一步一步写算法（之哈夫曼树 下）
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前面说到了哈夫曼树的创建，那下面一个重要的环节就是哈夫曼树的排序问题。但是由于排序的内容是数据结构，因此形式上说，我们需要采用通用数据排序算法，这在我之前的博客里面已经涉及到了（通用算法设计）。所以，我们所要做的就是编写compare和swap两个函数。通用冒泡代码如下所示，
void bubble_sort(void* array[], int length, int (*compare)(void*, void*), void(*swap)(void**, void**))
{
int outer;
int inner;
for(outer = length -1; outer >0; outer --){
for(inner = 0; inner < outer; inner ++){
if(compare(array[inner], array[inner + 1]))
swap(&array[inner], &array[inner + 1]);
}
}
return;
}
void bubble_sort(void* array[], int length, int (*compare)(void*, void*), void(*swap)(void**, void**))
{
int outer;
int inner;
for(outer = length -1; outer >0; outer --){
for(inner = 0; inner < outer; inner ++){
if(compare(array[inner], array[inner + 1]))
swap(&array[inner], &array[inner + 1]);
}
}
return;
}
compare和swap代码如下所示，
int compare (void* a, void* b)
{
HUFFMAN_NODE* node1 = (HUFFMAN_NODE*)a;
HUFFMAN_NODE* node2 = (HUFFMAN_NODE*)b;
return node1->frequence > node2->frequence ? 1 : 0;
}
void swap(void** a, void** b)
{
HUFFMAN_NODE* median;
HUFFMAN_NODE** node1 = (HUFFMAN_NODE**)a;
HUFFMAN_NODE** node2 = (HUFFMAN_NODE**)b;
median = *node1;
*node1 = *node2;
*node2 = median;
}
int compare (void* a, void* b)
{
HUFFMAN_NODE* node1 = (HUFFMAN_NODE*)a;
HUFFMAN_NODE* node2 = (HUFFMAN_NODE*)b;
return node1->frequence > node2->frequence ? 1 : 0;
}
void swap(void** a, void** b)
{
HUFFMAN_NODE* median;
HUFFMAN_NODE** node1 = (HUFFMAN_NODE**)a;
HUFFMAN_NODE** node2 = (HUFFMAN_NODE**)b;
median = *node1;
*node1 = *node2;
*node2 = median;
}
有了创建函数和排序函数，那么哈夫曼树就可以创建了，
HUFFMAN_NODE* create_huffman_tree(HUFFMAN_NODE* huffmanNode[], int length)
{
HUFFMAN_NODE* head = NULL;
if(NULL == huffmanNode || length <= 1)
return NULL;
while(length > 1){
bubble_sort((void**)huffmanNode, length, compare, swap);
head = create_new_node('/0', huffmanNode[0]->frequence + huffmanNode[1]->frequence);
assert(NULL != head);
head->left = huffmanNode[0];
head->right = huffmanNode[1];
huffmanNode[0]->parent = head;
huffmanNode[0]->symbol = 1;
huffmanNode[1]->parent = head;
huffmanNode[1]->symbol = 0;
memmove(&huffmanNode[0], &huffmanNode[2], sizeof(HUFFMAN_NODE*) * (length -2));
huffmanNode[length -2] = head;
length --;
}
return head;
}
HUFFMAN_NODE* create_huffman_tree(HUFFMAN_NODE* huffmanNode[], int length)
{
HUFFMAN_NODE* head = NULL;
if(NULL == huffmanNode || length <= 1)
return NULL;
while(length > 1){
bubble_sort((void**)huffmanNode, length, compare, swap);
head = create_new_node('/0', huffmanNode[0]->frequence + huffmanNode[1]->frequence);
assert(NULL != head);
head->left = huffmanNode[0];
head->right = huffmanNode[1];
huffmanNode[0]->parent = head;
huffmanNode[0]->symbol = 1;
huffmanNode[1]->parent = head;
huffmanNode[1]->symbol = 0;
memmove(&huffmanNode[0], &huffmanNode[2], sizeof(HUFFMAN_NODE*) * (length -2));
huffmanNode[length -2] = head;
length --;
}
return head;
} 上面的代码完整了写出了huffman树的创建过程，那么我们怎么知道符号的编码是多少呢？这其实不难，因为根节点都知道了，我们只要按照自下而上的顺序遍历节点就可以打印出编码，只不过编码是逆序的而已，
void print_code_for_str(HUFFMAN_NODE* pNode, HUFFMAN_NODE* head)
{
if(NULL == pNode || NULL == head)
return;
while(head != pNode){
printf("%d", pNode->symbol);
pNode = pNode->parent;
}
return;
}
void print_code_for_str(HUFFMAN_NODE* pNode, HUFFMAN_NODE* head)
{
if(NULL == pNode || NULL == head)
return;
while(head != pNode){
printf("%d", pNode->symbol);
pNode = pNode->parent;
}
return;
}
如果对代码本身还有怀疑，可以编译一个测试用例验证一下，
void test()
{
HUFFMAN_NODE* node1 = NULL;
HUFFMAN_NODE* node2 = NULL;
HUFFMAN_NODE* node3 = NULL;
HUFFMAN_NODE* node4 = NULL;
HUFFMAN_NODE* test[] = {node1 = create_new_node('a', 0.1),
node2 = create_new_node('b', 0.2),
node3 = create_new_node('c', 0.3),
node4 = create_new_node('d', 0.4),
};
HUFFMAN_NODE* head = create_huffman_tree(test, sizeof(test)/sizeof(HUFFMAN_NODE*));
print_code_for_str(node1, head);
print_code_for_str(node2, head);
print_code_for_str(node3, head);
print_code_for_str(node4, head);
}
void test()
{
HUFFMAN_NODE* node1 = NULL;
HUFFMAN_NODE* node2 = NULL;
HUFFMAN_NODE* node3 = NULL;
HUFFMAN_NODE* node4 = NULL;
HUFFMAN_NODE* test[] = {node1 = create_new_node('a', 0.1),
node2 = create_new_node('b', 0.2),
node3 = create_new_node('c', 0.3),
node4 = create_new_node('d', 0.4),
};
HUFFMAN_NODE* head = create_huffman_tree(test, sizeof(test)/sizeof(HUFFMAN_NODE*));
print_code_for_str(node1, head);
print_code_for_str(node2, head);
print_code_for_str(node3, head);
print_code_for_str(node4, head);
}
总结：
（1）哈夫曼树不复杂，如果手算可以成功，那么编程应该也没有什么问题
（2）复杂算法都是由小算法搭积木而成的，朋友们应该在基本算法上打下坚实的基础
（3）算法注意复用，这里就用到了原来讲到的通用算法内容