pairingheap.c

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/*-------------------------------------------------------------------------
 *
 * pairingheap.c
 *    A Pairing Heap implementation
 *
 * A pairing heap is a data structure that's useful for implementing
 * priority queues. It is simple to implement, and provides amortized O(1)
 * insert and find-min operations, and amortized O(log n) delete-min.
 *
 * The pairing heap was first described in this paper:
 *
 *  Michael L. Fredman, Robert Sedgewick, Daniel D. Sleator, and Robert E.
 *   Tarjan. 1986.
 *  The pairing heap: a new form of self-adjusting heap.
 *  Algorithmica 1, 1 (January 1986), pages 111-129. DOI: 10.1007/BF01840439
 *
 * Portions Copyright (c) 2012-2025, PostgreSQL Global Development Group
 *
 * IDENTIFICATION
 *    src/backend/lib/pairingheap.c
 *
 *-------------------------------------------------------------------------
 */
 
#include "postgres.h"
 
#include "lib/pairingheap.h"
 
static pairingheap_node *merge(pairingheap *heap, pairingheap_node *a,
                               pairingheap_node *b);
static pairingheap_node *merge_children(pairingheap *heap,
                                        pairingheap_node *children);
 
/*
 * pairingheap_allocate
 *
 * Returns a pointer to a newly-allocated heap, with the heap property defined
 * by the given comparator function, which will be invoked with the additional
 * argument specified by 'arg'.
 */
pairingheap *
pairingheap_allocate(pairingheap_comparator compare, void *arg)
{
    pairingheap *heap;
 
    heap = (pairingheap *) palloc(sizeof(pairingheap));
    pairingheap_initialize(heap, compare, arg);
 
    return heap;
}
 
/*
 * pairingheap_initialize
 *
 * Same as pairingheap_allocate(), but initializes the pairing heap in-place
 * rather than allocating a new chunk of memory.  Useful to store the pairing
 * heap in a shared memory.
 */
void
pairingheap_initialize(pairingheap *heap, pairingheap_comparator compare,
                       void *arg)
{
    heap->ph_compare = compare;
    heap->ph_arg = arg;
 
    heap->ph_root = NULL;
}
 
/*
 * pairingheap_free
 *
 * Releases memory used by the given pairingheap.
 *
 * Note: The nodes in the heap are not freed!
 */
void
pairingheap_free(pairingheap *heap)
{
    pfree(heap);
}
 
/*
 * A helper function to merge two subheaps into one.
 *
 * The subheap with smaller value is put as a child of the other one (assuming
 * a max-heap).
 *
 * The next_sibling and prev_or_parent pointers of the input nodes are
 * ignored. On return, the returned node's next_sibling and prev_or_parent
 * pointers are garbage.
 */
static pairingheap_node *
merge(pairingheap *heap, pairingheap_node *a, pairingheap_node *b)
{
    if (a == NULL)
        return b;
    if (b == NULL)
        return a;
 
    /* swap 'a' and 'b' so that 'a' is the one with larger value */
    if (heap->ph_compare(a, b, heap->ph_arg) < 0)
    {
        pairingheap_node *tmp;
 
        tmp = a;
        a = b;
        b = tmp;
    }
 
    /* and put 'b' as a child of 'a' */
    if (a->first_child)
        a->first_child->prev_or_parent = b;
    b->prev_or_parent = a;
    b->next_sibling = a->first_child;
    a->first_child = b;
 
    return a;
}
 
/*
 * pairingheap_add
 *
 * Adds the given node to the heap in O(1) time.
 */
void
pairingheap_add(pairingheap *heap, pairingheap_node *node)
{
    node->first_child = NULL;
 
    /* Link the new node as a new tree */
    heap->ph_root = merge(heap, heap->ph_root, node);
    heap->ph_root->prev_or_parent = NULL;
    heap->ph_root->next_sibling = NULL;
}
 
/*
 * pairingheap_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).
 */
pairingheap_node *
pairingheap_first(pairingheap *heap)
{
    Assert(!pairingheap_is_empty(heap));
 
    return heap->ph_root;
}
 
/*
 * pairingheap_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) amortized.
 */
pairingheap_node *
pairingheap_remove_first(pairingheap *heap)
{
    pairingheap_node *result;
    pairingheap_node *children;
 
    Assert(!pairingheap_is_empty(heap));
 
