斐波那契堆

概要

本章介绍斐波那契堆。和以往一样，本文会先对斐波那契堆的理论知识进行简单介绍，然后给出C语言的实现。后续再分别给出C++和Java版本的实现；实现的语言虽不同，但是原理如出一辙，选择其中之一进行了解即可。若文章有错误或不足的地方，请不吝指出！

目录
1. 斐波那契堆的介绍
2. 斐波那契堆的基本操作
3. 斐波那契堆的C实现(完整源码)
4. 斐波那契堆的C测试程序

转载请注明出处：斐波那契堆(一)之图文解析和 C语言的实现 - 如果天空不死 - 博客园

更多内容：数据结构与算法系列目录

(01) 斐波那契堆(一)之图文解析和 C语言的实现
(02) 斐波那契堆(二)之 C++的实现
(03) 斐波那契堆(三)之 Java的实现

斐波那契堆的介绍

斐波那契堆(Fibonacci heap)是堆中一种，它和二项堆一样，也是一种可合并堆；可用于实现合并优先队列。斐波那契堆比二项堆具有更好的平摊分析性能，它的合并操作的时间复杂度是O(1)。
与二项堆一样，它也是由一组堆最小有序树组成，并且是一种可合并堆。
与二项堆不同的是，斐波那契堆中的树不一定是二项树；而且二项堆中的树是有序排列的，但是斐波那契堆中的树都是有根而无序的。

斐波那契堆的基本操作

1. 基本定义

typedef int Type;typedef struct _FibonacciNode
{Type   key;                     // 关键字(键值)int degree;                     // 度数struct _FibonacciNode *left;    // 左兄弟struct _FibonacciNode *right;   // 右兄弟struct _FibonacciNode *child;   // 第一个孩子节点struct _FibonacciNode *parent;  // 父节点int marked;                     //是否被删除第1个孩子(1表示删除，0表示未删除)
}FibonacciNode, FibNode;

FibNode是斐波那契堆的节点类，它包含的信息较多。key是用于比较节点大小的，degree是记录节点的度，left和right分别是指向节点的左右兄弟，child是节点的第一个孩子，parent是节点的父节点，marked是记录该节点是否被删除第1个孩子(marked在删除节点时有用)。

typedef struct _FibonacciHeap{int   keyNum;                   // 堆中节点的总数int   maxDegree;                // 最大度struct _FibonacciNode *min;     // 最小节点(某个最小堆的根节点)struct _FibonacciNode **cons;   // 最大度的内存区域
}FibonacciHeap, FibHeap;

FibHeap是斐波那契堆对应的类。min是保存当前堆的最小节点，keyNum用于记录堆中节点的总数，maxDegree用于记录堆中最大度，而cons在删除节点时来暂时保存堆数据的临时空间。

下面看看斐波那契堆的内存结构图。

从图中可以看出，斐波那契堆是由一组最小堆组成，这些最小堆的根节点组成了双向链表(后文称为"根链表")；斐波那契堆中的最小节点就是"根链表中的最小节点"！

PS. 上面这幅图的结构和测试代码中的"基本信息"测试函数的结果是一致的；你可以通过测试程序来亲自验证！

2. 插入操作

插入操作非常简单：插入一个节点到堆中，直接将该节点插入到"根链表的min节点"之前即可；若被插入节点比"min节点"小，则更新"min节点"为被插入节点。

上面是插入操作的示意图。

斐波那契堆的根链表是"双向链表"，这里将min节点看作双向联表的表头(后文也是如此)。在插入节点时，每次都是"将节点插入到min节点之前(即插入到双链表末尾)"。此外，对于根链表中最小堆都只有一个节点的情况，插入操作就很演化成双向链表的插入操作。

此外，插入操作示意图与测试程序中的"插入操作"相对应，感兴趣的可以亲自验证。

插入操作代码

/** 将"单个节点node"加入"链表root"之前*   a …… root*   a …… node …… root** 注意： 此处node是单个节点，而root是双向链表
*/
static void fib_node_add(FibNode *node, FibNode *root)
{node->left        = root->left;root->left->right = node;node->right       = root;root->left        = node;
}/** 将节点node插入到斐波那契堆heap中*/
static void fib_heap_insert_node(FibHeap *heap, FibNode *node)
{if (heap->keyNum == 0)heap->min = node;else{fib_node_add(node, heap->min);if (node->key < heap->min->key)heap->min = node;}heap->keyNum++;
}

3. 合并操作

合并操作和插入操作的原理非常类似：将一个堆的根链表插入到另一个堆的根链表上即可。简单来说，就是将两个双链表拼接成一个双向链表。

上面是合并操作的示意图。该操作示意图与测试程序中的"合并操作"相对应！

合并操作代码

/** 将双向链表b链接到双向链表a的后面** 注意： 此处a和b都是双向链表
*/
static void fib_node_cat(FibNode *a, FibNode *b)
{FibNode *tmp;tmp            = a->right;a->right       = b->right;b->right->left = a;b->right       = tmp;tmp->left      = b;
}/** 将h1, h2合并成一个堆，并返回合并后的堆*/
FibHeap* fib_heap_union(FibHeap *h1, FibHeap *h2)
{FibHeap *tmp;if (h1==NULL)return h2;if (h2==NULL)return h1;// 以h1为"母"，将h2附加到h1上；下面是保证h1的度数大，尽可能的少操作。if(h2->maxDegree > h1->maxDegree){tmp = h1;h1 = h2;h2 = tmp;}if((h1->min) == NULL)                // h1无"最小节点"{h1->min = h2->min;h1->keyNum = h2->keyNum;free(h2->cons);free(h2);}else if((h2->min) == NULL)           // h1有"最小节点" && h2无"最小节点"{free(h2->cons);free(h2);}                                   // h1有"最小节点" && h2有"最小节点"else{// 将"h2中根链表"添加到"h1"中fib_node_cat(h1->min, h2->min);if (h1->min->key > h2->min->key)h1->min = h2->min;h1->keyNum += h2->keyNum;free(h2->cons);free(h2);}return h1;
}

4. 取出最小节点

抽取最小结点的操作是斐波那契堆中较复杂的操作。
(1）将要抽取最小结点的子树都直接串联在根表中；
(2）合并所有degree相等的树，直到没有相等的degree的树。

上面是取出最小节点的示意图。图中应该写的非常明白了，若有疑问，看代码。

此外，该操作示意图与测试程序中的"删除最小节点"相对应！有兴趣的可以亲自验证。

取出最小节点代码

/** 移除最小节点，并返回移除节点后的斐波那契堆*/
FibNode* _fib_heap_extract_min(FibHeap *heap)
{if (heap==NULL || heap->min==NULL)return NULL;FibNode *child = NULL;FibNode *min = heap->min;// 将min每一个儿子(儿子和儿子的兄弟)都添加到"斐波那契堆的根链表"中while (min->child != NULL){child = min->child;fib_node_remove(child);if (child->right == child)min->child = NULL;elsemin->child = child->right;fib_node_add(child, heap->min);child->parent = NULL;}// 将min从根链表中移除fib_node_remove(min);// 若min是堆中唯一节点，则设置堆的最小节点为NULL；// 否则，设置堆的最小节点为一个非空节点(min->right)，然后再进行调节。if (min->right == min)heap->min = NULL;else{heap->min = min->right;fib_heap_consolidate(heap);}heap->keyNum--;return min;
}

其中fib_heap_consolidate(heap)的作用是合并斐波那契堆的根链表中相同度数的树，它的相关代码如下：

View Code

5. 减小节点值

减少斐波那契堆中的节点的键值，这个操作的难点是：如果减少节点后破坏了"最小堆"性质，如何去维护呢？下面对一般性情况进行分析。
(1) 首先，将"被减小节点"从"它所在的最小堆"剥离出来；然后将"该节点"关联到"根链表"中。倘若被减小的节点不是单独一个节点，而是包含子树的树根。则是将以"被减小节点"为根的子树从"最小堆"中剥离出来，然后将该树关联到根链表中。
(2) 接着，对"被减少节点"的原父节点进行"级联剪切"。所谓"级联剪切"，就是在被减小节点破坏了最小堆性质，并被切下来之后；再从"它的父节点"进行递归级联剪切操作。
而级联操作的具体动作则是：若父节点(被减小节点的父节点)的marked标记为false，则将其设为true，然后退出。
否则，将父节点从最小堆中切下来(方式和"切被减小节点的方式"一样)；然后递归对祖父节点进行"级联剪切"。
marked标记的作用就是用来标记"该节点的子节点是否有被删除过"，它的作用是来实现级联剪切。而级联剪切的真正目的是为了防止"最小堆"由二叉树演化成链表。
(3) 最后，别忘了对根链表的最小节点进行更新。

上面是减小节点值的示意图。该操作示意图与测试程序中的"减小节点"相对应！

减小节点值的代码

/* * 将斐波那契堆heap中节点node的值减少为key*/
static void fib_heap_decrease(FibHeap *heap, FibNode *node, Type key)
{FibNode *parent;if (heap==NULL || heap->min==NULL ||node==NULL) return ;if ( key>=node->key){printf("decrease failed: the new key(%d) is no smaller than current key(%d)\n", key, node->key);return ;}node->key = key;parent = node->parent;if (parent!=NULL && node->key < parent->key){// 将node从父节点parent中剥离出来，并将node添加到根链表中fib_heap_cut(heap, node, parent);fib_heap_cascading_cut(heap, parent);}// 更新最小节点if (node->key < heap->min->key)heap->min = node;
}

