【C言語】キューとは【優先度キューの二項ヒープを紹介】

悩んでいる人

C言語のキューを教えて！

こういった悩みにお答えします．

本記事の信頼性

リアルタイムシステムの研究歴12年．
東大教員の時に，英語でOSの授業．
2012年9月～2013年8月にアメリカのノースカロライナ大学チャペルヒル校コンピュータサイエンス学部（2021年の世界大学学術ランキングで20位）で客員研究員として勤務．C言語でリアルタイムLinuxの研究開発．
プログラミング歴15年以上，習得している言語: C/C++，Solidity/Vyper，Java，Python，Ruby，HTML/CSS/JS/PHP，MATLAB，Assembler (x64，ARM)．
東大教員の時に，C++言語で開発した「LLVMコンパイラの拡張」，C言語で開発した独自のリアルタイムOS「Mcube Kernel」をGitHubにオープンソースとして公開．

こういった私から学べます．

1 キュー
2 C言語のキュー
3 C言語の優先度キューの例「二項ヒープ」
4 まとめ

キュー

キューとは，データを先入れ先出し（First In First Out）で保持するデータ構造です．

キューにデータに入れることをエンキュー（enqueue），データをキューから取り出すことをデキュー（dequeue）と呼びます．

他のデータ構造を知りたいあなたはこちらからどうぞ．

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C言語のキュー

C言語のシンプルなキューのコードは以下になります．

QUEUE_SIZE分のデータを格納できます．

/*
 * Author: Hiroyuki Chishiro
 * License: 2-Clause BSD
 */
#include <stdio.h>

#define QUEUE_SIZE 128

struct queue {
  int data[QUEUE_SIZE];
  size_t index;
  size_t num;
};

void init(struct queue *q)
{
  size_t i;

  for (i = 0; i < QUEUE_SIZE; i++) {
    q->data[i] = 0;
  }

  q->index = q->num = 0;
}

void print(struct queue *q)
{
  size_t i;
  printf("print(): ");

  for (i = q->index; i < q->index + q->num; i++) {
    printf("%d ", q->data[i % QUEUE_SIZE]);
  }

  printf("\n");
}

void increment(struct queue *q)
{
  q->index++;

  if (q->index == QUEUE_SIZE) {
    q->index = 0;
  }
}

int enqueue(struct queue *q, int data)
{
  if (q->num >= QUEUE_SIZE) {
    fprintf(stderr, "Error: queue is full.\n");
    return 1;
  }

  q->data[(q->index + q->num) % QUEUE_SIZE] = data;
  q->num++;

  return 0;
}

int dequeue(struct queue *q, int *data)
{
  if (q->num == 0) {
    fprintf(stderr, "Error: queue is empty.\n");
    return 1;
  }

  *data = q->data[q->index % QUEUE_SIZE];
  increment(q);
  q->num--;

  return 0;
}

void clear(struct queue *q)
{
  init(q);
}

int main(void)
{
  struct queue queue;
  size_t i;
  int data;

  init(&queue);

  for (i = 1; i <= 5; i++) {
    enqueue(&queue, i);
    print(&queue);
  }

  for (i = 1; i <= 3; i++) {
    if (dequeue(&queue, &data) == 0) {
      printf("data = %d\n", data);
    }

    print(&queue);
  }

  clear(&queue);
  print(&queue);
  return 0;
}

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* Author: Hiroyuki Chishiro

* License: 2-Clause BSD

#include <stdio.h>

#define QUEUE_SIZE 128

struct queue {

int data[QUEUE_SIZE];

size_t index;

size_t num;

};

void init(struct queue *q)

{

size_t i;

for (i = 0; i < QUEUE_SIZE; i++) {

q->data[i] = 0;

}

q->index = q->num = 0;

}

void print(struct queue *q)

{

size_t i;

printf("print(): ");

for (i = q->index; i < q->index + q->num; i++) {

printf("%d ", q->data[i % QUEUE_SIZE]);

}

printf("\n");

}

void increment(struct queue *q)

