547 lines
13 KiB
C
547 lines
13 KiB
C
/*-------------------------------------------------------------------------
|
|
*
|
|
* binaryheap.c
|
|
* A simple binary heap implementation
|
|
*
|
|
* Portions Copyright (c) 2012-2024, PostgreSQL Global Development Group
|
|
*
|
|
* IDENTIFICATION
|
|
* src/common/binaryheap.c
|
|
*
|
|
*-------------------------------------------------------------------------
|
|
*/
|
|
|
|
#ifdef FRONTEND
|
|
#include "postgres_fe.h"
|
|
#else
|
|
#include "postgres.h"
|
|
#endif
|
|
|
|
#include <math.h>
|
|
|
|
#ifdef FRONTEND
|
|
#include "common/logging.h"
|
|
#endif
|
|
#include "common/hashfn.h"
|
|
#include "lib/binaryheap.h"
|
|
|
|
/*
|
|
* Define parameters for hash table code generation. The interface is *also*
|
|
* declared in binaryheap.h (to generate the types, which are externally
|
|
* visible).
|
|
*/
|
|
#define SH_PREFIX bh_nodeidx
|
|
#define SH_ELEMENT_TYPE bh_nodeidx_entry
|
|
#define SH_KEY_TYPE bh_node_type
|
|
#define SH_KEY key
|
|
#define SH_HASH_KEY(tb, key) \
|
|
hash_bytes((const unsigned char *) &key, sizeof(bh_node_type))
|
|
#define SH_EQUAL(tb, a, b) (memcmp(&a, &b, sizeof(bh_node_type)) == 0)
|
|
#define SH_SCOPE extern
|
|
#ifdef FRONTEND
|
|
#define SH_RAW_ALLOCATOR pg_malloc0
|
|
#endif
|
|
#define SH_STORE_HASH
|
|
#define SH_GET_HASH(tb, a) a->hash
|
|
#define SH_DEFINE
|
|
#include "lib/simplehash.h"
|
|
|
|
static void sift_down(binaryheap *heap, int node_off);
|
|
static void sift_up(binaryheap *heap, int node_off);
|
|
|
|
/*
|
|
* binaryheap_allocate
|
|
*
|
|
* Returns a pointer to a newly-allocated heap with the given initial number
|
|
* of nodes, and with the heap property defined by the given comparator
|
|
* function, which will be invoked with the additional argument specified by
|
|
* 'arg'.
|
|
*
|
|
* If 'indexed' is true, we create a hash table to track each node's
|
|
* index in the heap, enabling to perform some operations such as
|
|
* binaryheap_remove_node_ptr() etc.
|
|
*/
|
|
binaryheap *
|
|
binaryheap_allocate(int num_nodes, binaryheap_comparator compare,
|
|
bool indexed, void *arg)
|
|
{
|
|
binaryheap *heap;
|
|
|
|
heap = (binaryheap *) palloc(sizeof(binaryheap));
|
|
heap->bh_space = num_nodes;
|
|
heap->bh_compare = compare;
|
|
heap->bh_arg = arg;
|
|
|
|
heap->bh_size = 0;
|
|
heap->bh_has_heap_property = true;
|
|
heap->bh_nodes = (bh_node_type *) palloc(sizeof(bh_node_type) * num_nodes);
|
|
heap->bh_nodeidx = NULL;
|
|
|
|
if (indexed)
|
|
{
|
|
#ifdef FRONTEND
|
|
heap->bh_nodeidx = bh_nodeidx_create(num_nodes, NULL);
|
|
#else
|
|
heap->bh_nodeidx = bh_nodeidx_create(CurrentMemoryContext, num_nodes,
|
|
NULL);
|
|
#endif
|
|
}
|
|
|
|
return heap;
|
|
}
|
|
|
|
/*
|
|
* binaryheap_reset
|
|
*
|
|
* Resets the heap to an empty state, losing its data content but not the
|
|
* parameters passed at allocation.
