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一、哈夫曼树概念

        哈夫曼树又称最优树给定N个权值作为N个叶子结点，构造一棵二叉树，若该树的带权路径长度达到最小，称这样的二叉树为最优二叉树，也称为哈夫曼树(Huffman Tree)。哈夫曼树是带权路径长度最短的树，权值较大的结点离根较近。

         例给定一个有序数组{3,5,6,9,10}，构造出一个哈夫曼树如下：

       树的带权路径长度规定为所有叶子结点的带权路径长度之和，记为WPL

        WPL = (3+5)*4 +  6*3 + 9*2 +10*1 = 98

二、实现代码

1、定义树结点

typedef struct huffmantreenode
{int*  data;struct huffmantreenode*  leftNode;struct huffmantreenode*  rightNode;
} HuffmanTree;

2、声明函数操作

/***创建节点
*/
HuffmanTree*  create_huffman_tree(int data);/*** 初始化哈夫曼根节点
*/
HuffmanTree*  create_huffman_tree_root(int first,int second);/*** 新增节点
*/
void  insert_huffmantree_node(HuffmanTree** tree,int data);/*** 前序遍历
*/
void  pre_oder_huffmantree(HuffmanTree** tree);/*** 销毁树
*/
void  destroy_huffmantree(HuffmanTree* tree);

3、函数定义

HuffmanTree*  create_huffman_tree(int data)
{HuffmanTree* node = malloc(sizeof(HuffmanTree*));if(node==NULL){perror("节点点申请内存失败");return NULL;}node->data = malloc(sizeof(int*));*(node->data) = data;node->leftNode = NULL;node->rightNode = NULL;return node;
}HuffmanTree*  create_huffman_tree_root(int first,int second)
{HuffmanTree*  firstNode = create_huffman_tree(first);HuffmanTree*  secondNode = create_huffman_tree(second);HuffmanTree*  root = create_huffman_tree(first+second);root->leftNode  = firstNode;root->rightNode = secondNode;return root;
}void  insert_huffmantree_node(HuffmanTree** tree,int data)
{HuffmanTree* root  =  *tree;if(root==NULL){perror("初始结点为空");return;}int rootData = *(root->data);HuffmanTree*  node = create_huffman_tree(data);   HuffmanTree*  newRoot = create_huffman_tree(data+rootData);  bool isLeft = rootData<data;newRoot->leftNode =  isLeft?root:node;newRoot->rightNode = isLeft?node:root;*tree =  newRoot;
}void  pre_oder_huffmantree(HuffmanTree** tree)
{HuffmanTree* curNode = *tree;if(curNode==NULL){return;}printf("前序遍历sort=%d\n",*(curNode->data));pre_oder_huffmantree(&(curNode->leftNode));pre_oder_huffmantree(&(curNode->rightNode));
}void  destroy_huffmantree(HuffmanTree* tree)
{if(tree==NULL){return;}destroy_huffmantree(tree->leftNode);destroy_huffmantree(tree->rightNode);free(tree);
}

4、测试函数

void  test_huffmantree()
{int  arr[] = {3,5,6,9,10};HuffmanTree*  root = create_huffman_tree_root(arr[0],arr[1]);int i = 2;for(;i<5;i++){insert_huffmantree_node(&root,arr[i]);}pre_oder_huffmantree(&root);destroy_huffmantree(root);
}