二叉树的实现

BTree *Create_BTree()//创建一个二叉树{BTree *btree = (BTree*)malloc(sizeof(BTree)/sizeof(char));if (btree == NULL)return NULL;btree->count = 0;btree->root  = NULL;return btree;}int Btree_Insert(BTree *tree, BTreeData data, int pos, int count, int flag)//增加孩子{if (tree == NULL || (flag != BLEFT && flag != BRIGHT))return FALSE;BTreeNode *node = (BTreeNode*)malloc(sizeof(BTreeNode)/sizeof(char));//创建一个节点if (node == NULL)return FALSE;node->data = data;node->lchild = NULL;node->rchild = NULL;BTreeNode *parent = NULL;BTreeNode *current = tree->root; int way;   // 保存当前走的位置while (count > 0 && current != NULL){way = pos & 1;    // 取出当前走的方向pos = pos >> 1;   // 移去走过的路线parent = current;if (way == BLEFT)   current = current->lchild;elsecurrent = current->rchild;count--;}if (flag == BLEFT)node->lchild = current;elsenode->rchild = current;if (parent != NULL){if (way == BLEFT)parent->lchild = node;elseparent->rchild = node;}else{tree->root = node;  // 替换根节点}tree->count ++;return TRUE;}void r_display(BTreeNode* node, Print_BTree pfunc,int gap)//打印孩子{int i;if (node == NULL){for (i = 0; i < gap; i++){printf ("-");}printf ("\n");return;}for (i = 0; i < gap; i++){printf ("-");}// 打印结点 printf ("%c\n", node->data);if (node->lchild != NULL || node->rchild != NULL){r_display (node->lchild, pfunc, gap+4);// 打印左孩子r_display (node->rchild, pfunc, gap+4);// 打印右孩子}}void Display (BTree* tree, Print_BTree pfunc)//打印树{if (tree == NULL)return;r_display(tree->root, pfunc, 0);}void r_delete (BTree *tree, BTreeNode* node)//删除孩子{if (node == NULL || tree == NULL)return ;r_delete (tree, node->lchild);// 先删除左孩子r_delete (tree, node->rchild);// 删除右孩子free (node);tree->count --;}int Delete (BTree *tree, int pos, int count)//删除{if (tree == NULL)return FALSE;BTreeNode* parent  = NULL;BTreeNode* current = tree->root;int way;while (count > 0 && current != NULL){way = pos & 1;pos = pos >> 1;parent = current;if (way == BLEFT)current = current->lchild;elsecurrent = current->rchild;count --;}if (parent != NULL){if (way == BLEFT)parent->lchild = NULL;elseparent->rchild = NULL;}else{tree->root = NULL;}r_delete (tree, current);return TRUE;}int r_height (BTreeNode *node)//得到孩子高{if (node == NULL)return 0;int lh = r_height (node->lchild);int rh = r_height (node->rchild);return (lh > rh ? lh+1 : rh+1);}int BTree_Height (BTree *tree)//得到树高{if (tree == NULL)return FALSE;int ret = r_height(tree->root);return ret;}int r_degree (BTreeNode * node)//得到度{if (node == NULL)return 0;int degree = 0;if (node->lchild != NULL)degree++;if (node->rchild != NULL)degree++;if (degree == 1){int ld = r_degree (node->lchild);if (ld == 2)return 2;int rd = r_degree (node->rchild);if (rd == 2)return 2;}return degree;}int BTree_Degree (BTree *tree)//度{if (tree == NULL)return FALSE;int ret = r_degree(tree->root);return ret;}int BTree_Clear (BTree *tree)//清空树{if (tree == NULL)return FALSE;Delete (tree, 0, 0); tree->root = NULL;return TRUE;}int BTree_Destroy (BTree **tree)//销毁树{if (tree == NULL)return FALSE;BTree_Clear(*tree);free (*tree);*tree = NULL;return TRUE;}void pre_order (BTreeNode *node)//前序遍历{if (node == NULL)return;printf ("%4c", node->data);pre_order (node->lchild);pre_order (node->rchild);}void mid_order (BTreeNode *node)//中序遍历{if (node == NULL)return;mid_order (node->lchild);printf ("%4c", node->data);mid_order (node->rchild);}void last_order (BTreeNode *node)//后序遍历{if (node == NULL)return;last_order (node->lchild);last_order (node->rchild);printf ("%4c", node->data);}

在计算机科学中，二叉树是每个节点最多有两个子树的树结构。通常子树被称作“左子树”（left subtree）和“右子树”（right subtree）。二叉树常被用于实现二叉查找树和二叉堆。

二叉树的每个结点至多只有二棵子树(不存在度大于2的结点)，二叉树的子树有左右之分，次序不能颠倒。二叉树的第i层至多有2^{i-1}个结点；深度为k的二叉树至多有2^k-1个结点；对任何一棵二叉树T，如果其终端结点数为n_0，度为2的结点数为n_2，则n_0=n_2+1。

一棵深度为k，且有2^k-1个节点称之为满二叉树；深度为k，有n个节点的二叉树，当且仅当其每一个节点都与深度为k的满二叉树中，序号为1至n的节点对应时，称之为完全二叉树。

1、先序遍历：先序遍历是先输出根节点，再输出左子树，最后输出右子树。先序遍历结果就是：ABCDEF

2、中序遍历：中序遍历是先输出左子树，再输出根节点，最后输出右子树。中序遍历结果就是：CBDAEF

3、后序遍历：后序遍历是先输出左子树，再输出右子树，最后输出根节点。后序遍历结果就是：CDBFEA