theap.c

/*
 * Copyright (c) 2019 TAOS Data, Inc. <jhtao@taosdata.com>
 *
 * This program is free software: you can use, redistribute, and/or modify
 * it under the terms of the GNU Affero General Public License, version 3
 * or later ("AGPL"), as published by the Free Software Foundation.
 *
 * This program is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.
 *
 * You should have received a copy of the GNU Affero General Public License
 * along with this program. If not, see <http://www.gnu.org/licenses/>.
 */

#define _DEFAULT_SOURCE
#include "theap.h"

size_t heapSize(Heap* heap) { return heap->nelts; }

Heap* heapCreate(HeapCompareFn fn) {
  Heap* heap = calloc(1, sizeof(Heap));
  if (heap == NULL) {
    return NULL;
  }

  heap->min = NULL;
  heap->nelts = 0;
  heap->compFn = fn;
  return heap;
}

void heapDestroy(Heap* heap) { free(heap); }

HeapNode* heapMin(const Heap* heap) { return heap->min; }

/* Swap parent with child. Child moves closer to the root, parent moves away. */
static void heapNodeSwap(Heap* heap, HeapNode* parent, HeapNode* child) {
  HeapNode* sibling;
  HeapNode  t;

  t = *parent;
  *parent = *child;
  *child = t;

  parent->parent = child;
  if (child->left == child) {
    child->left = parent;
    sibling = child->right;
  } else {
    child->right = parent;
    sibling = child->left;
  }
  if (sibling != NULL) sibling->parent = child;

  if (parent->left != NULL) parent->left->parent = parent;
  if (parent->right != NULL) parent->right->parent = parent;

  if (child->parent == NULL)
    heap->min = child;
  else if (child->parent->left == parent)
    child->parent->left = child;
  else
    child->parent->right = child;
}

void heapInsert(Heap* heap, HeapNode* newnode) {
  HeapNode** parent;
  HeapNode** child;
  uint32_t   path;
  uint32_t   n;
  uint32_t   k;

  newnode->left = NULL;
  newnode->right = NULL;
  newnode->parent = NULL;

  /* Calculate the path from the root to the insertion point.  This is a min
   * heap so we always insert at the left-most free node of the bottom row.
   */
  path = 0;
  for (k = 0, n = 1 + heap->nelts; n >= 2; k += 1, n /= 2) path = (path << 1) | (n & 1);

  /* Now traverse the heap using the path we calculated in the previous step. */
  parent = child = &heap->min;
  while (k > 0) {
    parent = child;
    if (path & 1)
      child = &(*child)->right;
    else
      child = &(*child)->left;
    path >>= 1;
    k -= 1;
  }

  /* Insert the new node. */
  newnode->parent = *parent;
  *child = newnode;
  heap->nelts += 1;

  /* Walk up the tree and check at each node if the heap property holds.
   * It's a min heap so parent < child must be true.
   */
  while (newnode->parent != NULL && (heap->compFn)(newnode, newnode->parent))
    heapNodeSwap(heap, newnode->parent, newnode);
}

void heapRemove(Heap* heap, HeapNode* node) {
  HeapNode*  smallest;
  HeapNode** max;
  HeapNode*  child;
  uint32_t   path;
  uint32_t   k;
  uint32_t   n;

  if (heap->nelts == 0) return;

  /* Calculate the path from the min (the root) to the max, the left-most node
   * of the bottom row.
   */
  path = 0;
  for (k = 0, n = heap->nelts; n >= 2; k += 1, n /= 2) path = (path << 1) | (n & 1);

  /* Now traverse the heap using the path we calculated in the previous step. */
  max = &heap->min;
  while (k > 0) {
    if (path & 1)
      max = &(*max)->right;
    else
      max = &(*max)->left;
    path >>= 1;
    k -= 1;
  }

  heap->nelts -= 1;

  /* Unlink the max node. */
  child = *max;
  *max = NULL;

  if (child == node) {
    /* We're removing either the max or the last node in the tree. */
    if (child == heap->min) {
      heap->min = NULL;
    }
    return;
  }

  /* Replace the to be deleted node with the max node. */
  child->left = node->left;
  child->right = node->right;
  child->parent = node->parent;

  if (child->left != NULL) {
    child->left->parent = child;
  }

  if (child->right != NULL) {
    child->right->parent = child;
  }

  if (node->parent == NULL) {
    heap->min = child;
  } else if (node->parent->left == node) {
    node->parent->left = child;
  } else {
    node->parent->right = child;
  }

  /* Walk down the subtree and check at each node if the heap property holds.
   * It's a min heap so parent < child must be true.  If the parent is bigger,
   * swap it with the smallest child.
   */
  for (;;) {
    smallest = child;
    if (child->left != NULL && (heap->compFn)(child->left, smallest)) smallest = child->left;
    if (child->right != NULL && (heap->compFn)(child->right, smallest)) smallest = child->right;
    if (smallest == child) break;
    heapNodeSwap(heap, child, smallest);
  }

  /* Walk up the subtree and check that each parent is less than the node
   * this is required, because `max` node is not guaranteed to be the
   * actual maximum in tree
   */
  while (child->parent != NULL && (heap->compFn)(child, child->parent)) heapNodeSwap(heap, child->parent, child);
}

void heapDequeue(Heap* heap) { heapRemove(heap, heap->min); }