其中，fib_heap_cut()和fib_heap_cascading_cut()的相关代码如下：

View Code

6. 增加节点值

增加节点值和减少节点值类似，这个操作的难点也是如何维护"最小堆"性质。思路如下：
(1) 将"被增加节点"的"左孩子和左孩子的所有兄弟"都链接到根链表中。
(2) 接下来，把"被增加节点"添加到根链表；但是别忘了对其进行级联剪切。

上面是增加节点值的示意图。该操作示意图与测试程序中的"增大节点"相对应！

增加节点值的代码

/* * 将斐波那契堆heap中节点node的值增加为key*/
static void fib_heap_increase(FibHeap *heap, FibNode *node, Type key)
{FibNode *child, *parent, *right;if (heap==NULL || heap->min==NULL ||node==NULL) return ;if (key <= node->key){printf("increase failed: the new key(%d) is no greater than current key(%d)\n", key, node->key);return ;}// 将node每一个儿子(不包括孙子,重孙,...)都添加到"斐波那契堆的根链表"中while (node->child != NULL){child = node->child;fib_node_remove(child);               // 将child从node的子链表中删除if (child->right == child)node->child = NULL;elsenode->child = child->right;fib_node_add(child, heap->min);       // 将child添加到根链表中child->parent = NULL;}node->degree = 0;node->key = key;// 如果node不在根链表中，//     则将node从父节点parent的子链接中剥离出来，//     并使node成为"堆的根链表"中的一员，//     然后进行"级联剪切"// 否则，则判断是否需要更新堆的最小节点parent = node->parent;if(parent != NULL){fib_heap_cut(heap, node, parent);fib_heap_cascading_cut(heap, parent);}else if(heap->min == node){right = node->right;while(right != node){if(node->key > right->key)heap->min = right;right = right->right;}}
}

7. 删除节点

删除节点，本文采用了操作是："取出最小节点"和"减小节点值"的组合。
(1) 先将被删除节点的键值减少。减少后的值要比"原最小节点的值"即可。
(2) 接着，取出最小节点即可。

删除节点值的代码

/** 删除结点node*/
static void _fib_heap_delete(FibHeap *heap, FibNode *node)
{Type min = heap->min->key;fib_heap_decrease(heap, node, min-1);_fib_heap_extract_min(heap);free(node);
}

注意：关于斐波那契堆的"更新"、"打印"、"销毁"等接口就不再单独介绍了。后文的源码中有给出它们的实现代码，Please RTFSC(Read The Fucking Source Code)！

斐波那契堆的C实现(完整源码)

斐波那契堆的头文件(fibonacci_heap.h)

#ifndef _FIBONACCI_HEAP_H_
#define _FIBONACCI_HEAP_H_typedef int Type;typedef struct _FibonacciNode
{Type   key;                        // 关键字(键值)int degree;                        // 度数struct _FibonacciNode *left;    // 左兄弟struct _FibonacciNode *right;    // 右兄弟struct _FibonacciNode *child;    // 第一个孩子节点struct _FibonacciNode *parent;    // 父节点int marked;                       //是否被删除第1个孩子(1表示删除，0表示未删除)
}FibonacciNode, FibNode;typedef struct _FibonacciHeap{int   keyNum;                    // 堆中节点的总数int   maxDegree;                // 最大度struct _FibonacciNode *min;        // 最小节点(某个最小堆的根节点)struct _FibonacciNode **cons;    // 最大度的内存区域
}FibonacciHeap, FibHeap;// 创建Fibonacci堆
FibHeap* fib_heap_make();
// 新建键值为key的节点，并将其插入到斐波那契堆中
void fib_heap_insert_key(FibHeap *heap, Type key);
// 删除键值为key的结点
void fib_heap_delete(FibHeap *heap, Type key);
// 移除最小节点
void fib_heap_extract_min(FibHeap *heap);
// 更新heap的中的oldkey为newkey
void fib_heap_update(FibHeap *heap, Type oldkey, Type newkey);
// 将h1, h2合并成一个堆，并返回合并后的堆
FibHeap* fib_heap_union(FibHeap *h1, FibHeap *h2);
// 在斐波那契堆heap中是否存在键值为key的节点；存在返回1，否则返回0。
int fib_heap_contains(FibHeap *heap, Type key);
// 获取最小节点对应的值(保存在pkey中)；成功返回1，失败返回0。
int fib_heap_get_min(FibHeap *heap, Type *pkey);
// 销毁斐波那契堆
void fib_heap_destroy(FibHeap *heap);
// 打印"斐波那契堆"
void fib_print(FibHeap *heap);#endif

斐波那契堆的实现文件(fibonacci_heap.c)

