【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，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．

: 【C言語】連結リストとは【片方向リスト，双方向リスト，双方向循環リスト】

こういった悩みにお答えします．こういった私から学べます．目次1 連結リスト2 C言語のリスト2.1 片方向リスト2.2 双方向リスト2.3 双方向循環リスト3 リストの実例：Linuxカーネル3. ...

続きを見る

: 【C言語】スタックとは【x86のアセンブリ言語で解説】

こういった悩みにお答えします．こういった私から学べます．目次1 スタック2 C言語のスタック3 x86の命令セットアーキテクチャでスタックを操作するpush/pop命令4 まとめスタックスタッ ...

続きを見る

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;
}

100

101

102

103

* 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．

: 元東大教員から学ぶリアルタイムシステム

こういった私から学べます．リアルタイムシステムとは，決められた時間（デッドライン）までに処理を完了しなければならない性質をもつシステムのことです．リアルタイムシステムは，ロボット，自動車や航空機な ...

続きを見る

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;
}

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

276

277

278

279

280

281

282

283

284

285

286

287

288

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

307

308

309

310

311

312

313

314

315

316

317

318

319

320

321

322

323

324

325

326

327

328

329

330

331

332

333

334

335

336

337

338

339

340

341

342

343

344

345

346

347

348

349

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

439

440

441

442

443

444

445

446

447

448

449

450

451

452

453

454

455

456

457

458

459

460

461

462

463

464

465

466

467

468

469

470

471

472

473

* 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");