【C言語】キューとは【FIFOキュー，優先度キュー，二項ヒープ，赤黒木】

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 【C言語】キューとは
2 FIFOキュー
3 優先度キュー
4 二項ヒープ
5 赤黒木
6 まとめ

【C言語】キューとは

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．

本記事では，C言語のキューを紹介していきます．

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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FIFOキュー

C言語のFIFO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>
#include <stdbool.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;
  }
}

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

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

  return true;
}

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

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

  return true;
}

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

    print(&queue);
  }

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

100

101

102

103

104

* Author: Hiroyuki Chishiro

* License: 2-Clause BSD

#include <stdio.h>

#include <stdbool.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;

}

bool enqueue(struct queue *q, int data)

{

if (q->num >= QUEUE_SIZE) {

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

return false;

}

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

q->num++;

return true;

}

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

{

if (q->num == 0) {

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

return false;

}

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

increment(q);

q->num--;

return true;

}

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)) {

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():

優先度キュー

優先度キューは，キューのデータを優先度順で管理するキューです．

優先度キューは，リアルタイムOSやLinuxカーネルのスケジューラ等で利用されます．

リアルタイムOSの技術であるリアルタイムシステムやLinuxカーネルを知りたいあなたはこちらからどうぞ．

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優先度キューのコードは以下になります．

データの数値が小さいほど高い優先度になり，最高優先度のデータは優先度キューの先頭に格納されます．

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

#define QUEUE_SIZE 128

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

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

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

  q->num = 0;
}

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

  for (i = 0; i <  q->num; i++) {
    printf("%d ", q->data[i]);
  }

  printf("\n");
}

bool enqueue(struct queue *q, int data)
{
  int i;

  if (q->num >= QUEUE_SIZE) {
    fprintf(stderr, "Error: queue is full.\n");
    return false;
  }

  for (i = q->num - 1; i >= 0 && data < q->data[i]; i--) {
    q->data[i + 1] = q->data[i];
  }

  q->data[i + 1] = data;
  q->num++;

  return true;
}

int dequeue(struct queue *q, int *data)
{
  int i;

  if (q->num == 0) {
    fprintf(stderr, "Error: queue is empty.\n");
    return false;
  }

  *data = q->data[0];

  for (i = 0; i < q->num; i++) {
    q->data[i] = q->data[i + 1];
  }

  q->num--;

  return true;
}

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

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

  init(&queue);

  enqueue(&queue, 2);
  enqueue(&queue, 3);
  enqueue(&queue, 1);
  print(&queue);

  if (dequeue(&queue, &data)) {
    printf("data = %d\n", data);
  }

  print(&queue);

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

100

101

102

103

104

* Author: Hiroyuki Chishiro

* License: 2-Clause BSD

#include <stdio.h>

#include <stdbool.h>

#include <limits.h>

#define QUEUE_SIZE 128

struct queue {

int data[QUEUE_SIZE];

size_t num;

};

void init(struct queue *q)

{

int i;

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

q->data[i] = INT_MAX;

}

q->num = 0;

}

void print(struct queue *q)

{

int i;

printf("print(): ");

for (i = 0; i < q->num; i++) {

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

}

printf("\n");

}

bool enqueue(struct queue *q, int data)

{

int i;

if (q->num >= QUEUE_SIZE) {

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

return false;

}

for (i = q->num - 1; i >= 0 && data < q->data[i]; i--) {

q->data[i + 1] = q->data[i];

}

q->data[i + 1] = data;

q->num++;

return true;

}

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

{

int i;

if (q->num == 0) {

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

return false;

}

*data = q->data[0];

for (i = 0; i < q->num; i++) {

q->data[i] = q->data[i + 1];

}

q->num--;

return true;

}

void clear(struct queue *q)

{

init(q);

}

int main(void)

{

struct queue queue;

int data;

init(&queue);

enqueue(&queue, 2);

enqueue(&queue, 3);

enqueue(&queue, 1);

print(&queue);

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

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．

$ gcc priority_queue.c
$ a.out 
print(): 1 2 3 
data = 1
print(): 2 3 
print():

$ gcc priority_queue.c

$ a.out

print(): 1 2 3

data = 1

print(): 2 3

print():

二項ヒープ

二項ヒープは，優先度キューを実現するデータ構造の一つです．

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

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");