binaryheap.c

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/*-------------------------------------------------------------------------
 *
 * binaryheap.c
 *    A simple binary heap implementaion
 *
 * Portions Copyright (c) 2012-2013, PostgreSQL Global Development Group
 *
 * IDENTIFICATION
 *    src/backend/lib/binaryheap.c
 *
 *-------------------------------------------------------------------------
 */

#include "postgres.h"

#include <math.h>

#include "lib/binaryheap.h"

static void sift_down(binaryheap *heap, int node_off);
static void sift_up(binaryheap *heap, int node_off);
static inline void swap_nodes(binaryheap *heap, int a, int b);

/*
 * binaryheap_allocate
 *
 * Returns a pointer to a newly-allocated heap that has the capacity to
 * store the given number of nodes, with the heap property defined by
 * the given comparator function, which will be invoked with the additional
 * argument specified by 'arg'.
 */
binaryheap *
binaryheap_allocate(int capacity, binaryheap_comparator compare, void *arg)
{
    int         sz;
    binaryheap *heap;

    sz = offsetof(binaryheap, bh_nodes) + sizeof(Datum) * capacity;
    heap = palloc(sz);
    heap->bh_size = 0;
    heap->bh_space = capacity;
    heap->bh_has_heap_property = true;
    heap->bh_compare = compare;
    heap->bh_arg = arg;

    return heap;
}

/*
 * binaryheap_free
 *
 * Releases memory used by the given binaryheap.
 */
void
binaryheap_free(binaryheap *heap)
{
    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;
}

/*
 * 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, Datum d)
{
    if (heap->bh_size >= heap->bh_space)
        elog(ERROR, "out of binary heap slots");
    heap->bh_has_heap_property = false;
    heap->bh_nodes[heap->bh_size] = d;
    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, Datum d)
{
    if (heap->bh_size >= heap->bh_space)
        elog(ERROR, "out of binary heap slots");
    heap->bh_nodes[heap->bh_size] = d;
    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).
 */
Datum
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.
 */
Datum
binaryheap_remove_first(binaryheap *heap)
{
    Assert(!binaryheap_empty(heap) && heap->bh_has_heap_property);

    if (heap->bh_size == 1)
    {
        heap->bh_size--;
        return heap->bh_nodes[0];
    }

    /*
     * Swap the root and last nodes, decrease the size of the heap (i.e.
     * remove the former root node) and sift the new root node down to its
     * correct position.
     */
    swap_nodes(heap, 0, heap->bh_size - 1);
    heap->bh_size--;
    sift_down(heap, 0);

    return heap->bh_nodes[heap->bh_size];
}

/*
 * 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, Datum d)
{
    Assert(!binaryheap_empty(heap) && heap->bh_has_heap_property);

    heap->bh_nodes[0] = d;

    if (heap->bh_size > 1)
        sift_down(heap, 0);
}

/*
 * Swap the contents of two nodes.
 */
static inline void
swap_nodes(binaryheap *heap, int a, int b)
{
    Datum   swap;

    swap = heap->bh_nodes[a];
    heap->bh_nodes[a] = heap->bh_nodes[b];
    heap->bh_nodes[b] = swap;
}

/*
 * Sift a node up to the highest position it can hold according to the
 * comparator.
 */
static void
sift_up(binaryheap *heap, int node_off)
{
    while (node_off != 0)
    {
        int         cmp;
        int         parent_off;

        /*
         * If this node is smaller than its parent, the heap condition is
         * satisfied, and we're done.
         */
        parent_off = parent_offset(node_off);
        cmp = heap->bh_compare(heap->bh_nodes[node_off],
                               heap->bh_nodes[parent_off],
                               heap->bh_arg);
        if (cmp <= 0)
            break;

        /*
         * Otherwise, swap the node and its parent and go on to check the
         * node's new parent.
         */
        swap_nodes(heap, node_off, parent_off);
        node_off = parent_off;
    }
}

/*
 * Sift a node down from its current position to satisfy the heap
 * property.
 */
static void
sift_down(binaryheap *heap, int node_off)
{
    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(heap->bh_nodes[node_off],
                             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(heap->bh_nodes[node_off],
                             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 node with the child that violates the heap
         * property; then go on to check its children.
         */
        swap_nodes(heap, swap_off, node_off);
        node_off = swap_off;
    }
}