/*** C语言实现的斐波那契堆** @author skywang* @date 2014/04/05*/#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <float.h>
#include "fibonacci_heap.h"#if 0
#define LOG2(x) ({ \unsigned int _i = 0; \__asm__("bsr %1, %0" : "=r" (_i) : "r" ((x))); \_i; })
#else   // 注意：通过gcc编译时，要添加 -lm 选项。
#define LOG2(x) ((log((double)(x))) / (log(2.0)))
#endifstatic FibNode *fib_heap_search(FibHeap *heap, Type key);/** 将node从双链表移除*/
static void fib_node_remove(FibNode *node)
{node->left->right = node->right;node->right->left = node->left;
}/** 将"单个节点node"加入"链表root"之前*   a …… root*   a …… node …… root** 注意： 此处node是单个节点，而root是双向链表
*/
static void fib_node_add(FibNode *node, FibNode *root)
{node->left        = root->left;root->left->right = node;node->right       = root;root->left        = node;
}/** 将双向链表b链接到双向链表a的后面** 注意： 此处a和b都是双向链表
*/
static void fib_node_cat(FibNode *a, FibNode *b)
{FibNode *tmp;tmp            = a->right;a->right       = b->right;b->right->left = a;b->right       = tmp;tmp->left      = b;
}/** 创建斐波那契堆*/
FibHeap* fib_heap_make()
{FibHeap* heap;heap = (FibHeap *) malloc(sizeof(FibHeap));if (heap == NULL){printf("Error: make FibHeap failed\n");return NULL;}heap->keyNum = 0;heap->maxDegree = 0;heap->min = NULL;heap->cons = NULL;return heap;
}/** 创建斐波那契堆的节点*/
static FibNode* fib_node_make(Type key)
{FibNode * node;node = (FibNode *) malloc(sizeof(FibNode));if (node == NULL){printf("Error: make Node failed\n");return NULL;}node->key    = key;node->degree = 0;node->left   = node;node->right  = node;node->parent = NULL;node->child  = NULL;return node;
}/** 将节点node插入到斐波那契堆heap中*/
static void fib_heap_insert_node(FibHeap *heap, FibNode *node)
{if (heap->keyNum == 0)heap->min = node;else{fib_node_add(node, heap->min);if (node->key < heap->min->key)heap->min = node;}heap->keyNum++;
}/** 新建键值为key的节点，并将其插入到斐波那契堆中*/
void fib_heap_insert_key(FibHeap *heap, Type key)
{FibNode *node;if (heap==NULL)return ;node = fib_node_make(key);if (node == NULL)return ;fib_heap_insert_node(heap, node);
}/** 将h1, h2合并成一个堆，并返回合并后的堆*/
FibHeap* fib_heap_union(FibHeap *h1, FibHeap *h2)
{FibHeap *tmp;if (h1==NULL)return h2;if (h2==NULL)return h1;// 以h1为"母"，将h2附加到h1上；下面是保证h1的度数大，尽可能的少操作。if(h2->maxDegree > h1->maxDegree){tmp = h1;h1 = h2;h2 = tmp;}if((h1->min) == NULL)                // h1无"最小节点"{h1->min = h2->min;h1->keyNum = h2->keyNum;free(h2->cons);free(h2);}else if((h2->min) == NULL)           // h1有"最小节点" && h2无"最小节点"{free(h2->cons);free(h2);}                                   // h1有"最小节点" && h2有"最小节点"else{// 将"h2中根链表"添加到"h1"中fib_node_cat(h1->min, h2->min);if (h1->min->key > h2->min->key)h1->min = h2->min;h1->keyNum += h2->keyNum;free(h2->cons);free(h2);}return h1;
}/** 将"堆的最小结点"从根链表中移除，* 这意味着"将最小节点所属的树"从堆中移除!*/
static FibNode *fib_heap_remove_min(FibHeap *heap)
{FibNode *min = heap->min;if (heap->min == min->right)heap->min = NULL;else{fib_node_remove(min);heap->min = min->right;}min->left = min->right = min;return min;
}/** 将node链接到root根结点*/
static void fib_heap_link(FibHeap * heap, FibNode * node, FibNode *root)
{// 将node从双链表中移除fib_node_remove(node);// 将node设为root的孩子if (root->child == NULL)root->child = node;elsefib_node_add(node, root->child);node->parent = root;root->degree++;node->marked = 0;
}/** 创建fib_heap_consolidate所需空间*/
static void fib_heap_cons_make(FibHeap * heap)
{int old = heap->maxDegree;// 计算log2(x)，"+1"意味着向上取整！// ex. log2(13) = 3，向上取整为3+1=4。heap->maxDegree = LOG2(heap->keyNum) + 1;// 如果原本空间不够，则再次分配内存if (old >= heap->maxDegree)return ;// 因为度为heap->maxDegree可能被合并，所以要maxDegree+1heap->cons = (FibNode **)realloc(heap->cons,sizeof(FibHeap *) * (heap->maxDegree + 1));
}/** 合并斐波那契堆的根链表中左右相同度数的树*/
static void fib_heap_consolidate(FibHeap *heap)
{int i, d, D;FibNode *x, *y, *tmp;fib_heap_cons_make(heap);//开辟哈希所用空间D = heap->maxDegree + 1;for (i = 0; i < D; i++)heap->cons[i] = NULL;// 合并相同度的根节点，使每个度数的树唯一while (heap->min != NULL){x = fib_heap_remove_min(heap);    // 取出堆中的最小树(最小节点所在的树)d = x->degree;                    // 获取最小树的度数// heap->cons[d] != NULL，意味着有两棵树(x和y)的"度数"相同。while (heap->cons[d] != NULL){y = heap->cons[d];            // y是"与x的度数相同的树"if (x->key > y->key)        // 保证x的键值比y小{tmp = x;x = y;y = tmp;}fib_heap_link(heap, y, x);    // 将y链接到x中heap->cons[d] = NULL;d++;}heap->cons[d] = x;}heap->min = NULL;// 将heap->cons中的结点重新加到根表中for (i=0; i<D; i++){if (heap->cons[i] != NULL){if (heap->min == NULL)heap->min = heap->cons[i];else{fib_node_add(heap->cons[i], heap->min);if ((heap->cons[i])->key < heap->min->key)heap->min = heap->cons[i];}}}
}/** 移除最小节点，并返回移除节点后的斐波那契堆*/
FibNode* _fib_heap_extract_min(FibHeap *heap)
{if (heap==NULL || heap->min==NULL)return NULL;FibNode *child = NULL;FibNode *min = heap->min;// 将min每一个儿子(儿子和儿子的兄弟)都添加到"斐波那契堆的根链表"中while (min->child != NULL){child = min->child;fib_node_remove(child);if (child->right == child)min->child = NULL;elsemin->child = child->right;fib_node_add(child, heap->min);child->parent = NULL;}// 将min从根链表中移除fib_node_remove(min);// 若min是堆中唯一节点，则设置堆的最小节点为NULL；// 否则，设置堆的最小节点为一个非空节点(min->right)，然后再进行调节。if (min->right == min)heap->min = NULL;else{heap->min = min->right;fib_heap_consolidate(heap);}heap->keyNum--;return min;
}void fib_heap_extract_min(FibHeap *heap)
{FibNode *node;if (heap==NULL || heap->min==NULL)return ;node = _fib_heap_extract_min(heap);if (node!=NULL)free(node);
}/** 在斐波那契堆heap中是否存在键值为key的节点；存在返回1，否则返回0。*/
int fib_heap_get_min(FibHeap *heap, Type *pkey)
{if (heap==NULL || heap->min==NULL || pkey==NULL)return 0;*pkey = heap->min->key;return 1;
}/** 修改度数*/
static void renew_degree(FibNode *parent, int degree)
{parent->degree -= degree;if (parent-> parent != NULL)renew_degree(parent->parent, degree);
}/** 将node从父节点parent的子链接中剥离出来，* 并使node成为"堆的根链表"中的一员。*/
static void fib_heap_cut(FibHeap *heap, FibNode *node, FibNode *parent)
{fib_node_remove(node);renew_degree(parent, node->degree);// node没有兄弟if (node == node->right)parent->child = NULL;elseparent->child = node->right;node->parent = NULL;node->left = node->right = node;node->marked = 0;// 将"node所在树"添加到"根链表"中fib_node_add(node, heap->min);
}/** 对节点node进行"级联剪切"** 级联剪切：如果减小后的结点破坏了最小堆性质，*     则把它切下来(即从所在双向链表中删除，并将*     其插入到由最小树根节点形成的双向链表中)，*     然后再从"被切节点的父节点"到所在树根节点递归执行级联剪枝*/
static void fib_heap_cascading_cut(FibHeap *heap, FibNode *node)
{FibNode *parent = node->parent;if (parent != NULL)return ;if (node->marked == 0)node->marked = 1;else{fib_heap_cut(heap, node, parent);fib_heap_cascading_cut(heap, parent);}
}/** 将斐波那契堆heap中节点node的值减少为key*/
static void fib_heap_decrease(FibHeap *heap, FibNode *node, Type key)
{FibNode *parent;if (heap==NULL || heap->min==NULL ||node==NULL)return ;if ( key>=node->key){printf("decrease failed: the new key(%d) is no smaller than current key(%d)\n", key, node->key);return ;}node->key = key;parent = node->parent;if (parent!=NULL && node->key < parent->key){// 将node从父节点parent中剥离出来，并将node添加到根链表中fib_heap_cut(heap, node, parent);fib_heap_cascading_cut(heap, parent);}// 更新最小节点if (node->key < heap->min->key)heap->min = node;
}/** 将斐波那契堆heap中节点node的值增加为key*/
static void fib_heap_increase(FibHeap *heap, FibNode *node, Type key)
{FibNode *child, *parent, *right;if (heap==NULL || heap->min==NULL ||node==NULL)return ;if (key <= node->key){printf("increase failed: the new key(%d) is no greater than current key(%d)\n", key, node->key);return ;}// 将node每一个儿子(不包括孙子,重孙,...)都添加到"斐波那契堆的根链表"中while (node->child != NULL){child = node->child;fib_node_remove(child);               // 将child从node的子链表中删除if (child->right == child)node->child = NULL;elsenode->child = child->right;fib_node_add(child, heap->min);       // 将child添加到根链表中child->parent = NULL;}node->degree = 0;node->key = key;// 如果node不在根链表中，//     则将node从父节点parent的子链接中剥离出来，//     并使node成为"堆的根链表"中的一员，//     然后进行"级联剪切"// 否则，则判断是否需要更新堆的最小节点parent = node->parent;if(parent != NULL){fib_heap_cut(heap, node, parent);fib_heap_cascading_cut(heap, parent);}else if(heap->min == node){right = node->right;while(right != node){if(node->key > right->key)heap->min = right;right = right->right;}}
}/** 更新二项堆heap的节点node的键值为key*/
void _fib_heap_update(FibHeap *heap, FibNode *node, Type key)
{if(key < node->key)fib_heap_decrease(heap, node, key);else if(key > node->key)fib_heap_increase(heap, node, key);elseprintf("No need to update!!!\n");
}void fib_heap_update(FibHeap *heap, Type oldkey, Type newkey)
{FibNode *node;if (heap==NULL)return ;node = fib_heap_search(heap, oldkey);if (node!=NULL)_fib_heap_update(heap, node, newkey);
}/** 在最小堆root中查找键值为key的节点*/
static FibNode* fib_node_search(FibNode *root, Type key)
{FibNode *t = root;    // 临时节点FibNode *p = NULL;    // 要查找的节点if (root==NULL)return root;do{if (t->key == key){p = t;break;}else{if ((p = fib_node_search(t->child, key)) != NULL)break;}t = t->right;} while (t != root);return p;
}/** 在斐波那契堆heap中查找键值为key的节点*/
static FibNode *fib_heap_search(FibHeap *heap, Type key)
{if (heap==NULL || heap->min==NULL)return NULL;return fib_node_search(heap->min, key);
}/** 在斐波那契堆heap中是否存在键值为key的节点。* 存在返回1，否则返回0。*/
int fib_heap_contains(FibHeap *heap, Type key)
{return fib_heap_search(heap,key)!=NULL ? 1: 0;
}/** 删除结点node*/
static void _fib_heap_delete(FibHeap *heap, FibNode *node)
{Type min = heap->min->key;fib_heap_decrease(heap, node, min-1);_fib_heap_extract_min(heap);free(node);
}void fib_heap_delete(FibHeap *heap, Type key)
{FibNode *node;if (heap==NULL || heap->min==NULL)return ;node = fib_heap_search(heap, key);if (node==NULL)return ;_fib_heap_delete(heap, node);
}/** 销毁斐波那契堆*/
static void fib_node_destroy(FibNode *node)
{FibNode *start = node;if(node == NULL)return;do {fib_node_destroy(node->child);// 销毁node，并将node指向下一个node = node->right;free(node->left);} while(node != start);
}void fib_heap_destroy(FibHeap *heap)
{fib_node_destroy(heap->min);free(heap->cons);free(heap);
}/** 打印"斐波那契堆"** 参数说明：*     node       -- 当前节点*     prev       -- 当前节点的前一个节点(父节点or兄弟节点)*     direction  --  1，表示当前节点是一个左孩子;*                    2，表示当前节点是一个兄弟节点。*/
static void _fib_print(FibNode *node, FibNode *prev, int direction)
{FibonacciNode *start=node;if (node==NULL)return ;do{if (direction == 1)printf("%8d(%d) is %2d's child\n", node->key, node->degree, prev->key);elseprintf("%8d(%d) is %2d's next\n", node->key, node->degree, prev->key);if (node->child != NULL)_fib_print(node->child, node, 1);// 兄弟节点prev = node;node = node->right;direction = 2;} while(node != start);
}void fib_print(FibHeap *heap)
{int i=0;FibonacciNode *p;if (heap==NULL || heap->min==NULL)return ;printf("== 斐波那契堆的详细信息: ==\n");p = heap->min;do {i++;printf("%2d. %4d(%d) is root\n", i, p->key, p->degree);_fib_print(p->child, p, 1);p = p->right;} while (p != heap->min);printf("\n");
}