{

q->index++;

if (q->index == QUEUE_SIZE) {

q->index = 0;

}

int enqueue(struct queue *q, int data)

{

if (q->num >= QUEUE_SIZE) {

fprintf(stderr, "Error: queue is full.\n");

return 1;

}

q->data[(q->index + q->num) % QUEUE_SIZE] = data;

q->num++;

return 0;

}

int dequeue(struct queue *q, int *data)

{

if (q->num == 0) {

fprintf(stderr, "Error: queue is empty.\n");

return 1;

}

*data = q->data[q->index % QUEUE_SIZE];

increment(q);

q->num--;

return 0;

}

void clear(struct queue *q)

{

init(q);

}

int main(void)

{

struct queue queue;

size_t i;

int data;

init(&queue);

for (i = 1; i <= 5; i++) {

enqueue(&queue, i);

print(&queue);

}

for (i = 1; i <= 3; i++) {

if (dequeue(&queue, &data) == 0) {

printf("data = %d\n", data);

}

print(&queue);

}

clear(&queue);

print(&queue);

return 0;

}

実行結果は以下になります．

データをFIFOで操作していることがわかります．

$ gcc queue.c 
$ a.out 
print(): 1 
print(): 1 2 
print(): 1 2 3 
print(): 1 2 3 4 
print(): 1 2 3 4 5 
data = 1
print(): 2 3 4 5 
data = 2
print(): 3 4 5 
data = 3
print(): 4 5 
print():

$ gcc queue.c

$ a.out

print(): 1

print(): 1 2

print(): 1 2 3

print(): 1 2 3 4

print(): 1 2 3 4 5

data = 1

print(): 2 3 4 5

data = 2

print(): 3 4 5

data = 3

print(): 4 5

print():

C言語の優先度キューの例「二項ヒープ」

キューの応用として，データを優先度付きで管理する優先度キューが挙げられます．

優先度キューでは，主に最高優先度のデータをキューから取り除くため，リアルタイムOSにおけるタスクのキューで利用されています．

優先度キューにより，リアルタイム性を保証しつつタスクをデッドラインまでに実行することが可能になります．

リアルタイムOSに使われる技術であるリアルタイムシステムを知りたいあなたはこちらからどうぞ．

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本記事では，優先度キューの例として二項ヒープを紹介します．

二項ヒープの特徴は以下になります．

二分ヒープとよく似たデータ構造であるが，二項ヒープは2つのヒープを素早くマージする操作をサポート
特殊な木構造「二項木」を利用して実現
マージ可能な抽象データ型ヒープの実装

C言語の二項ヒープのコードは以下になります．

とても複雑なので，時間をかけて読みましょう．難しかったら読み飛ばしても構いません．

二項ヒープのコードで実装されている主な関数は以下になります．

enqueue_bheap_queue関数：二項ヒープにノードをエンキュー
dequeue_bheap_queue関数：二項ヒープからノードをデキュー
pick_next_value関数：二項ヒープから最高優先度ノードの値（struct value型）を取得
print_bheap関数：二項ヒープのノードを表示

/*
 * Author: Hiroyuki Chishiro
 * License: 2-Clause BSD
 */
#include <stdio.h>
#include <stdbool.h>
#include <limits.h>

#define QUEUE_SIZE 128
#define NOT_IN_BHEAP ULONG_MAX

#ifdef PDEBUG
#define PDEBUG(fmt, args...) fprintf(stderr, fmt, ## args)
#else
#define PDEBUG(fmt, args...)
#endif

struct value {
  unsigned long id;
  unsigned long priority;
  int value;
  struct bheap_node *node;
};

struct bheap_node {
  unsigned long node_id;
  struct bheap_node *parent;
  struct bheap_node *next;
  struct bheap_node *child;
  unsigned long degree;
  struct value *value;
};

struct bheap_queue {
  unsigned long id;
  struct bheap_node *head;
  struct bheap_node *min;
};

void print_bheap(struct bheap_queue *bq, struct bheap_node *h)
{
  static int nr_tabs = 0;
  int i;