|
|
*/
|
|
void
|
|
binaryheap_reset(binaryheap *heap)
|
|
{
|
|
heap->bh_size = 0;
|
|
heap->bh_has_heap_property = true;
|
|
|
|
if (binaryheap_indexed(heap))
|
|
bh_nodeidx_reset(heap->bh_nodeidx);
|
|
}
|
|
|
|
/*
|
|
* binaryheap_free
|
|
*
|
|
* Releases memory used by the given binaryheap.
|
|
*/
|
|
void
|
|
binaryheap_free(binaryheap *heap)
|
|
{
|
|
if (binaryheap_indexed(heap))
|
|
bh_nodeidx_destroy(heap->bh_nodeidx);
|
|
|
|
pfree(heap->bh_nodes);
|
|
pfree(heap);
|
|
}
|
|
|
|
/*
|
|
* These utility functions return the offset of the left child, right
|
|
* child, and parent of the node at the given index, respectively.
|
|
*
|
|
* The heap is represented as an array of nodes, with the root node
|
|
* stored at index 0. The left child of node i is at index 2*i+1, and
|
|
* the right child at 2*i+2. The parent of node i is at index (i-1)/2.
|
|
*/
|
|
|
|
static inline int
|
|
left_offset(int i)
|
|
{
|
|
return 2 * i + 1;
|
|
}
|
|
|
|
static inline int
|
|
right_offset(int i)
|
|
{
|
|
return 2 * i + 2;
|
|
}
|
|
|
|
static inline int
|
|
parent_offset(int i)
|
|
{
|
|
return (i - 1) / 2;
|
|
}
|
|
|
|
/*
|
|
* Double the space allocated for nodes.
|
|
*/
|
|
static void
|
|
enlarge_node_array(binaryheap *heap)
|
|
{
|
|
heap->bh_space *= 2;
|
|
heap->bh_nodes = repalloc(heap->bh_nodes,
|
|
sizeof(bh_node_type) * heap->bh_space);
|
|
}
|
|
|
|
/*
|
|
* Set the given node at the 'index' and track it if required.
|
|
*
|
|
* Return true if the node's index is already tracked.
|
|
*/
|
|
static bool
|
|
set_node(binaryheap *heap, bh_node_type node, int index)
|
|
{
|
|
bool found = false;
|
|
|
|
/* Set the node to the nodes array */
|
|
heap->bh_nodes[index] = node;
|
|
|
|
if (binaryheap_indexed(heap))
|
|
{
|
|
bh_nodeidx_entry *ent;
|
|
|
|
/* Keep track of the node index */
|
|
ent = bh_nodeidx_insert(heap->bh_nodeidx, node, &found);
|
|
ent->index = index;
|
|
}
|
|
|
|
return found;
|
|
}
|
|
|
|
/*
|
|
* Remove the node's index from the hash table if the heap is indexed.
|
|
*/
|
|
static inline void
|
|
delete_nodeidx(binaryheap *heap, bh_node_type node)
|
|
{
|
|
if (binaryheap_indexed(heap))
|
|
bh_nodeidx_delete(heap->bh_nodeidx, node);
|
|
}
|
|
|
|
/*
|
|
* Replace the existing node at 'idx' with the given 'new_node'. Also
|
|
* update their positions accordingly. Note that we assume the new_node's
|
|
* position is already tracked if enabled, i.e. the new_node is already
|
|
* present in the heap.
|
|
*/
|
|
static void
|
|
replace_node(binaryheap *heap, int index, bh_node_type new_node)
|
|
{
|
|
bool found PG_USED_FOR_ASSERTS_ONLY;
|
|
|
|
/* Quick return if not necessary to move */
|
|
if (heap->bh_nodes[index] == new_node)
|
|
return;
|
|
|
|
/* Remove the overwritten node's index */
|
|
delete_nodeidx(heap, heap->bh_nodes[index]);
|
|
|
|
/*
|
|
* Replace it with the given new node. This node's position must also be
|
|
* tracked as we assume to replace the node with the existing node.