斐波那契堆的测试程序(main.c)

/*** C语言实现的斐波那契堆** @author skywang* @date 2014/04/06*/#include <stdio.h>
#include "fibonacci_heap.h"#define DEBUG 0#if DEBUG
#define log(x, ...)   printf(x, __VA_ARGS__)
#else
#define log(x, ...)
#endif#define LENGTH(a) ( (sizeof(a)) / (sizeof(a[0])) )// 共8个
int a[] = {12,  7, 25, 15, 28,33, 41, 1};
// 共14个
int b[] = {18, 35, 20, 42,  9,31, 23,  6, 48, 11,24, 52, 13, 2};// 验证"基本信息(斐波那契堆的结构)"
void test_basic()
{int i;int blen=LENGTH(b);FibHeap *hb = fib_heap_make();// 斐波那契堆hbprintf("== 斐波那契堆(hb)中依次添加: ");for(i=0; i<blen; i++){printf("%d ", b[i]);fib_heap_insert_key(hb, b[i]);}printf("\n");printf("== 斐波那契堆(hb)删除最小节点\n");fib_heap_extract_min(hb);fib_print(hb);fib_heap_destroy(hb);
}// 验证"插入操作"
void test_insert()
{int i;int alen=LENGTH(a);FibHeap *ha = fib_heap_make();// 斐波那契堆haprintf("== 斐波那契堆(ha)中依次添加: ");for(i=0; i<alen; i++){printf("%d ", a[i]);fib_heap_insert_key(ha, a[i]);}printf("\n");printf("== 斐波那契堆(ha)删除最小节点\n");fib_heap_extract_min(ha);fib_print(ha);// 插入50printf("== 插入50\n");fib_heap_insert_key(ha, 50);fib_print(ha);fib_heap_destroy(ha);
}// 验证"合并操作"
void test_union()
{int i;int alen=LENGTH(a);int blen=LENGTH(b);FibHeap *ha = fib_heap_make();FibHeap *hb = fib_heap_make();// 斐波那契堆haprintf("== 斐波那契堆(ha)中依次添加: ");for(i=0; i<alen; i++){printf("%d ", a[i]);fib_heap_insert_key(ha, a[i]);}printf("\n");printf("== 斐波那契堆(ha)删除最小节点\n");fib_heap_extract_min(ha);fib_print(ha);// 斐波那契堆hbprintf("== 斐波那契堆(hb)中依次添加: ");for(i=0; i<blen; i++){printf("%d ", b[i]);fib_heap_insert_key(hb, b[i]);}printf("\n");printf("== 斐波那契堆(hb)删除最小节点\n");fib_heap_extract_min(hb);fib_print(hb);// 将"斐波那契堆hb"合并到"斐波那契堆ha"中。printf("== 合并ha和hb\n");ha = fib_heap_union(ha, hb);fib_print(ha);// 销毁堆fib_heap_destroy(ha);
}// 验证"删除最小节点"
void test_remove_min()
{int i;int alen=LENGTH(a);int blen=LENGTH(b);FibHeap *ha = fib_heap_make();FibHeap *hb = fib_heap_make();// 斐波那契堆haprintf("== 斐波那契堆(ha)中依次添加: ");for(i=0; i<alen; i++){printf("%d ", a[i]);fib_heap_insert_key(ha, a[i]);}printf("\n");printf("== 斐波那契堆(ha)删除最小节点\n");fib_heap_extract_min(ha);//fib_print(ha);// 斐波那契堆hbprintf("== 斐波那契堆(hb)中依次添加: ");for(i=0; i<blen; i++){printf("%d ", b[i]);fib_heap_insert_key(hb, b[i]);}printf("\n");printf("== 斐波那契堆(hb)删除最小节点\n");fib_heap_extract_min(hb);//fib_print(hb);// 将"斐波那契堆hb"合并到"斐波那契堆ha"中。printf("== 合并ha和hb\n");ha = fib_heap_union(ha, hb);fib_print(ha);printf("== 删除最小节点\n");fib_heap_extract_min(ha);fib_print(ha);// 销毁堆fib_heap_destroy(ha);
}// 验证"减小节点"
void test_decrease()
{int i;int blen=LENGTH(b);FibHeap *hb = fib_heap_make();// 斐波那契堆hbprintf("== 斐波那契堆(hb)中依次添加: ");for(i=0; i<blen; i++){printf("%d ", b[i]);fib_heap_insert_key(hb, b[i]);}printf("\n");printf("== 斐波那契堆(hb)删除最小节点\n");fib_heap_extract_min(hb);fib_print(hb);printf("== 将20减小为2\n");fib_heap_update(hb, 20, 2);fib_print(hb);fib_heap_destroy(hb);
}// 验证"增大节点"
void test_increase()
{int i;int blen=LENGTH(b);FibHeap *hb = fib_heap_make();// 斐波那契堆hbprintf("== 斐波那契堆(hb)中依次添加: ");for(i=0; i<blen; i++){printf("%d ", b[i]);fib_heap_insert_key(hb, b[i]);}printf("\n");printf("== 斐波那契堆(hb)删除最小节点\n");fib_heap_extract_min(hb);fib_print(hb);fib_heap_update(hb, 20, 60);printf("== 将20增加为60\n");fib_print(hb);fib_heap_destroy(hb);
}// 验证"删除节点"
void test_delete()
{int i;int blen=LENGTH(b);FibHeap *hb = fib_heap_make();// 斐波那契堆hbprintf("== 斐波那契堆(hb)中依次添加: ");for(i=0; i<blen; i++){printf("%d ", b[i]);fib_heap_insert_key(hb, b[i]);}printf("\n");printf("== 斐波那契堆(hb)删除最小节点\n");fib_heap_extract_min(hb);fib_print(hb);fib_heap_delete(hb, 20);printf("== 删除节点20\n");fib_print(hb);fib_heap_destroy(hb);
}void main()
{// 验证"基本信息(斐波那契堆的结构)"test_basic();// 验证"插入操作"//test_insert();// 验证"合并操作"//test_union();// 验证"删除最小节点"//test_remove_min();// 验证"减小节点"//test_decrease();// 验证"增大节点"//test_increase();// 验证"删除节点"//test_delete();
}

斐波那契堆的C测试程序

斐波那契堆的测试程序包括了"插入"、"合并"、"增大"、"减小"、"删除"、"基本信息"等几种功能的测试代码。默认是运行的"基本信息(验证斐波那契堆的结构)"测试代码，你可以根据自己的需要来对相应的功能进行验证！

注意：C语言版的斐波那契堆的LOG2宏定义中使用了math.h，记得引入math库。例如，若你是在Linux下通过gcc编译，记得添加-lm参数(gcc *.c -lm)。

下面是基本信息测试代码的运行结果：

== 斐波那契堆(hb)中依次添加: 18 35 20 42 9 31 23 6 48 11 24 52 13 2 
== 斐波那契堆(hb)删除最小节点
== 斐波那契堆的详细信息: ==1.    6(3) is root9(0) is  6's child18(1) is  9's next35(0) is 18's child20(2) is 18's next42(0) is 20's child23(1) is 42's next31(0) is 23's child2.   11(2) is root48(0) is 11's child24(1) is 48's next52(0) is 24's child3.   13(0) is root

斐波那契堆的C++实现(完整源码)

斐波那契堆的实现文件(FibHeap.cpp)