  if (!h) {
    printf("NULL\n");

    for (i = 0; i < nr_tabs; i++) {
      printf("\t");
    }

    return;
  }

  printf("node_id(%lu)id(%lu)deg(%lu)->", h->node_id, h->value->id, h->degree);
  nr_tabs++;
  print_bheap(bq, h->child);
  nr_tabs--;
  print_bheap(bq, h->next);
}

bool empty_bheap(struct bheap_queue *bq)
{
  return !(bq->head) && !(bq->min);
}

bool is_higher_priority(struct value *a, struct value *b)
{
  /* Smaller priority has higher priority.
   * In the tie-breaking rule, smaller id has higher priority.
   */
  return a->priority < b->priority
         || ((a->priority == b->priority) && (a->id < b->id));
}

void link_bheap(struct bheap_node *root, struct bheap_node *child)
{
  child->parent = root;
  child->next = root->child;
  root->child = child;
  root->degree++;
}

struct bheap_node *merge_bheap(struct bheap_node *p, struct bheap_node *q)
{
  struct bheap_node *head = NULL;
  struct bheap_node **pos = &head;

  while (p && q) {
    if (p->degree < q->degree) {
      *pos = p;
      p = p->next;
    } else {
      *pos = q;
      q = q->next;
    }

    pos = &(*pos)->next;
  }

  if (p) {
    *pos = p;
  } else {
    *pos = q;
  }

  return head;
}

struct bheap_node *reverse_bheap(struct bheap_node *h)
{
  struct bheap_node *tail = NULL;
  struct bheap_node *next;

  if (!h) {
    return h;
  }

  h->parent = NULL;

  while (h->next) {
    next = h->next;
    h->next = tail;
    tail = h;
    h = next;
    h->parent = NULL;
  }

  h->next = tail;
  return h;
}

void min_bheap(struct bheap_queue *bq, struct bheap_node **prev,
               struct bheap_node **node)
{
  struct bheap_node *_prev, *cur;
  *prev = NULL;

  if (!bq->head) {
    *node = NULL;
    return;
  }

  *node = bq->head;
  _prev = bq->head;
  cur = bq->head->next;

  while (cur) {
    PDEBUG("min_bheap(): cur->value->id = %lu (*node)->value->id = %lu\n",
           cur->value->id, (*node)->value->id);

    if (is_higher_priority(cur->value, (*node)->value)) {
      *node = cur;
      *prev = _prev;
    }

    _prev = cur;
    cur = cur->next;
  }
}

void union_bheap(struct bheap_queue *bq, struct bheap_node *h2)
{
  struct bheap_node *h1;
  struct bheap_node *prev, *x, *next;

  if (!h2) {
    return;
  }

  h1 = bq->head;

  if (!h1) {
    bq->head = h2;
    return;
  }

  h1 = merge_bheap(h1, h2);
  prev = NULL;
  x = h1;
  next = x->next;

  while (next) {
    if ((x->degree != next->degree) ||
        (next->next && (next->next->degree == x->degree))) {
      /* nothing to do, advance. */
      prev = x;
      x = next;
    } else if (is_higher_priority(x->value, next->value)) {
      /* x becomes the root of next. */
      PDEBUG("union_bheap(): x->value->id = %lu priority = %lu becomes the root of next.\n",
             x->value->id, x->value->priority);
      PDEBUG("union_bheap(): next->value->id = %lu priority = %lu\n",
             next->value->id, next->value->priority);
      x->next = next->next;
      link_bheap(x, next);
    } else {
      /* next becomes the root of x. */
      if (prev) {
        prev->next = next;
      } else {
        h1 = next;
      }

      link_bheap(next, x);
      x = next;
    }

    next = x->next;
  }

  bq->head = h1;
}

struct bheap_node *min_bheap_extract(struct bheap_queue *bq)
{
  struct bheap_node *prev, *node;
  min_bheap(bq, &prev, &node);

  if (!node) {
    return NULL;
  }

  if (prev) {
    prev->next = node->next;
  } else {
    bq->head = node->next;
  }