|
|
*/
|
|
found = set_node(heap, new_node, index);
|
|
Assert(!binaryheap_indexed(heap) || found);
|
|
}
|
|
|
|
/*
|
|
* binaryheap_add_unordered
|
|
*
|
|
* Adds the given datum to the end of the heap's list of nodes in O(1) without
|
|
* preserving the heap property. This is a convenience to add elements quickly
|
|
* to a new heap. To obtain a valid heap, one must call binaryheap_build()
|
|
* afterwards.
|
|
*/
|
|
void
|
|
binaryheap_add_unordered(binaryheap *heap, bh_node_type d)
|
|
{
|
|
/* make sure enough space for a new node */
|
|
if (heap->bh_size >= heap->bh_space)
|
|
enlarge_node_array(heap);
|
|
|
|
heap->bh_has_heap_property = false;
|
|
set_node(heap, d, heap->bh_size);
|
|
heap->bh_size++;
|
|
}
|
|
|
|
/*
|
|
* binaryheap_build
|
|
*
|
|
* Assembles a valid heap in O(n) from the nodes added by
|
|
* binaryheap_add_unordered(). Not needed otherwise.
|
|
*/
|
|
void
|
|
binaryheap_build(binaryheap *heap)
|
|
{
|
|
int i;
|
|
|
|
for (i = parent_offset(heap->bh_size - 1); i >= 0; i--)
|
|
sift_down(heap, i);
|
|
heap->bh_has_heap_property = true;
|
|
}
|
|
|
|
/*
|
|
* binaryheap_add
|
|
*
|
|
* Adds the given datum to the heap in O(log n) time, while preserving
|
|
* the heap property.
|
|
*/
|
|
void
|
|
binaryheap_add(binaryheap *heap, bh_node_type d)
|
|
{
|
|
/* make sure enough space for a new node */
|
|
if (heap->bh_size >= heap->bh_space)
|
|
enlarge_node_array(heap);
|
|
|
|
set_node(heap, d, heap->bh_size);
|
|
heap->bh_size++;
|
|
sift_up(heap, heap->bh_size - 1);
|
|
}
|
|
|
|
/*
|
|
* binaryheap_first
|
|
*
|
|
* Returns a pointer to the first (root, topmost) node in the heap
|
|
* without modifying the heap. The caller must ensure that this
|
|
* routine is not used on an empty heap. Always O(1).
|
|
*/
|
|
bh_node_type
|
|
binaryheap_first(binaryheap *heap)
|
|
{
|
|
Assert(!binaryheap_empty(heap) && heap->bh_has_heap_property);
|
|
return heap->bh_nodes[0];
|
|
}
|
|
|
|
/*
|
|
* binaryheap_remove_first
|
|
*
|
|
* Removes the first (root, topmost) node in the heap and returns a
|
|
* pointer to it after rebalancing the heap. The caller must ensure
|
|
* that this routine is not used on an empty heap. O(log n) worst
|
|
* case.
|
|
*/
|
|
bh_node_type
|
|
binaryheap_remove_first(binaryheap *heap)
|
|
{
|
|
bh_node_type result;
|
|
|
|
Assert(!binaryheap_empty(heap) && heap->bh_has_heap_property);
|
|
|
|
/* extract the root node, which will be the result */
|
|
result = heap->bh_nodes[0];
|
|
|
|
/* easy if heap contains one element */
|
|
if (heap->bh_size == 1)
|
|
{
|
|
heap->bh_size--;
|
|
delete_nodeidx(heap, result);
|
|
|
|
return result;
|
|
}
|
|
|
|
/*
|
|
* Remove the last node, placing it in the vacated root entry, and sift
|
|
* the new root node down to its correct position.
|
|
*/
|
|
replace_node(heap, 0, heap->bh_nodes[--heap->bh_size]);
|
|
sift_down(heap, 0);
|
|
|
|
return result;
|
|
}
|
|
|
|
/*
|
|
* binaryheap_remove_node
|
|
*
|
|
* Removes the nth (zero based) node from the heap. The caller must ensure
|
|
* that there are at least (n + 1) nodes in the heap. O(log n) worst case.
