_child = next;
}
if ( node->parent->marked == FALSE )
node->parent->marked = TRUE;
else
cut_from_parent( queue, node->parent );
queue->minimum = append_lists( queue, node, queue->minimum );
node->parent = NULL;
}
else
{
if( node->key < queue->minimum->key )
queue->minimum = node;
}
}
fibonacci_node* pq_insert( fibonacci_heap *queue, item_type item, key_type key )
{
fibonacci_node* wrapper = pq_alloc_node( queue->map, 0 );
ITEM_ASSIGN( wrapper->item, item );
wrapper->key = key;
wrapper->next_sibling = wrapper;
wrapper->prev_sibling = wrapper;
queue->size++;
queue->minimum = append_lists( queue, queue->minimum, wrapper );
return wrapper;
}
node *quicksort(node *list)
{
node *first_node; /* first node */
node *list_sorted, *list_sorted_final; /* copied list */
node *list_left, *list_right, *sorted_list_left, *sorted_list_right; /* left and right side of original list */
node *item; /* variable used in for loop condition */
list_left = NULL;
list_right = NULL;
if (list == NULL || list->next == NULL)
{
list_sorted = copy_list(list);
return list_sorted;
}
first_node = create_node(list->data, NULL); /* Copy the first node of list */
for (item = list->next; item != NULL; item = item->next)
{
if (item->data < first_node->data)
{
list_left = create_node(item->data, list_left);
}
else /* item >= first_node */
{
list_right = create_node(item->data, list_right);
}
}
sorted_list_left = quicksort(list_left);
sorted_list_right = quicksort(list_right);
list_sorted = append_lists(sorted_list_left, first_node);
list_sorted_final = append_lists(list_sorted, sorted_list_right);
free_list(list_left);
free_list(list_right);
free_list(sorted_list_left);
free_list(sorted_list_right);
free_list(list_sorted);
free_list(first_node);
assert(is_sorted(list_sorted_final));
return list_sorted_final;
}
/**
* Links two trees, making the item with lesser key the parent, breaking
* ties arbitrarily.
*
* @param queue Queue to which roots belong
* @param a First root
* @param b Second root
* @return The resulting merged tree
*/
static fibonacci_node* link( fibonacci_heap *queue, fibonacci_node *a,
fibonacci_node *b )
{
fibonacci_node *parent, *child;
if ( b->key < a->key ) {
parent = b;
child = a;
}
else {
parent = a;
child = b;
}
// roots are automatically unmarked
child->marked = FALSE;
child->parent = parent;
child->next_sibling = child;
child->prev_sibling = child;
parent->first_child = append_lists( queue, parent->first_child, child );
parent->rank++;
return parent;
}
key_type pq_delete( fibonacci_heap *queue, fibonacci_node *node )
{
if( node == queue->minimum )
return pq_delete_min( queue );
key_type key = node->key;
fibonacci_node *child = node->first_child;
// remove from sibling list
node->next_sibling->prev_sibling = node->prev_sibling;
node->prev_sibling->next_sibling = node->next_sibling;
if ( node->parent != NULL )
{
node->parent->rank--;
// if not a root, see if we need to update parent's first child
if ( node->parent->first_child == node )
{
if ( node->parent->rank == 0 )
node->parent->first_child = NULL;
else
node->parent->first_child = node->next_sibling;
}
if ( node->parent->marked == FALSE )
node->parent->marked = TRUE;
else
cut_from_parent( queue, node->parent );
}
pq_free_node( queue->map, 0, node );
queue->size--;
append_lists( queue, queue->minimum, child );
return key;
}
/**
* Merges two node lists into one to update the root system of the queue.
* Iteratively links the roots such that no two roots of the same rank
* remain. Assumes that the roots array is empty to begin with, and clears out
* this array before completing execution. Breaks list of roots to simplify
* insertion and linking, and rebuilds the circular list at the end.
*
* @param queue Queue to which the two lists belong
* @param a First node list
* @param b Second node list
*/
static void merge_and_fix_roots( fibonacci_heap *queue, fibonacci_node *a,
fibonacci_node *b )
{
fibonacci_node *start = append_lists( queue, a, b );
fibonacci_node *current, *next;
int32_t i, rank;
if ( start == NULL )
return;
// break the circular list
start->prev_sibling->next_sibling = NULL;
start->prev_sibling = NULL;
// insert an initial node
queue->roots[start->rank] = start;
queue->largest_rank = start->rank;
start->parent = NULL;
current = start->next_sibling;
// insert the rest of the nodes
while( current != NULL )
{
// extract from the list
next = current->next_sibling;
if( next != NULL )
next->prev_sibling = NULL;
current->next_sibling = NULL;
current->parent = NULL;
// insert into the registry
while ( !attempt_insert( queue, current ) )
{
rank = current->rank;
current = link( queue, current, queue->roots[rank] );
queue->roots[rank] = NULL;
}
current = next;
}
// pick the largest tree out of the registry to start reforming the list
start = queue->roots[queue->largest_rank];
queue->roots[queue->largest_rank] = NULL;
queue->minimum = start;
current = start;
// pull the rest out and clear the registry for later use
for ( i = queue->largest_rank - 1; i >= 0; i-- )
{
if( queue->roots[i] != NULL )
{
if( queue->roots[i]->key < queue->minimum->key )
queue->minimum = queue->roots[i];
current->prev_sibling = queue->roots[i];
queue->roots[i]->next_sibling = current;
current = queue->roots[i];
queue->roots[i] = NULL;
}
}
current->prev_sibling = start;
start->next_sibling = current;
queue->largest_rank = 0;
}
/*
* Does: Sorts a linked list using the quicksort algorithm.
* Arguments:
* -- list: A pointer to the first node of the linked list to
* be sorted.
* Returns: A pointer to the first node of the sorted linked list.
*/
node *
quicksort(node *list)
{
node *first_node;
node *left_half = NULL;
node *sorted_left_half = NULL;
node *right_half = NULL;
node *sorted_right_half = NULL;
node *head;
node *sorted_list;
node *sorted_list2;
int pivot;
int head_data;
/* If a null list or single node, return a copy of it */
if (list == NULL || list->next == NULL)
{
return copy_list(list);
}
else /* Else, partition the list into left and right lists */
{
first_node = copy_list(list);
free_list(first_node->next);
first_node->next = NULL;
/* Value with which data fields are compared against */
pivot = first_node->data;
head = list->next;
while (head != NULL)
{
head_data = head->data;
if (head_data < pivot)
{
/* Add nodes to left_half, creating the left_half list */
left_half = create_node(head_data, left_half);
}
else
{
/* Add nodes to right_half, creating the right_half list */
right_half = create_node(head_data, right_half);
}
head = head->next;
}
/* Sort the left_half recursively using quicksort */
sorted_left_half = quicksort(left_half);
free_list(left_half);
left_half = sorted_left_half;
/* Sort the right_half recursively using quicksort */
sorted_right_half = quicksort(right_half);
free_list(right_half);
right_half = sorted_right_half;
/*
* Append the left and right halves with the first node in the
* middle to create a sorted list.
*/
sorted_list = append_lists(left_half, first_node);
sorted_list2 = append_lists(sorted_list, right_half);
/* Free memory */
free_list(sorted_list);
free_list(first_node);
free_list(left_half);
free_list(right_half);
assert(is_sorted(sorted_list2));
return sorted_list2;
}
}