  union_bheap(bq, reverse_bheap(node->child));
  return node;
}

void insert_bheap(struct bheap_queue *bq, struct bheap_node *node)
{
  struct bheap_node *min;
  PDEBUG("insert_bheap(): node = %lx node->value->id = %lu\n",
         (unsigned long) node, node->value->id);
  node->child = NULL;
  node->parent = NULL;
  node->next = NULL;
  node->degree = 0;

  if (bq->min && is_higher_priority(node->value, bq->min->value)) {
    /* swap min cache */
    min = bq->min;
    min->child = NULL;
    min->parent = NULL;
    min->next = NULL;
    min->degree = 0;
    union_bheap(bq, min);
    bq->min = node;
  } else {
    union_bheap(bq, node);
  }
}

void min_bheap_uncache(struct bheap_queue *bq)
{
  struct bheap_node *min;

  if (bq->min) {
    min = bq->min;
    bq->min = NULL;
    insert_bheap(bq, min);
  }
}

/* merge addition into target */
void union_bheap_uncache(struct bheap_queue *target,
                         struct bheap_queue *addition)
{
  /* first insert any cached minima, if necessary */
  min_bheap_uncache(target);
  min_bheap_uncache(addition);
  union_bheap(target, addition->head);
  /* this is a destructive merge */
  addition->head = NULL;
}


void decrease_bheap(struct bheap_queue *bq, struct bheap_node *node)
{
  struct bheap_node *parent;
  void *tmp;
  unsigned long node_id;

  if (!node) {
    return;
  }

  if (bq->min != node) {
    /* bubble up */
    parent = node->parent;

    while (parent && is_higher_priority(node->value, parent->value)) {
      /* swap parent and node */
      tmp = parent->value;
      node_id = parent->node_id;

      parent->value = node->value;
      parent->node_id = node->node_id;

      node->value = (struct value *) tmp;
      node->node_id = node_id;

      /* swap value->node */
      tmp = node->value->node;
      node->value->node = parent->value->node;
      parent->value->node = (struct bheap_node *) tmp;

      /* step up */
      node = parent;
      parent = node->parent;
    }
  }
}

void delete_bheap(struct bheap_queue *bq, struct bheap_node *node)
{
  struct bheap_node *parent, *prev, *pos;
  void *tmp;
  unsigned long node_id;

  if (!node) {
    return;
  }

  PDEBUG("delete_bheap(): node->id = %lu\n", node->node_id);

  if (bq->min != node) {
    /* bubble up */
    parent = node->parent;

    while (parent) {
      /* swap parent and node */
      tmp = parent->value;
      node_id = parent->node_id;

      parent->value = node->value;
      parent->node_id = node->node_id;

      node->value = (struct value *) tmp;
      node->node_id = node_id;

      /* swap value->node */
      tmp = node->value->node;
      node->value->node = parent->value->node;
      parent->value->node = (struct bheap_node *) tmp;

      /* step up */
      node = parent;
      parent = node->parent;
    }

    /* now delete:
     * first find prev */
    prev = NULL;
    pos = bq->head;

    while (pos != node) {
      prev = pos;
      pos = pos->next;
    }

    /* we have prev, now remove node */
    if (prev) {
      prev->next = node->next;
    } else {
      bq->head = node->next;
    }

    union_bheap(bq, reverse_bheap(node->child));
  } else {
    bq->min = NULL;
  }

  node->degree = NOT_IN_BHEAP;
}


void enqueue_bheap_queue(struct bheap_queue *bq, struct value *value_node)
{
  insert_bheap(bq, value_node->node);
}

void dequeue_bheap_queue(struct bheap_queue *bq, struct value *value_node)
{
  delete_bheap(bq, value_node->node);
}

struct value *pick_next_value(struct bheap_queue *bh_queue)
{
  struct value *value_node = NULL;
  struct bheap_node *bn;

  if (!empty_bheap(bh_queue)) {
    struct bheap_node *prev;
    min_bheap(bh_queue, &prev, &bn);
    value_node = bn->value;
  }