/*** C++: 斐波那契堆** @author skywang* @date 2014/04/06*/#ifndef _FIBONACCI_TREE_HPP_
#define _FIBONACCI_TREE_HPP_#include <iomanip>
#include <iostream>
#include <cstdlib>
#include <cmath>
using namespace std;template <class T>
class FibNode {public:T key;                // 关键字(键值)int degree;            // 度数FibNode<T> *left;    // 左兄弟FibNode<T> *right;    // 右兄弟FibNode<T> *child;    // 第一个孩子节点FibNode<T> *parent;    // 父节点bool marked;        // 是否被删除第一个孩子FibNode(T value):key(value), degree(0), marked(false),left(NULL),right(NULL),child(NULL),parent(NULL) {key    = value;degree = 0;marked = false;left   = this;right  = this;parent = NULL;child  = NULL;}
};template <class T>
class FibHeap {private:int keyNum;         // 堆中节点的总数int maxDegree;      // 最大度FibNode<T> *min;    // 最小节点(某个最小堆的根节点)FibNode<T> **cons;    // 最大度的内存区域public:FibHeap();~FibHeap();// 新建key对应的节点，并将其插入到斐波那契堆中void insert(T key);// 移除斐波那契堆中的最小节点void removeMin();// 将other合并到当前堆中void combine(FibHeap<T> *other);// 获取斐波那契堆中最小键值，并保存到pkey中；成功返回true，否则返回false。bool minimum(T *pkey);// 将斐波那契堆中键值oldkey更新为newkeyvoid update(T oldkey, T newkey);// 删除键值为key的节点void remove(T key);// 斐波那契堆中是否包含键值keybool contains(T key);// 打印斐波那契堆void print();// 销毁void destroy();private:// 将node从双链表移除void removeNode(FibNode<T> *node);// 将node堆结点加入root结点之前(循环链表中)void addNode(FibNode<T> *node, FibNode<T> *root);// 将双向链表b链接到双向链表a的后面void catList(FibNode<T> *a, FibNode<T> *b);// 将节点node插入到斐波那契堆中void insert(FibNode<T> *node);// 将"堆的最小结点"从根链表中移除，FibNode<T>* extractMin();// 将node链接到root根结点void link(FibNode<T>* node, FibNode<T>* root);// 创建consolidate所需空间void makeCons();// 合并斐波那契堆的根链表中左右相同度数的树void consolidate();// 修改度数void renewDegree(FibNode<T> *parent, int degree);// 将node从父节点parent的子链接中剥离出来，并使node成为"堆的根链表"中的一员。void cut(FibNode<T> *node, FibNode<T> *parent);// 对节点node进行"级联剪切"void cascadingCut(FibNode<T> *node) ;// 将斐波那契堆中节点node的值减少为keyvoid decrease(FibNode<T> *node, T key);// 将斐波那契堆中节点node的值增加为keyvoid increase(FibNode<T> *node, T key);// 更新斐波那契堆的节点node的键值为keyvoid update(FibNode<T> *node, T key);// 在最小堆root中查找键值为key的节点FibNode<T>* search(FibNode<T> *root, T key);// 在斐波那契堆中查找键值为key的节点FibNode<T>* search(T key);// 删除结点nodevoid remove(FibNode<T> *node);// 销毁斐波那契堆void destroyNode(FibNode<T> *node);// 打印"斐波那契堆"void print(FibNode<T> *node, FibNode<T> *prev, int direction);
};/** 构造函数*/
template <class T>
FibHeap<T>::FibHeap()
{keyNum = 0;maxDegree = 0;min = NULL;cons = NULL;
}/** 析构函数*/
template <class T>
FibHeap<T>::~FibHeap()
{
}/** 将node从双链表移除*/
template <class T>
void FibHeap<T>::removeNode(FibNode<T> *node)
{node->left->right = node->right;node->right->left = node->left;
}/** 将node堆结点加入root结点之前(循环链表中)*   a …… root*   a …… node …… root
*/
template <class T>
void FibHeap<T>::addNode(FibNode<T> *node, FibNode<T> *root)
{node->left        = root->left;root->left->right = node;node->right       = root;root->left        = node;
}/** 将节点node插入到斐波那契堆中*/
template <class T>
void FibHeap<T>::insert(FibNode<T> *node)
{if (keyNum == 0)min = node;else{addNode(node, min);if (node->key < min->key)min = node;}keyNum++;
}/** 新建键值为key的节点，并将其插入到斐波那契堆中*/
template <class T>
void FibHeap<T>::insert(T key)
{FibNode<T> *node;node = new FibNode<T>(key);if (node == NULL)return ;insert(node);
}/** 将双向链表b链接到双向链表a的后面** 注意： 此处a和b都是双向链表*/
template <class T>
void FibHeap<T>::catList(FibNode<T> *a, FibNode<T> *b)
{FibNode<T> *tmp;tmp            = a->right;a->right       = b->right;b->right->left = a;b->right       = tmp;tmp->left      = b;
}/** 将other合并到当前堆中*/
template <class T>
void FibHeap<T>::combine(FibHeap<T> *other)
{if (other==NULL)return ;if(other->maxDegree > this->maxDegree)swap(*this, *other);if((this->min) == NULL)                // this无"最小节点"{this->min = other->min;this->keyNum = other->keyNum;free(other->cons);delete other;}else if((other->min) == NULL)           // this有"最小节点" && other无"最小节点"{free(other->cons);delete other;}                                       // this有"最小节点" && other有"最小节点"else{// 将"other中根链表"添加到"this"中catList(this->min, other->min);if (this->min->key > other->min->key)this->min = other->min;this->keyNum += other->keyNum;free(other->cons);delete other;}
}/** 将"堆的最小结点"从根链表中移除，* 这意味着"将最小节点所属的树"从堆中移除!*/
template <class T>
FibNode<T>* FibHeap<T>::extractMin()
{FibNode<T> *p = min;if (p == p->right)min = NULL;else{removeNode(p);min = p->right;}p->left = p->right = p;return p;
}/** 将node链接到root根结点*/
template <class T>
void FibHeap<T>::link(FibNode<T>* node, FibNode<T>* root)
{// 将node从双链表中移除removeNode(node);// 将node设为root的孩子if (root->child == NULL)root->child = node;elseaddNode(node, root->child);node->parent = root;root->degree++;node->marked = false;
}/** 创建consolidate所需空间*/
template <class T>
void FibHeap<T>::makeCons()
{int old = maxDegree;// 计算log2(keyNum)，"+1"意味着向上取整！// ex. log2(13) = 3，向上取整为3+1=4。maxDegree = (log(keyNum)/log(2.0)) + 1;if (old >= maxDegree)return ;// 因为度为maxDegree可能被合并，所以要maxDegree+1cons = (FibNode<T> **)realloc(cons,sizeof(FibHeap<T> *) * (maxDegree + 1));
}/** 合并斐波那契堆的根链表中左右相同度数的树*/
template <class T>
void FibHeap<T>::consolidate()
{int i, d, D;FibNode<T> *x, *y, *tmp;makeCons();//开辟哈希所用空间D = maxDegree + 1;for (i = 0; i < D; i++)cons[i] = NULL;// 合并相同度的根节点，使每个度数的树唯一while (min != NULL){x = extractMin();                // 取出堆中的最小树(最小节点所在的树)d = x->degree;                    // 获取最小树的度数// cons[d] != NULL，意味着有两棵树(x和y)的"度数"相同。while (cons[d] != NULL){y = cons[d];                // y是"与x的度数相同的树"if (x->key > y->key)        // 保证x的键值比y小swap(x, y);link(y, x);    // 将y链接到x中cons[d] = NULL;d++;}cons[d] = x;}min = NULL;// 将cons中的结点重新加到根表中for (i=0; i<D; i++){if (cons[i] != NULL){if (min == NULL)min = cons[i];else{addNode(cons[i], min);if ((cons[i])->key < min->key)min = cons[i];}}}
}/** 移除最小节点*/
template <class T>
void FibHeap<T>::removeMin()
{if (min==NULL)return ;FibNode<T> *child = NULL;FibNode<T> *m = min;// 将min每一个儿子(儿子和儿子的兄弟)都添加到"斐波那契堆的根链表"中while (m->child != NULL){child = m->child;removeNode(child);if (child->right == child)m->child = NULL;elsem->child = child->right;addNode(child, min);child->parent = NULL;}// 将m从根链表中移除removeNode(m);// 若m是堆中唯一节点，则设置堆的最小节点为NULL；// 否则，设置堆的最小节点为一个非空节点(m->right)，然后再进行调节。if (m->right == m)min = NULL;else{min = m->right;consolidate();}keyNum--;delete m;
}/** 获取斐波那契堆中最小键值，并保存到pkey中；成功返回true，否则返回false。*/
template <class T>
bool FibHeap<T>::minimum(T *pkey)
{if (min==NULL || pkey==NULL)return false;*pkey = min->key;return true;
}/** 修改度数*/
template <class T>
void FibHeap<T>::renewDegree(FibNode<T> *parent, int degree)
{parent->degree -= degree;if (parent-> parent != NULL)renewDegree(parent->parent, degree);
}/** 将node从父节点parent的子链接中剥离出来，* 并使node成为"堆的根链表"中的一员。*/
template <class T>
void FibHeap<T>::cut(FibNode<T> *node, FibNode<T> *parent)
{removeNode(node);renewDegree(parent, node->degree);// node没有兄弟if (node == node->right)parent->child = NULL;elseparent->child = node->right;node->parent = NULL;node->left = node->right = node;node->marked = false;// 将"node所在树"添加到"根链表"中addNode(node, min);
}/** 对节点node进行"级联剪切"** 级联剪切：如果减小后的结点破坏了最小堆性质，*     则把它切下来(即从所在双向链表中删除，并将*     其插入到由最小树根节点形成的双向链表中)，*     然后再从"被切节点的父节点"到所在树根节点递归执行级联剪枝*/
template <class T>
void FibHeap<T>::cascadingCut(FibNode<T> *node)
{FibNode<T> *parent = node->parent;if (parent != NULL){if (node->marked == false)node->marked = true;else{cut(node, parent);cascadingCut(parent);}}
}/** 将斐波那契堆中节点node的值减少为key*/
template <class T>
void FibHeap<T>::decrease(FibNode<T> *node, T key)
{FibNode<T> *parent;if (min==NULL ||node==NULL)return ;if ( key>=node->key){cout << "decrease failed: the new key(" << key <<") "<< "is no smaller than current key(" << node->key <<")" << endl;return ;}node->key = key;parent = node->parent;if (parent!=NULL && node->key < parent->key){// 将node从父节点parent中剥离出来，并将node添加到根链表中cut(node, parent);cascadingCut(parent);}// 更新最小节点if (node->key < min->key)min = node;
}/** 将斐波那契堆中节点node的值增加为key*/
template <class T>
void FibHeap<T>::increase(FibNode<T> *node, T key)
{FibNode<T> *child, *parent, *right;if (min==NULL ||node==NULL)return ;if (key <= node->key){cout << "increase failed: the new key(" << key <<") "<< "is no greater than current key(" << node->key <<")" << endl;return ;}// 将node每一个儿子(不包括孙子,重孙,...)都添加到"斐波那契堆的根链表"中while (node->child != NULL){child = node->child;removeNode(child);               // 将child从node的子链表中删除if (child->right == child)node->child = NULL;elsenode->child = child->right;addNode(child, min);       // 将child添加到根链表中child->parent = NULL;}node->degree = 0;node->key = key;// 如果node不在根链表中，//     则将node从父节点parent的子链接中剥离出来，//     并使node成为"堆的根链表"中的一员，//     然后进行"级联剪切"// 否则，则判断是否需要更新堆的最小节点parent = node->parent;if(parent != NULL){cut(node, parent);cascadingCut(parent);}else if(min == node){right = node->right;while(right != node){if(node->key > right->key)min = right;right = right->right;}}
}/** 更新斐波那契堆的节点node的键值为key*/
template <class T>
void FibHeap<T>::update(FibNode<T> *node, T key)
{if(key < node->key)decrease(node, key);else if(key > node->key)increase(node, key);elsecout << "No need to update!!!" << endl;
}template <class T>
void FibHeap<T>::update(T oldkey, T newkey)
{FibNode<T> *node;node = search(oldkey);if (node!=NULL)update(node, newkey);
}/** 在最小堆root中查找键值为key的节点*/
template <class T>
FibNode<T>* FibHeap<T>::search(FibNode<T> *root, T key)
{FibNode<T> *t = root;    // 临时节点FibNode<T> *p = NULL;    // 要查找的节点if (root==NULL)return root;do{if (t->key == key){p = t;break;}else{if ((p = search(t->child, key)) != NULL)break;}t = t->right;} while (t != root);return p;
}/** 在斐波那契堆中查找键值为key的节点*/
template <class T>
FibNode<T>* FibHeap<T>::search(T key)
{if (min==NULL)return NULL;return search(min, key);
}/** 在斐波那契堆中是否存在键值为key的节点。* 存在返回true，否则返回false。*/
template <class T>
bool FibHeap<T>::contains(T key)
{return search(key)!=NULL ? true: false;
}/** 删除结点node*/
template <class T>
void FibHeap<T>::remove(FibNode<T> *node)
{T m = min->key-1;decrease(node, m-1);removeMin();
}template <class T>
void FibHeap<T>::remove(T key)
{FibNode<T> *node;if (min==NULL)return ;node = search(key);if (node==NULL)return ;remove(node);
}/** 销毁斐波那契堆*/
template <class T>
void FibHeap<T>::destroyNode(FibNode<T> *node)
{FibNode<T> *start = node;if(node == NULL)return;do {destroyNode(node->child);// 销毁node，并将node指向下一个node = node->right;delete node->left;} while(node != start);
}template <class T>
void FibHeap<T>::destroy()
{destroyNode(min);free(cons);
}/** 打印"斐波那契堆"** 参数说明：*     node       -- 当前节点*     prev       -- 当前节点的前一个节点(父节点or兄弟节点)*     direction  --  1，表示当前节点是一个左孩子;*                    2，表示当前节点是一个兄弟节点。*/
template <class T>
void FibHeap<T>::print(FibNode<T> *node, FibNode<T> *prev, int direction)
{FibNode<T> *start=node;if (node==NULL)return ;do{if (direction == 1)cout << setw(8) << node->key << "(" << node->degree << ") is "<< setw(2) << prev->key << "'s child" << endl;elsecout << setw(8) << node->key << "(" << node->degree << ") is "<< setw(2) << prev->key << "'s next" << endl;if (node->child != NULL)print(node->child, node, 1);// 兄弟节点prev = node;node = node->right;direction = 2;} while(node != start);
}template <class T>
void FibHeap<T>::print()
{int i=0;FibNode<T> *p;if (min==NULL)return ;cout << "== 斐波那契堆的详细信息: ==" << endl;p = min;do {i++;cout << setw(2) << i << ". " << setw(4) << p->key << "(" << p->degree << ") is root" << endl;print(p->child, p, 1);p = p->right;} while (p != min);cout << endl;
}#endif