    /* Remove the root, and form a new heap of its children. */
    result = heap->ph_root;
    children = result->first_child;
 
    heap->ph_root = merge_children(heap, children);
    if (heap->ph_root)
    {
        heap->ph_root->prev_or_parent = NULL;
        heap->ph_root->next_sibling = NULL;
    }
 
    return result;
}
 
/*
 * Remove 'node' from the heap. O(log n) amortized.
 */
void
pairingheap_remove(pairingheap *heap, pairingheap_node *node)
{
    pairingheap_node *children;
    pairingheap_node *replacement;
    pairingheap_node *next_sibling;
    pairingheap_node **prev_ptr;
 
    /*
     * If the removed node happens to be the root node, do it with
     * pairingheap_remove_first().
     */
    if (node == heap->ph_root)
    {
        (void) pairingheap_remove_first(heap);
        return;
    }
 
    /*
     * Before we modify anything, remember the removed node's first_child and
     * next_sibling pointers.
     */
    children = node->first_child;
    next_sibling = node->next_sibling;
 
    /*
     * Also find the pointer to the removed node in its previous sibling, or
     * if this is the first child of its parent, in its parent.
     */
    if (node->prev_or_parent->first_child == node)
        prev_ptr = &node->prev_or_parent->first_child;
    else
        prev_ptr = &node->prev_or_parent->next_sibling;
    Assert(*prev_ptr == node);
 
    /*
     * If this node has children, make a new subheap of the children and link
     * the subheap in place of the removed node. Otherwise just unlink this
     * node.
     */
    if (children)
    {
        replacement = merge_children(heap, children);
 
        replacement->prev_or_parent = node->prev_or_parent;
        replacement->next_sibling = node->next_sibling;
        *prev_ptr = replacement;
        if (next_sibling)
            next_sibling->prev_or_parent = replacement;
    }
    else
    {
        *prev_ptr = next_sibling;
        if (next_sibling)
            next_sibling->prev_or_parent = node->prev_or_parent;
    }
}
 
/*
 * Merge a list of subheaps into a single heap.
 *
 * This implements the basic two-pass merging strategy, first forming pairs
 * from left to right, and then merging the pairs.
 */
static pairingheap_node *
merge_children(pairingheap *heap, pairingheap_node *children)
{
    pairingheap_node *curr,
               *next;
    pairingheap_node *pairs;
    pairingheap_node *newroot;
 
    if (children == NULL || children->next_sibling == NULL)
        return children;
 
    /* Walk the subheaps from left to right, merging in pairs */
    next = children;
    pairs = NULL;
    for (;;)
    {
        curr = next;
 
        if (curr == NULL)
            break;
 
        if (curr->next_sibling == NULL)
        {
            /* last odd node at the end of list */
            curr->next_sibling = pairs;
            pairs = curr;
            break;
        }
 
        next = curr->next_sibling->next_sibling;
 
        /* merge this and the next subheap, and add to 'pairs' list. */
 
        curr = merge(heap, curr, curr->next_sibling);
        curr->next_sibling = pairs;
        pairs = curr;
    }
 
    /*
     * Merge all the pairs together to form a single heap.
     */
    newroot = pairs;
    next = pairs->next_sibling;
    while (next)
    {
        curr = next;
        next = curr->next_sibling;
 
        newroot = merge(heap, newroot, curr);
    }
 
    return newroot;
}
 
/*
 * A debug function to dump the contents of the heap as a string.
 *
 * The 'dumpfunc' callback appends a string representation of a single node
 * to the StringInfo. 'opaque' can be used to pass more information to the
 * callback.
 */
#ifdef PAIRINGHEAP_DEBUG
static void
pairingheap_dump_recurse(StringInfo buf,
                         pairingheap_node *node,
                         void (*dumpfunc) (pairingheap_node *node, StringInfo buf, void *opaque),
                         void *opaque,
                         int depth,
                         pairingheap_node *prev_or_parent)
{
    while (node)
    {
        Assert(node->prev_or_parent == prev_or_parent);
 
        appendStringInfoSpaces(buf, depth * 4);
        dumpfunc(node, buf, opaque);
        appendStringInfoChar(buf, '\n');
        if (node->first_child)
            pairingheap_dump_recurse(buf, node->first_child, dumpfunc, opaque, depth + 1, node);
        prev_or_parent = node;
        node = node->next_sibling;
    }
}
 
char *
pairingheap_dump(pairingheap *heap,
                 void (*dumpfunc) (pairingheap_node *node, StringInfo buf, void *opaque),
                 void *opaque)
{
    StringInfoData buf;
 
    if (!heap->ph_root)
        return pstrdup("(empty)");
 
    initStringInfo(&buf);
 
    pairingheap_dump_recurse(&buf, heap->ph_root, dumpfunc, opaque, 0, NULL);
 
    return buf.data;
}
#endif