  return value_node;
}

void init_bheap_node(struct bheap_node *h, struct value *value_node)
{
  h->parent = NULL;
  h->next = NULL;
  h->child = NULL;
  h->degree = NOT_IN_BHEAP;
  h->value = value_node;
  h->node_id = value_node->id;
}

void init_value_node(struct value *value_node, unsigned long id,
                     struct bheap_node *h)
{
  value_node->id = id;
  value_node->priority = id;
  value_node->value = id;
  value_node->node = h;
}

void init_bheap(struct bheap_queue *bh_queue,
                struct bheap_node bh_nodes[QUEUE_SIZE],
                struct value value_nodes[QUEUE_SIZE])
{
  int i;

  bh_queue->head = bh_queue->min = NULL;

  for (i = 0; i < QUEUE_SIZE; i++) {
    init_value_node(&value_nodes[i], i + 1, &bh_nodes[i]);
    init_bheap_node(&bh_nodes[i], &value_nodes[i]);
    value_nodes[i].node = &bh_nodes[i];
  }
}

int main(void)
{
  struct bheap_queue bh_queue;
  struct bheap_node bh_nodes[QUEUE_SIZE];
  struct value value_nodes[QUEUE_SIZE];
  struct value *value;

  init_bheap(&bh_queue, bh_nodes, value_nodes);
  printf("print_bheap():\n");
  print_bheap(&bh_queue, bh_queue.head);

  enqueue_bheap_queue(&bh_queue, &value_nodes[0]);
  printf("print_bheap():\n");
  print_bheap(&bh_queue, bh_queue.head);

  enqueue_bheap_queue(&bh_queue, &value_nodes[2]);
  printf("print_bheap():\n");
  print_bheap(&bh_queue, bh_queue.head);

  enqueue_bheap_queue(&bh_queue, &value_nodes[1]);
  printf("print_bheap():\n");
  print_bheap(&bh_queue, bh_queue.head);

  dequeue_bheap_queue(&bh_queue, &value_nodes[2]);
  printf("print_bheap():\n");
  print_bheap(&bh_queue, bh_queue.head);

  value = pick_next_value(&bh_queue);
  printf("pick_next_value(): value->id = %lu\n", value->id);
  printf("print_bheap():\n");
  print_bheap(&bh_queue, bh_queue.head);

  return 0;
}

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* Author: Hiroyuki Chishiro

* License: 2-Clause BSD

#include <stdio.h>

#include <stdbool.h>

#include <limits.h>

#define QUEUE_SIZE 128

#define NOT_IN_BHEAP ULONG_MAX

#ifdef PDEBUG

#define PDEBUG(fmt, args...) fprintf(stderr, fmt, ## args)

#else

#define PDEBUG(fmt, args...)

#endif

struct value {

unsigned long id;

unsigned long priority;

int value;

struct bheap_node *node;

};

struct bheap_node {

unsigned long node_id;

struct bheap_node *parent;

struct bheap_node *next;

struct bheap_node *child;

unsigned long degree;

struct value *value;

};

struct bheap_queue {

unsigned long id;

struct bheap_node *head;

struct bheap_node *min;

};

void print_bheap(struct bheap_queue *bq, struct bheap_node *h)

{

static int nr_tabs = 0;

int i;

if (!h) {

printf("NULL\n");

for (i = 0; i < nr_tabs; i++) {

printf("\t");

}

return;

}

printf("node_id(%lu)id(%lu)deg(%lu)->", h->node_id, h->value->id, h->degree);

nr_tabs++;

print_bheap(bq, h->child);

nr_tabs--;

print_bheap(bq, h->next);

}

bool empty_bheap(struct bheap_queue *bq)

{

return !(bq->head) && !(bq->min);

}

bool is_higher_priority(struct value *a, struct value *b)

{

/* Smaller priority has higher priority.