斐波那契堆的测试程序(Main.cpp)

/*** C 语言: 斐波那契堆** @author skywang* @date 2014/04/06*/#include <iostream>
#include "FibHeap.h"
using namespace std;#define DEBUG 0// 共8个
int a[] = {12,  7, 25, 15, 28,33, 41,  1};
// 共14个
int b[] = {18, 35, 20, 42,  9,31, 23,  6, 48, 11,24, 52, 13,  2};// 验证"基本信息(斐波那契堆的结构)"
void testBasic()
{int i;int blen=sizeof(b)/sizeof(b[0]);FibHeap<int>* hb=new FibHeap<int>();// 斐波那契堆hbcout << "== 斐波那契堆(hb)中依次添加: ";for(i=0; i<blen; i++){cout << b[i] <<" ";hb->insert(b[i]);}cout << endl;cout << "== 斐波那契堆(hb)删除最小节点" << endl;hb->removeMin();hb->print();
}// 验证"插入操作"
void testInsert()
{int i;int alen=sizeof(a)/sizeof(a[0]);FibHeap<int>* ha=new FibHeap<int>();cout << "== 斐波那契堆(ha)中依次添加: ";for(i=0; i<alen; i++){cout << a[i] <<" ";ha->insert(a[i]);}cout << endl;cout << "== 斐波那契堆(ha)删除最小节点" << endl;ha->removeMin();ha->print();// 斐波那契堆hbcout << "== 插入50" << endl;ha->insert(50);ha->print();
}// 验证"合并操作"
void testUnion()
{int i;int alen=sizeof(a)/sizeof(a[0]);int blen=sizeof(b)/sizeof(b[0]);FibHeap<int>* ha=new FibHeap<int>();FibHeap<int>* hb=new FibHeap<int>();cout << "== 斐波那契堆(ha)中依次添加: ";for(i=0; i<alen; i++){cout << a[i] <<" ";ha->insert(a[i]);}cout << endl;cout << "== 斐波那契堆(ha)删除最小节点" << endl;ha->removeMin();ha->print();// 斐波那契堆hbcout << "== 斐波那契堆(hb)中依次添加: ";for(i=0; i<blen; i++){cout << b[i] <<" ";hb->insert(b[i]);}cout << endl;cout << "== 斐波那契堆(hb)删除最小节点" << endl;hb->removeMin();hb->print();// 将"斐波那契堆hb"合并到"斐波那契堆ha"中。cout << "== 合并ha和hb" << endl;ha->combine(hb);ha->print();
}// 验证"删除最小节点"
void testRemoveMin()
{int i;int alen=sizeof(a)/sizeof(a[0]);int blen=sizeof(b)/sizeof(b[0]);FibHeap<int>* ha=new FibHeap<int>();FibHeap<int>* hb=new FibHeap<int>();cout << "== 斐波那契堆(ha)中依次添加: ";for(i=0; i<alen; i++){cout << a[i] <<" ";ha->insert(a[i]);}cout << endl;cout << "== 斐波那契堆(ha)删除最小节点" << endl;ha->removeMin();//ha->print();// 斐波那契堆hbcout << "== 斐波那契堆(hb)中依次添加: ";for(i=0; i<blen; i++){cout << b[i] <<" ";hb->insert(b[i]);}cout << endl;cout << "== 斐波那契堆(hb)删除最小节点" << endl;hb->removeMin();//hb->print();// 将"斐波那契堆hb"合并到"斐波那契堆ha"中。cout << "== 合并ha和hb" << endl;ha->combine(hb);ha->print();cout << "== 删除最小节点" << endl;ha->removeMin();ha->print();
}// 验证"减小节点"
void testDecrease()
{int i;int blen=sizeof(b)/sizeof(b[0]);FibHeap<int>* hb=new FibHeap<int>();// 斐波那契堆hbcout << "== 斐波那契堆(hb)中依次添加: ";for(i=0; i<blen; i++){cout << b[i] <<" ";hb->insert(b[i]);}cout << endl;cout << "== 斐波那契堆(hb)删除最小节点" << endl;hb->removeMin();hb->print();cout << "== 将20减小为2" << endl;hb->update(20, 2);hb->print();
}// 验证"增大节点"
void testIncrease()
{int i;int blen=sizeof(b)/sizeof(b[0]);FibHeap<int>* hb=new FibHeap<int>();// 斐波那契堆hbcout << "== 斐波那契堆(hb)中依次添加: ";for(i=0; i<blen; i++){cout << b[i] <<" ";hb->insert(b[i]);}cout << endl;cout << "== 斐波那契堆(hb)删除最小节点" << endl;hb->removeMin();hb->print();cout << "== 将20增加为60" << endl;hb->update(20, 60);hb->print();
}// 验证"删除节点"
void testDelete()
{int i;int blen=sizeof(b)/sizeof(b[0]);FibHeap<int>* hb=new FibHeap<int>();// 斐波那契堆hbcout << "== 斐波那契堆(hb)中依次添加: ";for(i=0; i<blen; i++){cout << b[i] <<" ";hb->insert(b[i]);}cout << endl;cout << "== 斐波那契堆(hb)删除最小节点" << endl;hb->removeMin();hb->print();cout << "== 删除节点20" << endl;hb->remove(20);hb->print();
}int main()
{// 验证"基本信息(斐波那契堆的结构)"testBasic();// 验证"插入操作"//testInsert();// 验证"合并操作"//testUnion();// 验证"删除最小节点"//testRemoveMin();// 验证"减小节点"//testDecrease();// 验证"增大节点"//testIncrease();// 验证"删除节点"//testDelete();return 0;
}

