init

Author: neesenk

Makefile

@@ -0,0 +1,11 @@
+CFLAGS += -O0 -g -Wall
+all: test test2
+
+test: test.o heap.h heap.o
+	$(CC) $(CFLAGS) test.o heap.o -o test
+
+test2: test2.o fibheap.h fibheap.o
+	$(CC) $(CFLAGS) test2.o fibheap.o -o test2
+
+clean:
+	rm -rf *.o test2 test

fibheap.c

@@ -0,0 +1,224 @@
+/**
+ * author: Liu Zhiyong<[email protected]>
+ */
+
+#include <limits.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <assert.h>
+#include "fibheap.h"
+
+static fibnode_t *fibnode_remove(fibnode_t *node)
+{
+	fibnode_t *ret = (node != node->left) ? node->left : NULL;
+
+	node->right->left = node->left;
+	node->left->right = node->right;
+	node->left = node;
+	node->right = node;
+
+	return ret;
+}
+
+static void fibnode_insert(fibnode_t *a, fibnode_t *b)
+{
+	b->left = a;
+	b->right = a->right;
+
+	a->right->left = b;
+	a->right = b;
+}
+
+static void fibnode_union(fibnode_t *a, fibnode_t *b)
+{
+	fibnode_t *atail = a->right;
+	fibnode_t *btail = b->right;
+
+	atail->left = b;
+	b->right = atail;
+
+	a->right = btail;
+	btail->left = a;
+}
+
+static void fibheap_link(fibnode_t *node, fibnode_t *parent)
+{
+	if (parent->child == NULL)
+		parent->child = node;
+	else
+		fibnode_insert(parent->child, node);
+	node->parent = parent;
+	node->mark = 0;
+	parent->degree++;
+}
+
+static void fibheap_cut(fibheap_t *fib, fibnode_t *node, fibnode_t *parent)
+{
+	parent->degree--;
+	parent->child = fibnode_remove(node);
+
+	node->parent  = NULL;
+	node->mark    = 0;
+
+	fibnode_insert(fib->min, node);
+}
+
+static void __fibheap_insert(fibheap_t *fib, fibnode_t *node)
+{
+	if (fib->min == NULL) {
+		fib->min = node;
+	} else {
+		fibnode_insert(fib->min, node);
+		if (node->key < fib->min->key)
+			fib->min = node;
+	}
+}
+
+static void fibheap_consolidate(fibheap_t *fib)
+{
+	int i, max = 0;
+	fibnode_t *tmp, *node, *min, *stack[1 + 8 * sizeof(long)] = {NULL};
+
+	while ((min = fib->min) != NULL) {
+		fib->min = fibnode_remove(min);
+		for (i = min->degree; stack[i] != NULL; i++) {
+			node = stack[i], stack[i] = NULL;
+			if (min->key > node->key)
+				tmp = min, min = node, node = tmp;
+
+			fibheap_link(node, min);
+		}
+		stack[i] = min;
+		if (i > max)
+			max = i;
+	}
+
+	assert(max < 1 + 8 * sizeof(long));
+	for (i = 0; i <= max; i++) {
+		if (stack[i])
+			__fibheap_insert(fib, stack[i]);
+	}
+}
+
+static void fibheap_cascading_cut(fibheap_t *fib, fibnode_t *node)
+{
+	fibnode_t *parent;
+	while ((parent = node->parent) != NULL) {
+		if (node->mark == 0) {
+			node->mark = 1;
+			return;
+		}
+		fibheap_cut(fib, node, parent);
+		node = parent;
+	}
+}
+
+static fibnode_t *__fibheap_extract_min(fibheap_t *fib)
+{
+	fibnode_t *n, *min = fib->min;
+
+	// 将min的子节点合并到堆的根节点上
+	if (min->child) {
+		min->child->parent = NULL;
+		for (n = min->child->left; n != min->child; n = n->left)
+			n->parent = NULL;
+		fibnode_union(min, min->child);
+	}
+
+	fib->nodes--;
+	fib->min = fibnode_remove(min);
+	fibheap_consolidate(fib);
+
+	FIBNODE_INIT(min);
+	return min;
+}
+
+void fibheap_init(fibheap_t *fib)
+{
+	*fib = FIBHEAP_INIT();
+}
+
+void fibheap_fini(fibheap_t *fib)
+{
+	while (fib->min) {
+		fibnode_t *min = __fibheap_extract_min(fib);
+		FIBNODE_INIT(min);
+	}
+	*fib = FIBHEAP_INIT();
+}
+
+int fibheap_insert(fibheap_t *fib, fibnode_t *node)
+{
+	assert(node->key > FIBHEAP_MINKEY);
+
+	FIBNODE_INIT(node);
+	__fibheap_insert(fib, node);
+	fib->nodes++;
+
+	return 0;
+}
+
+fibnode_t *fibheap_min(fibheap_t *fib)
+{
+	return fib->min ? fib->min : NULL;
+}
+
+fibnode_t *fibheap_extract_min(fibheap_t *fib)
+{
+	return fib->min ? __fibheap_extract_min(fib) : NULL;
+}
+
+int fibheap_union(fibheap_t *fib, fibheap_t *other)
+{
+	if (!fib->min || !other->min) {
+		if (!fib->min)
+			*fib = *other;
+		goto DONE;
+	}
+
+	// 链接两个堆的根的双向链表
+	fibnode_union(fib->min, other->min);
+	// 比较最小的节点
+	if (fib->min->key > other->min->key)
+		fib->min = other->min;
+	fib->nodes += other->nodes;
+DONE:
+	*other = FIBHEAP_INIT();
+	return 0;
+}
+
+static int __fibheap_decrease_key(fibheap_t *fib, fibnode_t *node, long key)
+{
+	fibnode_t *parent = node->parent;
+	node->key = key;
+
+	if (parent && node->key <= parent->key) {
+		fibheap_cut(fib, node, parent);
+		fibheap_cascading_cut(fib, parent);
+	}
+
+	if (node->key <= fib->min->key)
+		fib->min = node;
+
+	return 0;
+}
+
+int fibheap_decrease_key(fibheap_t *fib, fibnode_t *node, long key)
+{
+	assert(key > FIBHEAP_MINKEY && node->key > key);
+	return node->key != key ? __fibheap_decrease_key(fib, node, key) : 0;
+}
+
+int fibheap_delete(fibheap_t *fib, fibnode_t *node)
+{
+	long okey = node->key;
+
+	__fibheap_decrease_key(fib, node, FIBHEAP_MINKEY);
+	assert(node == fib->min);
+	__fibheap_extract_min(fib);
+
+	node->key = okey;
+
+	return 0;
+}