* In the tie-breaking rule, smaller id has higher priority.

return a->priority < b->priority

|| ((a->priority == b->priority) && (a->id < b->id));

}

void link_bheap(struct bheap_node *root, struct bheap_node *child)

{

child->parent = root;

child->next = root->child;

root->child = child;

root->degree++;

}

struct bheap_node *merge_bheap(struct bheap_node *p, struct bheap_node *q)

{

struct bheap_node *head = NULL;

struct bheap_node **pos = &head;

while (p && q) {

if (p->degree < q->degree) {

*pos = p;

p = p->next;

} else {

*pos = q;

q = q->next;

}

pos = &(*pos)->next;

}

if (p) {

*pos = p;

} else {

*pos = q;

}

return head;

}

struct bheap_node *reverse_bheap(struct bheap_node *h)

{

struct bheap_node *tail = NULL;

struct bheap_node *next;

if (!h) {

return h;

}

h->parent = NULL;

while (h->next) {

next = h->next;

h->next = tail;

tail = h;

h = next;

h->parent = NULL;

}

h->next = tail;

return h;

}

void min_bheap(struct bheap_queue *bq, struct bheap_node **prev,

struct bheap_node **node)

{

struct bheap_node *_prev, *cur;

*prev = NULL;

if (!bq->head) {

*node = NULL;

return;

}

*node = bq->head;

_prev = bq->head;

cur = bq->head->next;

while (cur) {

PDEBUG("min_bheap(): cur->value->id = %lu (*node)->value->id = %lu\n",

cur->value->id, (*node)->value->id);

if (is_higher_priority(cur->value, (*node)->value)) {

*node = cur;

*prev = _prev;

}

_prev = cur;

cur = cur->next;

}

void union_bheap(struct bheap_queue *bq, struct bheap_node *h2)

{

struct bheap_node *h1;

struct bheap_node *prev, *x, *next;

if (!h2) {

return;

}

h1 = bq->head;

if (!h1) {

bq->head = h2;

return;

}

h1 = merge_bheap(h1, h2);

prev = NULL;

x = h1;

next = x->next;

while (next) {

if ((x->degree != next->degree) ||

(next->next && (next->next->degree == x->degree))) {

/* nothing to do, advance. */

prev = x;

x = next;

} else if (is_higher_priority(x->value, next->value)) {

/* x becomes the root of next. */

PDEBUG("union_bheap(): x->value->id = %lu priority = %lu becomes the root of next.\n",

x->value->id, x->value->priority);

PDEBUG("union_bheap(): next->value->id = %lu priority = %lu\n",

next->value->id, next->value->priority);

x->next = next->next;

link_bheap(x, next);

} else {

/* next becomes the root of x. */

if (prev) {

prev->next = next;

} else {

h1 = next;

}

link_bheap(next, x);

x = next;

}

next = x->next;

}

bq->head = h1;

}

struct bheap_node *min_bheap_extract(struct bheap_queue *bq)

{

struct bheap_node *prev, *node;

min_bheap(bq, &prev, &node);

if (!node) {

return NULL;

}

if (prev) {

prev->next = node->next;

} else {

bq->head = node->next;

}

union_bheap(bq, reverse_bheap(node->child));

return node;

}

void insert_bheap(struct bheap_queue *bq, struct bheap_node *node)

{

struct bheap_node *min;

PDEBUG("insert_bheap(): node = %lx node->value->id = %lu\n",

(unsigned long) node, node->value->id);

node->child = NULL;

node->parent = NULL;

node->next = NULL;

node->degree = 0;

if (bq->min && is_higher_priority(node->value, bq->min->value)) {

/* swap min cache */

min = bq->min;

min->child = NULL;

min->parent = NULL;

min->next = NULL;

min->degree = 0;

union_bheap(bq, min);

bq->min = node;

} else {

union_bheap(bq, node);

}

void min_bheap_uncache(struct bheap_queue *bq)

{

struct bheap_node *min;

if (bq->min) {

min = bq->min;

bq->min = NULL;

insert_bheap(bq, min);

}

/* merge addition into target */

void union_bheap_uncache(struct bheap_queue *target,

struct bheap_queue *addition)