斐波那契堆的C++测试程序

下面是基本信息测试代码的运行结果：

== 斐波那契堆(hb)中依次添加: 18 35 20 42 9 31 23 6 48 11 24 52 13 2 
== 斐波那契堆(hb)删除最小节点
== 斐波那契堆的详细信息: ==1.    6(3) is root9(0) is  6's child18(1) is  9's next35(0) is 18's child20(2) is 18's next42(0) is 20's child23(1) is 42's next31(0) is 23's child2.   11(2) is root48(0) is 11's child24(1) is 48's next52(0) is 24's child3.   13(0) is root

斐波那契堆的Java实现(完整源码)

斐波那契堆的实现文件(FibHeap.java)

/*** Java 语言: 斐波那契堆** @author skywang* @date 2014/04/07*/public class FibHeap {private int keyNum;         // 堆中节点的总数private FibNode min;        // 最小节点(某个最小堆的根节点)private class FibNode {int key;            // 关键字(键值)int degree;            // 度数FibNode left;        // 左兄弟FibNode right;        // 右兄弟FibNode child;        // 第一个孩子节点FibNode parent;        // 父节点boolean marked;     // 是否被删除第一个孩子public FibNode(int key) {this.key    = key;this.degree = 0;this.marked = false;this.left   = this;this.right  = this;this.parent = null;this.child  = null;}}public FibHeap() {this.keyNum = 0;this.min = null;}/** 将node从双链表移除*/private void removeNode(FibNode node) {node.left.right = node.right;node.right.left = node.left;}/** 将node堆结点加入root结点之前(循环链表中)*   a …… root*   a …… node …… root*/private void addNode(FibNode node, FibNode root) {node.left        = root.left;root.left.right  = node;node.right       = root;root.left        = node;}/** 将节点node插入到斐波那契堆中*/private void insert(FibNode node) {if (keyNum == 0)min = node;else {addNode(node, min);if (node.key < min.key)min = node;}keyNum++;}/** 新建键值为key的节点，并将其插入到斐波那契堆中*/public void insert(int key) {FibNode node;node = new FibNode(key);if (node == null)return ;insert(node);}/** 将双向链表b链接到双向链表a的后面*/private void catList(FibNode a, FibNode b) {FibNode tmp;tmp           = a.right;a.right       = b.right;b.right.left  = a;b.right       = tmp;tmp.left      = b;}/** 将other合并到当前堆中*/public void union(FibHeap other) {if (other==null)return ;if((this.min) == null) {                // this无"最小节点"this.min = other.min;this.keyNum = other.keyNum;other = null;} else if((other.min) == null) {        // this有"最小节点" && other无"最小节点"other = null;} else {                                // this有"最小节点" && other有"最小节点"// 将"other中根链表"添加到"this"中catList(this.min, other.min) ;if (this.min.key > other.min.key)this.min = other.min;this.keyNum += other.keyNum;other = null;;}}/** 将"堆的最小结点"从根链表中移除，* 这意味着"将最小节点所属的树"从堆中移除!*/private FibNode extractMin() {FibNode p = min;if (p == p.right)min = null;else {removeNode(p);min = p.right;}p.left = p.right = p;return p;}/** 将node链接到root根结点*/private void link(FibNode node, FibNode root) {// 将node从双链表中移除removeNode(node);// 将node设为root的孩子if (root.child == null)root.child = node;elseaddNode(node, root.child);node.parent = root;root.degree++;node.marked = false;}/** 合并斐波那契堆的根链表中左右相同度数的树*/private void consolidate() {// 计算log2(keyNum)，floor意味着向上取整！// ex. log2(13) = 3，向上取整为4。int maxDegree = (int) Math.floor(Math.log(keyNum) / Math.log(2.0));int D = maxDegree + 1;FibNode[] cons = new FibNode[D+1];for (int i = 0; i < D; i++)cons[i] = null;// 合并相同度的根节点，使每个度数的树唯一while (min != null) {FibNode x = extractMin();            // 取出堆中的最小树(最小节点所在的树)int d = x.degree;                        // 获取最小树的度数// cons[d] != null，意味着有两棵树(x和y)的"度数"相同。while (cons[d] != null) {FibNode y = cons[d];                // y是"与x的度数相同的树"if (x.key > y.key) {    // 保证x的键值比y小FibNode tmp = x;x = y;y = tmp;}link(y, x);    // 将y链接到x中cons[d] = null;d++;}cons[d] = x;}min = null;// 将cons中的结点重新加到根表中for (int i=0; i<D; i++) {if (cons[i] != null) {if (min == null)min = cons[i];else {addNode(cons[i], min);if ((cons[i]).key < min.key)min = cons[i];}}}}/** 移除最小节点*/public void removeMin() {if (min==null)return ;FibNode m = min;// 将min每一个儿子(儿子和儿子的兄弟)都添加到"斐波那契堆的根链表"中while (m.child != null) {FibNode child = m.child;removeNode(child);if (child.right == child)m.child = null;elsem.child = child.right;addNode(child, min);child.parent = null;}// 将m从根链表中移除removeNode(m);// 若m是堆中唯一节点，则设置堆的最小节点为null；// 否则，设置堆的最小节点为一个非空节点(m.right)，然后再进行调节。if (m.right == m)min = null;else {min = m.right;consolidate();}keyNum--;m = null;}/** 获取斐波那契堆中最小键值；失败返回-1*/public int minimum() {if (min==null)return -1;return min.key;}/** 修改度数*/private void renewDegree(FibNode parent, int degree) {parent.degree -= degree;if (parent. parent != null)renewDegree(parent.parent, degree);}/** 将node从父节点parent的子链接中剥离出来，* 并使node成为"堆的根链表"中的一员。*/private void cut(FibNode node, FibNode parent) {removeNode(node);renewDegree(parent, node.degree);// node没有兄弟if (node == node.right)parent.child = null;elseparent.child = node.right;node.parent = null;node.left = node.right = node;node.marked = false;// 将"node所在树"添加到"根链表"中addNode(node, min);}/** 对节点node进行"级联剪切"** 级联剪切：如果减小后的结点破坏了最小堆性质，*     则把它切下来(即从所在双向链表中删除，并将*     其插入到由最小树根节点形成的双向链表中)，*     然后再从"被切节点的父节点"到所在树根节点递归执行级联剪枝*/private void cascadingCut(FibNode node) {FibNode parent = node.parent;if (parent != null) {if (node.marked == false)node.marked = true;else {cut(node, parent);cascadingCut(parent);}}}/** 将斐波那契堆中节点node的值减少为key*/private void decrease(FibNode node, int key) {if (min==null ||node==null)return ;if (key > node.key) {System.out.printf("decrease failed: the new key(%d) is no smaller than current key(%d)\n", key, node.key);return ;}FibNode parent = node.parent;node.key = key;if (parent!=null && (node.key < parent.key)) {// 将node从父节点parent中剥离出来，并将node添加到根链表中cut(node, parent);cascadingCut(parent);}// 更新最小节点if (node.key < min.key)min = node;}/** 将斐波那契堆中节点node的值增加为key*/private void increase(FibNode node, int key) {if (min==null ||node==null)return ;if ( key <= node.key) {System.out.printf("increase failed: the new key(%d) is no greater than current key(%d)\n", key, node.key);return ;}// 将node每一个儿子(不包括孙子,重孙,...)都添加到"斐波那契堆的根链表"中while (node.child != null) {FibNode child = node.child;removeNode(child);               // 将child从node的子链表中删除if (child.right == child)node.child = null;elsenode.child = child.right;addNode(child, min);       // 将child添加到根链表中child.parent = null;}node.degree = 0;node.key = key;// 如果node不在根链表中，//     则将node从父节点parent的子链接中剥离出来，//     并使node成为"堆的根链表"中的一员，//     然后进行"级联剪切"// 否则，则判断是否需要更新堆的最小节点FibNode parent = node.parent;if(parent != null) {cut(node, parent);cascadingCut(parent);} else if(min == node) {FibNode right = node.right;while(right != node) {if(node.key > right.key)min = right;right = right.right;}}}/** 更新斐波那契堆的节点node的键值为key*/private void update(FibNode node, int key) {if(key < node.key)decrease(node, key);else if(key > node.key)increase(node, key);elseSystem.out.printf("No need to update!!!\n");}public void update(int oldkey, int newkey) {FibNode node;node = search(oldkey);if (node!=null)update(node, newkey);}/** 在最小堆root中查找键值为key的节点*/private FibNode search(FibNode root, int key) {FibNode t = root;    // 临时节点FibNode p = null;    // 要查找的节点if (root==null)return root;do {if (t.key == key) {p = t;break;} else {if ((p = search(t.child, key)) != null)break;}t = t.right;} while (t != root);return p;}/** 在斐波那契堆中查找键值为key的节点*/private FibNode search(int key) {if (min==null)return null;return search(min, key);}/** 在斐波那契堆中是否存在键值为key的节点。* 存在返回true，否则返回false。*/public boolean contains(int key) {return search(key)!=null ? true: false;}/** 删除结点node*/private void remove(FibNode node) {int m = min.key;decrease(node, m-1);removeMin();}public void remove(int key) {if (min==null)return ;FibNode node = search(key);if (node==null)return ;remove(node);}/** 销毁斐波那契堆*/private void destroyNode(FibNode node) {if(node == null)return;FibNode start = node;do {destroyNode(node.child);// 销毁node，并将node指向下一个node = node.right;node.left = null;} while(node != start);}public void destroy() {destroyNode(min);}/** 打印"斐波那契堆"** 参数说明：*     node       -- 当前节点*     prev       -- 当前节点的前一个节点(父节点or兄弟节点)*     direction  --  1，表示当前节点是一个左孩子;*                    2，表示当前节点是一个兄弟节点。*/private void print(FibNode node, FibNode prev, int direction) {FibNode start=node;if (node==null)return ;do {if (direction == 1)System.out.printf("%8d(%d) is %2d's child\n", node.key, node.degree, prev.key);elseSystem.out.printf("%8d(%d) is %2d's next\n", node.key, node.degree, prev.key);if (node.child != null)print(node.child, node, 1);// 兄弟节点prev = node;node = node.right;direction = 2;} while(node != start);}public void print() {if (min==null)return ;int i=0;FibNode p = min;System.out.printf("== 斐波那契堆的详细信息: ==\n");do {i++;System.out.printf("%2d. %4d(%d) is root\n", i, p.key, p.degree);print(p.child, p, 1);p = p.right;} while (p != min);System.out.printf("\n");}
}