|
|
*/
|
|
void
|
|
binaryheap_remove_node(binaryheap *heap, int n)
|
|
{
|
|
int cmp;
|
|
|
|
Assert(!binaryheap_empty(heap) && heap->bh_has_heap_property);
|
|
Assert(n >= 0 && n < heap->bh_size);
|
|
|
|
/* compare last node to the one that is being removed */
|
|
cmp = heap->bh_compare(heap->bh_nodes[--heap->bh_size],
|
|
heap->bh_nodes[n],
|
|
heap->bh_arg);
|
|
|
|
/* remove the last node, placing it in the vacated entry */
|
|
replace_node(heap, n, heap->bh_nodes[heap->bh_size]);
|
|
|
|
/* sift as needed to preserve the heap property */
|
|
if (cmp > 0)
|
|
sift_up(heap, n);
|
|
else if (cmp < 0)
|
|
sift_down(heap, n);
|
|
}
|
|
|
|
/*
|
|
* binaryheap_remove_node_ptr
|
|
*
|
|
* Similar to binaryheap_remove_node() but removes the given node. The caller
|
|
* must ensure that the given node is in the heap. O(log n) worst case.
|
|
*
|
|
* This function can be used only if the heap is indexed.
|
|
*/
|
|
void
|
|
binaryheap_remove_node_ptr(binaryheap *heap, bh_node_type d)
|
|
{
|
|
bh_nodeidx_entry *ent;
|
|
|
|
Assert(!binaryheap_empty(heap) && heap->bh_has_heap_property);
|
|
Assert(binaryheap_indexed(heap));
|
|
|
|
ent = bh_nodeidx_lookup(heap->bh_nodeidx, d);
|
|
Assert(ent);
|
|
|
|
binaryheap_remove_node(heap, ent->index);
|
|
}
|
|
|
|
/*
|
|
* Workhorse for binaryheap_update_up and binaryheap_update_down.
|
|
*/
|
|
static void
|
|
resift_node(binaryheap *heap, bh_node_type node, bool sift_dir_up)
|
|
{
|
|
bh_nodeidx_entry *ent;
|
|
|
|
Assert(!binaryheap_empty(heap) && heap->bh_has_heap_property);
|
|
Assert(binaryheap_indexed(heap));
|
|
|
|
ent = bh_nodeidx_lookup(heap->bh_nodeidx, node);
|
|
Assert(ent);
|
|
Assert(ent->index >= 0 && ent->index < heap->bh_size);
|
|
|
|
if (sift_dir_up)
|
|
sift_up(heap, ent->index);
|
|
else
|
|
sift_down(heap, ent->index);
|
|
}
|
|
|
|
/*
|
|
* binaryheap_update_up
|
|
*
|
|
* Sift the given node up after the node's key is updated. The caller must
|
|
* ensure that the given node is in the heap. O(log n) worst case.
|
|
*
|
|
* This function can be used only if the heap is indexed.
|
|
*/
|
|
void
|
|
binaryheap_update_up(binaryheap *heap, bh_node_type d)
|
|
{
|
|
resift_node(heap, d, true);
|
|
}
|
|
|
|
/*
|
|
* binaryheap_update_down
|
|
*
|
|
* Sift the given node down after the node's key is updated. The caller must
|
|
* ensure that the given node is in the heap. O(log n) worst case.
|
|
*
|
|
* This function can be used only if the heap is indexed.
|
|
*/
|
|
void
|
|
binaryheap_update_down(binaryheap *heap, bh_node_type d)
|
|
{
|
|
resift_node(heap, d, false);
|
|
}
|
|
|
|
/*
|
|
* binaryheap_replace_first
|
|
*
|
|
* Replace the topmost element of a non-empty heap, preserving the heap
|
|
* property. O(1) in the best case, or O(log n) if it must fall back to
|
|
* sifting the new node down.