{

/* first insert any cached minima, if necessary */

min_bheap_uncache(target);

min_bheap_uncache(addition);

union_bheap(target, addition->head);

/* this is a destructive merge */

addition->head = NULL;

}

void decrease_bheap(struct bheap_queue *bq, struct bheap_node *node)

{

struct bheap_node *parent;

void *tmp;

unsigned long node_id;

if (!node) {

return;

}

if (bq->min != node) {

/* bubble up */

parent = node->parent;

while (parent && is_higher_priority(node->value, parent->value)) {

/* swap parent and node */

tmp = parent->value;

node_id = parent->node_id;

parent->value = node->value;

parent->node_id = node->node_id;

node->value = (struct value *) tmp;

node->node_id = node_id;

/* swap value->node */

tmp = node->value->node;

node->value->node = parent->value->node;

parent->value->node = (struct bheap_node *) tmp;

/* step up */

node = parent;

parent = node->parent;

}

void delete_bheap(struct bheap_queue *bq, struct bheap_node *node)

{

struct bheap_node *parent, *prev, *pos;

void *tmp;

unsigned long node_id;

if (!node) {

return;

}

PDEBUG("delete_bheap(): node->id = %lu\n", node->node_id);

if (bq->min != node) {

/* bubble up */

parent = node->parent;

while (parent) {

/* swap parent and node */

tmp = parent->value;

node_id = parent->node_id;

parent->value = node->value;

parent->node_id = node->node_id;

node->value = (struct value *) tmp;

node->node_id = node_id;

/* swap value->node */

tmp = node->value->node;

node->value->node = parent->value->node;

parent->value->node = (struct bheap_node *) tmp;

/* step up */

node = parent;

parent = node->parent;

}

/* now delete:

* first find prev */

prev = NULL;

pos = bq->head;

while (pos != node) {

prev = pos;

pos = pos->next;

}

/* we have prev, now remove node */

if (prev) {

prev->next = node->next;

} else {

bq->head = node->next;

}

union_bheap(bq, reverse_bheap(node->child));

} else {

bq->min = NULL;

}

node->degree = NOT_IN_BHEAP;

}

void enqueue_bheap_queue(struct bheap_queue *bq, struct value *value_node)

{

insert_bheap(bq, value_node->node);

}

void dequeue_bheap_queue(struct bheap_queue *bq, struct value *value_node)

{

delete_bheap(bq, value_node->node);

}

struct value *pick_next_value(struct bheap_queue *bh_queue)

{

struct value *value_node = NULL;

struct bheap_node *bn;

if (!empty_bheap(bh_queue)) {

struct bheap_node *prev;

min_bheap(bh_queue, &prev, &bn);

value_node = bn->value;

}

return value_node;

}

void init_bheap_node(struct bheap_node *h, struct value *value_node)

{

h->parent = NULL;

h->next = NULL;

h->child = NULL;

h->degree = NOT_IN_BHEAP;

h->value = value_node;

h->node_id = value_node->id;

}

void init_value_node(struct value *value_node, unsigned long id,

struct bheap_node *h)

{

value_node->id = id;

value_node->priority = id;

value_node->value = id;

value_node->node = h;

}

void init_bheap(struct bheap_queue *bh_queue,

struct bheap_node bh_nodes[QUEUE_SIZE],

struct value value_nodes[QUEUE_SIZE])

{

int i;

bh_queue->head = bh_queue->min = NULL;

for (i = 0; i < QUEUE_SIZE; i++) {

init_value_node(&value_nodes[i], i + 1, &bh_nodes[i]);

init_bheap_node(&bh_nodes[i], &value_nodes[i]);

value_nodes[i].node = &bh_nodes[i];

}

int main(void)

{

struct bheap_queue bh_queue;

struct bheap_node bh_nodes[QUEUE_SIZE];

struct value value_nodes[QUEUE_SIZE];

struct value *value;

init_bheap(&bh_queue, bh_nodes, value_nodes);

printf("print_bheap():\n");