斐波那契堆的测试程序(Main.java)

/*** Java 语言: 斐波那契堆** @author skywang* @date 2014/04/07*/public class Main {private static final boolean DEBUG = false;// 共8个private static int a[] = {12,  7, 25, 15, 28, 33, 41, 1};// 共14个private static int b[] = {18, 35, 20, 42,  9,31, 23,  6, 48, 11,24, 52, 13,  2 };// 验证"基本信息(斐波那契堆的结构)"public static void testBasic() {FibHeap hb=new FibHeap();// 斐波那契堆hbSystem.out.printf("== 斐波那契堆(hb)中依次添加: ");for(int i=0; i<b.length; i++) {System.out.printf("%d ", b[i]);hb.insert(b[i]);}System.out.printf("\n");System.out.printf("== 斐波那契堆(hb)删除最小节点\n");hb.removeMin();hb.print(); // 打印斐波那契堆hb}// 验证"插入操作"public static void testInsert() {FibHeap ha=new FibHeap();// 斐波那契堆haSystem.out.printf("== 斐波那契堆(ha)中依次添加: ");for(int i=0; i<a.length; i++) {System.out.printf("%d ", a[i]);ha.insert(a[i]);}System.out.printf("\n");System.out.printf("== 斐波那契堆(ha)删除最小节点\n");ha.removeMin();ha.print(); // 打印斐波那契堆haSystem.out.printf("== 插入50\n");ha.insert(50);ha.print();}// 验证"合并操作"public static void testUnion() {FibHeap ha=new FibHeap();FibHeap hb=new FibHeap();// 斐波那契堆haSystem.out.printf("== 斐波那契堆(ha)中依次添加: ");for(int i=0; i<a.length; i++) {System.out.printf("%d ", a[i]);ha.insert(a[i]);}System.out.printf("\n");System.out.printf("== 斐波那契堆(ha)删除最小节点\n");ha.removeMin();ha.print(); // 打印斐波那契堆ha// 斐波那契堆hbSystem.out.printf("== 斐波那契堆(hb)中依次添加: ");for(int i=0; i<b.length; i++) {System.out.printf("%d ", b[i]);hb.insert(b[i]);}System.out.printf("\n");System.out.printf("== 斐波那契堆(hb)删除最小节点\n");hb.removeMin();hb.print(); // 打印斐波那契堆hb// 将"斐波那契堆hb"合并到"斐波那契堆ha"中。System.out.printf("== 合并ha和hb\n");ha.union(hb);ha.print();}// 验证"删除最小节点"public static void testRemoveMin() {FibHeap ha=new FibHeap();FibHeap hb=new FibHeap();// 斐波那契堆haSystem.out.printf("== 斐波那契堆(ha)中依次添加: ");for(int i=0; i<a.length; i++) {System.out.printf("%d ", a[i]);ha.insert(a[i]);}System.out.printf("\n");System.out.printf("== 斐波那契堆(ha)删除最小节点\n");ha.removeMin();//ha.print(); // 打印斐波那契堆ha// 斐波那契堆hbSystem.out.printf("== 斐波那契堆(hb)中依次添加: ");for(int i=0; i<b.length; i++) {System.out.printf("%d ", b[i]);hb.insert(b[i]);}System.out.printf("\n");System.out.printf("== 斐波那契堆(hb)删除最小节点\n");hb.removeMin();//hb.print(); // 打印斐波那契堆hb// 将"斐波那契堆hb"合并到"斐波那契堆ha"中。System.out.printf("== 合并ha和hb\n");ha.union(hb);ha.print();System.out.printf("== 删除最小节点\n");ha.removeMin();ha.print();}// 验证"减小节点"public static void testDecrease() {FibHeap hb=new FibHeap();// 斐波那契堆hbSystem.out.printf("== 斐波那契堆(hb)中依次添加: ");for(int i=0; i<b.length; i++) {System.out.printf("%d ", b[i]);hb.insert(b[i]);}System.out.printf("\n");System.out.printf("== 斐波那契堆(hb)删除最小节点\n");hb.removeMin();hb.print(); // 打印斐波那契堆hbSystem.out.printf("== 将20减小为2\n");hb.update(20, 2);hb.print();}// 验证"增大节点"public static void testIncrease() {FibHeap hb=new FibHeap();// 斐波那契堆hbSystem.out.printf("== 斐波那契堆(hb)中依次添加: ");for(int i=0; i<b.length; i++) {System.out.printf("%d ", b[i]);hb.insert(b[i]);}System.out.printf("\n");System.out.printf("== 斐波那契堆(hb)删除最小节点\n");hb.removeMin();hb.print(); // 打印斐波那契堆hbSystem.out.printf("== 将20增加为60\n");hb.update(20, 60);hb.print();}// 验证"删除节点"public static void testDelete() {FibHeap hb=new FibHeap();// 斐波那契堆hbSystem.out.printf("== 斐波那契堆(hb)中依次添加: ");for(int i=0; i<b.length; i++) {System.out.printf("%d ", b[i]);hb.insert(b[i]);}System.out.printf("\n");System.out.printf("== 斐波那契堆(hb)删除最小节点\n");hb.removeMin();hb.print(); // 打印斐波那契堆hbSystem.out.printf("== 删除节点20\n");hb.remove(20);hb.print();}public static void main(String[] args) {// 验证"基本信息(斐波那契堆的结构)"testBasic();// 验证"插入操作"//testInsert();// 验证"合并操作"//testUnion();// 验证"删除最小节点"//testRemoveMin();// 验证"减小节点"//testDecrease();// 验证"增大节点"//testIncrease();// 验证"删除节点"//testDelete();}
}

斐波那契堆的Java测试程序

下面是基本信息测试代码的运行结果：

== 斐波那契堆(hb)中依次添加: 18 35 20 42 9 31 23 6 48 11 24 52 13 2 
== 斐波那契堆(hb)删除最小节点
== 斐波那契堆的详细信息: ==1.    6(3) is root9(0) is  6's child18(1) is  9's next35(0) is 18's child20(2) is 18's next42(0) is 20's child23(1) is 42's next31(0) is 23's child2.   11(2) is root48(0) is 11's child24(1) is 48's next52(0) is 24's child3.   13(0) is root