|
|
*/
|
|
void
|
|
binaryheap_replace_first(binaryheap *heap, bh_node_type d)
|
|
{
|
|
Assert(!binaryheap_empty(heap) && heap->bh_has_heap_property);
|
|
|
|
replace_node(heap, 0, d);
|
|
|
|
if (heap->bh_size > 1)
|
|
sift_down(heap, 0);
|
|
}
|
|
|
|
/*
|
|
* Sift a node up to the highest position it can hold according to the
|
|
* comparator.
|
|
*/
|
|
static void
|
|
sift_up(binaryheap *heap, int node_off)
|
|
{
|
|
bh_node_type node_val = heap->bh_nodes[node_off];
|
|
|
|
/*
|
|
* Within the loop, the node_off'th array entry is a "hole" that
|
|
* notionally holds node_val, but we don't actually store node_val there
|
|
* till the end, saving some unnecessary data copying steps.
|
|
*/
|
|
while (node_off != 0)
|
|
{
|
|
int cmp;
|
|
int parent_off;
|
|
bh_node_type parent_val;
|
|
|
|
/*
|
|
* If this node is smaller than its parent, the heap condition is
|
|
* satisfied, and we're done.
|
|
*/
|
|
parent_off = parent_offset(node_off);
|
|
parent_val = heap->bh_nodes[parent_off];
|
|
cmp = heap->bh_compare(node_val,
|
|
parent_val,
|
|
heap->bh_arg);
|
|
if (cmp <= 0)
|
|
break;
|
|
|
|
/*
|
|
* Otherwise, swap the parent value with the hole, and go on to check
|
|
* the node's new parent.
|
|
*/
|
|
set_node(heap, parent_val, node_off);
|
|
node_off = parent_off;
|
|
}
|
|
/* Re-fill the hole */
|
|
set_node(heap, node_val, node_off);
|
|
}
|
|
|
|
/*
|
|
* Sift a node down from its current position to satisfy the heap
|
|
* property.
|
|
*/
|
|
static void
|
|
sift_down(binaryheap *heap, int node_off)
|
|
{
|
|
bh_node_type node_val = heap->bh_nodes[node_off];
|
|
|
|
/*
|
|
* Within the loop, the node_off'th array entry is a "hole" that
|
|
* notionally holds node_val, but we don't actually store node_val there
|
|
* till the end, saving some unnecessary data copying steps.
|
|
*/
|
|
while (true)
|
|
{
|
|
int left_off = left_offset(node_off);
|
|
int right_off = right_offset(node_off);
|
|
int swap_off = 0;
|
|
|
|
/* Is the left child larger than the parent? */
|
|
if (left_off < heap->bh_size &&
|
|
heap->bh_compare(node_val,
|
|
heap->bh_nodes[left_off],
|
|
heap->bh_arg) < 0)
|
|
swap_off = left_off;
|
|
|
|
/* Is the right child larger than the parent? */
|
|
if (right_off < heap->bh_size &&
|
|
heap->bh_compare(node_val,
|
|
heap->bh_nodes[right_off],
|
|
heap->bh_arg) < 0)
|
|
{
|
|
/* swap with the larger child */
|
|
if (!swap_off ||
|
|
heap->bh_compare(heap->bh_nodes[left_off],
|
|
heap->bh_nodes[right_off],
|
|
heap->bh_arg) < 0)
|
|
swap_off = right_off;
|
|
}
|
|
|
|
/*
|
|
* If we didn't find anything to swap, the heap condition is
|
|
* satisfied, and we're done.
|
|
*/
|
|
if (!swap_off)
|
|
break;
|
|
|
|
/*
|
|
* Otherwise, swap the hole with the child that violates the heap
|
|
* property; then go on to check its children.
|
|
*/
|
|
set_node(heap, heap->bh_nodes[swap_off], node_off);
|
|
node_off = swap_off;
|
|
}
|
|
/* Re-fill the hole */
|
|
set_node(heap, node_val, node_off);
|
|
}
|