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/*
* A Pairing Heap implementation.
*
* "The Pairing Heap: A New Form of Self-Adjusting Heap"
* https://www.cs.cmu.edu/~sleator/papers/pairing-heaps.pdf
*
* With auxiliary twopass list, described in a follow on paper.
*
* "Pairing Heaps: Experiments and Analysis"
* http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.106.2988&rep=rep1&type=pdf
*
*******************************************************************************
*/
#ifndef PH_H_
#define PH_H_
/* Node structure. */
#define phn(a_type) \
struct { \
a_type *phn_prev; \
a_type *phn_next; \
a_type *phn_lchild; \
}
/* Root structure. */
#define ph(a_type) \
struct { \
a_type *ph_root; \
}
/* Internal utility macros. */
#define phn_lchild_get(a_type, a_field, a_phn) \
(a_phn->a_field.phn_lchild)
#define phn_lchild_set(a_type, a_field, a_phn, a_lchild) do { \
a_phn->a_field.phn_lchild = a_lchild; \
} while (0)
#define phn_next_get(a_type, a_field, a_phn) \
(a_phn->a_field.phn_next)
#define phn_prev_set(a_type, a_field, a_phn, a_prev) do { \
a_phn->a_field.phn_prev = a_prev; \
} while (0)
#define phn_prev_get(a_type, a_field, a_phn) \
(a_phn->a_field.phn_prev)
#define phn_next_set(a_type, a_field, a_phn, a_next) do { \
a_phn->a_field.phn_next = a_next; \
} while (0)
#define phn_merge_ordered(a_type, a_field, a_phn0, a_phn1, a_cmp) do { \
a_type *phn0child; \
\
assert(a_phn0 != NULL); \
assert(a_phn1 != NULL); \
assert(a_cmp(a_phn0, a_phn1) <= 0); \
\
phn_prev_set(a_type, a_field, a_phn1, a_phn0); \
phn0child = phn_lchild_get(a_type, a_field, a_phn0); \
phn_next_set(a_type, a_field, a_phn1, phn0child); \
if (phn0child != NULL) { \
phn_prev_set(a_type, a_field, phn0child, a_phn1); \
} \
phn_lchild_set(a_type, a_field, a_phn0, a_phn1); \
} while (0)
#define phn_merge(a_type, a_field, a_phn0, a_phn1, a_cmp, r_phn) do { \
if (a_phn0 == NULL) { \
r_phn = a_phn1; \
} else if (a_phn1 == NULL) { \
r_phn = a_phn0; \
} else if (a_cmp(a_phn0, a_phn1) < 0) { \
phn_merge_ordered(a_type, a_field, a_phn0, a_phn1, \
a_cmp); \
r_phn = a_phn0; \
} else { \
phn_merge_ordered(a_type, a_field, a_phn1, a_phn0, \
a_cmp); \
r_phn = a_phn1; \
} \
} while (0)
#define ph_merge_siblings(a_type, a_field, a_phn, a_cmp, r_phn) do { \
a_type *head = NULL; \
a_type *tail = NULL; \
a_type *phn0 = a_phn; \
a_type *phn1 = phn_next_get(a_type, a_field, phn0); \
\
/* \
* Multipass merge, wherein the first two elements of a FIFO \
* are repeatedly merged, and each result is appended to the \
* singly linked FIFO, until the FIFO contains only a single \
* element. We start with a sibling list but no reference to \
* its tail, so we do a single pass over the sibling list to \
* populate the FIFO. \
*/ \
if (phn1 != NULL) { \
a_type *phnrest = phn_next_get(a_type, a_field, phn1); \
if (phnrest != NULL) { \
phn_prev_set(a_type, a_field, phnrest, NULL); \
} \
phn_prev_set(a_type, a_field, phn0, NULL); \
phn_next_set(a_type, a_field, phn0, NULL); \
phn_prev_set(a_type, a_field, phn1, NULL); \
phn_next_set(a_type, a_field, phn1, NULL); \
phn_merge(a_type, a_field, phn0, phn1, a_cmp, phn0); \
head = tail = phn0; \
phn0 = phnrest; \
while (phn0 != NULL) { \
phn1 = phn_next_get(a_type, a_field, phn0); \
if (phn1 != NULL) { \
phnrest = phn_next_get(a_type, a_field, \
phn1); \
if (phnrest != NULL) { \
phn_prev_set(a_type, a_field, \
phnrest, NULL); \
} \
phn_prev_set(a_type, a_field, phn0, \
NULL); \
phn_next_set(a_type, a_field, phn0, \
NULL); \
phn_prev_set(a_type, a_field, phn1, \
NULL); \
phn_next_set(a_type, a_field, phn1, \
NULL); \