fibheap.h

@@ -0,0 +1,46 @@
+/**
+ * author: Liu Zhiyong<[email protected]>
+ *
+ * fibheap_union  O(1)
+ * fibheap_insert O(1)
+ * fibheap_min	  O(1)
+ * fibheap_delete O(lgn) amortized, O(n) worst case
+ * fibheap_extract_min  O(lgn) amortized, O(n) worst case
+ * fibheap_decrease_key O(1) amortized, O(lgn) worst case
+ */
+
+#ifndef __FIBHEAP_H__
+#define __FIBHEAP_H__
+
+#define FIBHEAP_MINKEY	LONG_MIN
+
+#define FIBHEAP_INIT() (fibheap_t){0, NULL}
+#define FIBNODE_INIT(_n) do { fibnode_t *n = _n; n->parent=n->child=NULL;n->left=n->right=n;} while (0)
+
+typedef struct fibnode {
+	long   key;
+	char   mark;		// 标记节点成为另一个节点的子节点后失去过子节点
+	unsigned short degree;	// 子节点数目
+	struct fibnode *parent;	// 父指针
+	struct fibnode *child;	// 字节点
+	struct fibnode *left;	// 左兄节点
+	struct fibnode *right;	// 右兄节点, 这两个指针窜成一个双向链表, 没有大小次序
+} fibnode_t;
+
+typedef struct fibheap {
+	size_t nodes;		// 包含的关键字数目
+	struct fibnode *min;	// 指向fibheap中最小关键字的根节点
+} fibheap_t;
+
+void fibheap_init(fibheap_t *fib);
+void fibheap_fini(fibheap_t *fib);
+
+int fibheap_union(fibheap_t *fib, fibheap_t *other);
+
+int fibheap_insert(fibheap_t *fib, fibnode_t *node);
+int fibheap_delete(fibheap_t *fib, fibnode_t *node);
+int fibheap_decrease_key(fibheap_t *fib, fibnode_t *node, long key);
+fibnode_t *fibheap_extract_min(fibheap_t *fib);
+fibnode_t *fibheap_min(fibheap_t *fib);
+
+#endif /* _FIBHEAP_H_ */