phn_merge(a_type, a_field, phn0, phn1, \
a_cmp, phn0); \
phn_next_set(a_type, a_field, tail, \
phn0); \
tail = phn0; \
phn0 = phnrest; \
} else { \
phn_next_set(a_type, a_field, tail, \
phn0); \
tail = phn0; \
phn0 = NULL; \
} \
} \
phn0 = head; \
phn1 = phn_next_get(a_type, a_field, phn0); \
if (phn1 != NULL) { \
while (true) { \
head = phn_next_get(a_type, a_field, \
phn1); \
assert(phn_prev_get(a_type, a_field, \
phn0) == NULL); \
phn_next_set(a_type, a_field, phn0, \
NULL); \
assert(phn_prev_get(a_type, a_field, \
phn1) == NULL); \
phn_next_set(a_type, a_field, phn1, \
NULL); \
phn_merge(a_type, a_field, phn0, phn1, \
a_cmp, phn0); \
if (head == NULL) { \
break; \
} \
phn_next_set(a_type, a_field, tail, \
phn0); \
tail = phn0; \
phn0 = head; \
phn1 = phn_next_get(a_type, a_field, \
phn0); \
} \
} \
} \
r_phn = phn0; \
} while (0)
#define ph_merge_aux(a_type, a_field, a_ph, a_cmp) do { \
a_type *phn = phn_next_get(a_type, a_field, a_ph->ph_root); \
if (phn != NULL) { \
phn_prev_set(a_type, a_field, a_ph->ph_root, NULL); \
phn_next_set(a_type, a_field, a_ph->ph_root, NULL); \
phn_prev_set(a_type, a_field, phn, NULL); \
ph_merge_siblings(a_type, a_field, phn, a_cmp, phn); \
assert(phn_next_get(a_type, a_field, phn) == NULL); \
phn_merge(a_type, a_field, a_ph->ph_root, phn, a_cmp, \
a_ph->ph_root); \
} \
} while (0)
#define ph_merge_children(a_type, a_field, a_phn, a_cmp, r_phn) do { \
a_type *lchild = phn_lchild_get(a_type, a_field, a_phn); \
if (lchild == NULL) { \
r_phn = NULL; \
} else { \
ph_merge_siblings(a_type, a_field, lchild, a_cmp, \
r_phn); \
} \
} while (0)
/*
* The ph_proto() macro generates function prototypes that correspond to the
* functions generated by an equivalently parameterized call to ph_gen().
*/
#define ph_proto(a_attr, a_prefix, a_ph_type, a_type) \
a_attr void a_prefix##new(a_ph_type *ph); \
a_attr bool a_prefix##empty(a_ph_type *ph); \
a_attr a_type *a_prefix##first(a_ph_type *ph); \
a_attr a_type *a_prefix##any(a_ph_type *ph); \
a_attr void a_prefix##insert(a_ph_type *ph, a_type *phn); \
a_attr a_type *a_prefix##remove_first(a_ph_type *ph); \
a_attr a_type *a_prefix##remove_any(a_ph_type *ph); \
a_attr void a_prefix##remove(a_ph_type *ph, a_type *phn);
/*
* The ph_gen() macro generates a type-specific pairing heap implementation,
* based on the above cpp macros.
*/
#define ph_gen(a_attr, a_prefix, a_ph_type, a_type, a_field, a_cmp) \
a_attr void \
a_prefix##new(a_ph_type *ph) { \
memset(ph, 0, sizeof(ph(a_type))); \
} \
a_attr bool \
a_prefix##empty(a_ph_type *ph) { \
return (ph->ph_root == NULL); \
} \
a_attr a_type * \
a_prefix##first(a_ph_type *ph) { \
if (ph->ph_root == NULL) { \
return NULL; \
} \
ph_merge_aux(a_type, a_field, ph, a_cmp); \
return ph->ph_root; \
} \
a_attr a_type * \
a_prefix##any(a_ph_type *ph) { \
if (ph->ph_root == NULL) { \
return NULL; \
} \
a_type *aux = phn_next_get(a_type, a_field, ph->ph_root); \
if (aux != NULL) { \
return aux; \
} \
return ph->ph_root; \
} \
a_attr void \
a_prefix##insert(a_ph_type *ph, a_type *phn) { \
memset(&phn->a_field, 0, sizeof(phn(a_type))); \
\
/* \
* Treat the root as an aux list during insertion, and lazily \
* merge during a_prefix##remove_first(). For elements that \
* are inserted, then removed via a_prefix##remove() before the \
* aux list is ever processed, this makes insert/remove \
* constant-time, whereas eager merging would make insert \
* O(log n). \
*/ \
if (ph->ph_root == NULL) { \
ph->ph_root = phn; \
} else { \
phn_next_set(a_type, a_field, phn, phn_next_get(a_type, \
a_field, ph->ph_root)); \
if (phn_next_get(a_type, a_field, ph->ph_root) != \
NULL) { \
phn_prev_set(a_type, a_field, \
phn_next_get(a_type, a_field, ph->ph_root), \
phn); \
} \
phn_prev_set(a_type, a_field, phn, ph->ph_root); \
phn_next_set(a_type, a_field, ph->ph_root, phn); \
} \
} \
a_attr a_type * \
a_prefix##remove_first(a_ph_type *ph) { \
a_type *ret; \
\
if (ph->ph_root == NULL) { \
return NULL; \
} \
ph_merge_aux(a_type, a_field, ph, a_cmp); \
\
ret = ph->ph_root; \
\
ph_merge_children(a_type, a_field, ph->ph_root, a_cmp, \
ph->ph_root); \
\
return ret; \
} \
a_attr a_type * \
a_prefix##remove_any(a_ph_type *ph) { \
/* \
* Remove the most recently inserted aux list element, or the \
* root if the aux list is empty. This has the effect of \
* behaving as a LIFO (and insertion/removal is therefore \
* constant-time) if a_prefix##[remove_]first() are never \
* called. \
*/ \
if (ph->ph_root == NULL) { \
return NULL; \
} \
a_type *ret = phn_next_get(a_type, a_field, ph->ph_root); \
if (ret != NULL) { \
a_type *aux = phn_next_get(a_type, a_field, ret); \
phn_next_set(a_type, a_field, ph->ph_root, aux); \
if (aux != NULL) { \
phn_prev_set(a_type, a_field, aux, \
ph->ph_root); \
} \
return ret; \
} \
ret = ph->ph_root; \
ph_merge_children(a_type, a_field, ph->ph_root, a_cmp, \
ph->ph_root); \
return ret; \
} \
a_attr void \
a_prefix##remove(a_ph_type *ph, a_type *phn) { \
a_type *replace, *parent; \
\
if (ph->ph_root == phn) { \
/* \
* We can delete from aux list without merging it, but \
* we need to merge if we are dealing with the root \
* node and it has children. \
*/ \
if (phn_lchild_get(a_type, a_field, phn) == NULL) { \
ph->ph_root = phn_next_get(a_type, a_field, \
phn); \
if (ph->ph_root != NULL) { \
phn_prev_set(a_type, a_field, \
ph->ph_root, NULL); \
} \
return; \
} \
ph_merge_aux(a_type, a_field, ph, a_cmp); \
if (ph->ph_root == phn) { \
ph_merge_children(a_type, a_field, ph->ph_root, \
a_cmp, ph->ph_root); \
return; \
} \
} \
\
/* Get parent (if phn is leftmost child) before mutating. */ \
if ((parent = phn_prev_get(a_type, a_field, phn)) != NULL) { \
if (phn_lchild_get(a_type, a_field, parent) != phn) { \
parent = NULL; \
} \
} \
/* Find a possible replacement node, and link to parent. */ \
ph_merge_children(a_type, a_field, phn, a_cmp, replace); \
/* Set next/prev for sibling linked list. */ \
if (replace != NULL) { \
if (parent != NULL) { \
phn_prev_set(a_type, a_field, replace, parent); \
phn_lchild_set(a_type, a_field, parent, \
replace); \
} else { \
phn_prev_set(a_type, a_field, replace, \
phn_prev_get(a_type, a_field, phn)); \
if (phn_prev_get(a_type, a_field, phn) != \
NULL) { \
phn_next_set(a_type, a_field, \
phn_prev_get(a_type, a_field, phn), \
replace); \
} \
} \
phn_next_set(a_type, a_field, replace, \
phn_next_get(a_type, a_field, phn)); \
if (phn_next_get(a_type, a_field, phn) != NULL) { \
phn_prev_set(a_type, a_field, \
phn_next_get(a_type, a_field, phn), \
replace); \
} \
} else { \
if (parent != NULL) { \
a_type *next = phn_next_get(a_type, a_field, \
phn); \
phn_lchild_set(a_type, a_field, parent, next); \
if (next != NULL) { \
phn_prev_set(a_type, a_field, next, \
parent); \
} \
} else { \
assert(phn_prev_get(a_type, a_field, phn) != \
NULL); \
phn_next_set(a_type, a_field, \
phn_prev_get(a_type, a_field, phn), \
phn_next_get(a_type, a_field, phn)); \
} \
if (phn_next_get(a_type, a_field, phn) != NULL) { \
phn_prev_set(a_type, a_field, \
phn_next_get(a_type, a_field, phn), \
phn_prev_get(a_type, a_field, phn)); \
} \
} \
}
#endif /* PH_H_ */
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