Construction of Binary Sort Tree
The binary sort tree has a certain rule, that is, the left subtree is smaller than the root node and smaller than the grapefruit tree.
The idea is: first define a root node, enter a number, its left and right subtrees are NULL, and then enter the numbers in turn, starting from the root node each time. If it is smaller than it, go to the left subtree, until a certain node subtree is NULL, assign it to it, and go to the right when it is greater than or equal to the root node, and the others are similar.
If you master the middle order traversal, you can quickly get started
Construct a binary sort tree
void CreatBTree(T_NODE &tree)
{
/*前面构造一个根节点*/
tree = new BTree;
cout << "请输入一个元素" << endl;
elementype c;
cin >> c;
tree->lef_child = NULL;
tree->rig_child = NULL;
if (c != 65535)
{
tree->data = c;
}
//后面用递归排序 输入元素
while (c != 65535)
{
cin >> c;
if (c != 65535)
{
InSerChild(tree, c);
}
}
}
void InSerChild(T_NODE &tree, elementype c)
{
if (c<tree->data)
{
//如果小于根节点元素 则先判断左孩子是否存在
if (tree->lef_child == NULL)//如果左孩子不存在
{
tree->lef_child = new BTree;
tree->lef_child->lef_child = NULL;
tree->lef_child->rig_child = NULL;
tree->lef_child->data = c;
}
else//左孩子存在
{
InSerChild(tree->lef_child, c);
}
}
else
{
if (tree->rig_child == NULL)
{
tree->rig_child = new BTree;
tree->rig_child->lef_child = NULL;
tree->rig_child->rig_child = NULL;
tree->rig_child->data = c;
}
else
{
InSerChild(tree->rig_child, c);
}
}
}
Binary sort tree search
void FindBTree(T_NODE &tree, elementype x)
{
if (x<tree->data)
{
if (tree->lef_child != NULL)
{
FindBTree(tree->lef_child, x);
}
else
{
cout << "此内容小于根节点元素，且树中无此元素" << endl;
}
}
else if (x>tree->data)
{
if (tree->rig_child != NULL)
{
FindBTree(tree->rig_child, x);
}
else
{
cout << "此内容大于根节点元素，且树中无此元素" << endl;
}
}
else
{
cout << "存在" << endl;
}
}
Deletion of Binary Sort Tree
/*二叉树的删除*/
//首先得先进行查找
void Del_Fin_BT(T_NODE &tree, elementype x)
{
if (x<tree->data)
{
if (tree->lef_child != NULL)
{
Del_Fin_BT(tree->lef_child, x);
}
else
{
cout << "此内容小于根节点元素，且树中无此元素" << endl;
}
}
else if (x>tree->data)
{
if (tree->rig_child != NULL)
{
Del_Fin_BT(tree->rig_child, x);
}
else
{
cout << "此内容大于根节点元素，且树中无此元素" << endl;
}
}
else
{
Del_BT(tree);
}
}
void Del_BT(T_NODE &tree)
{
//删除该节点内容，然后为了保持二叉排序树的结构
//应该，寻找该结点的前序和后继元素，取其一替代该节点
T_NODE q, s;
q = new BTree;
s= new BTree;
if (tree->lef_child == NULL)
{
q = tree;//先将其用q表示
tree = tree->rig_child;//柚子树替代 这里就是关键了 如果柚子树存在则直接取代，否则的话 还存在，右子树原本就是NULL 取代之后也是NULL 所以也删除了
free(q);//释放该节点
}
else if (tree->rig_child==NULL)
{
q = tree;
tree = tree->rig_child;
free(q);
}
else//如果都不为空，那么就要选择了
{
/*q->lef_child = tree->lef_child;
q->rig_child = tree->rig_child;
q->data = tree->data;*/
q = tree;
s = tree->lef_child;//选择该结点t的左子树最大的一个，也就是最接近它的一个
while (s->rig_child)//最大的在结点柚子树 所以寻找右侧的
{
q = s;//用q记录最大柚子树的 根结点
s = s->rig_child;//最大柚子树
}
tree->data = s->data;//直接赋值进去
if (q != tree)//有树状结构时，直接使得最大柚子树的左子树取代其位置
{
q->rig_child = s->lef_child;
}
else//只有一个元素时
{
q->lef_child = s->lef_child;
}
free(s);
}
}
To delete a binary sort tree, remember that the deleted element will be deleted, and the left (right) will replace the previous node in its position.
So use q to record the root node of the largest grapefruit tree. This is also true when traversing the binary tree in order
All the code is easy to read later
#include<iostream>
#include<malloc.h>
using namespace std;
typedef int elementype;
typedef int Status;
typedef struct BTree
{
elementype data;
struct BTree *lef_child, *rig_child;
}*T_NODE, Bnode;
void InSerChild(T_NODE &tree, elementype c);
//void FindBTree(T_NODE &tree, elementype x);
void Del_BT(T_NODE &tree);
void CreatBTree(T_NODE &tree)
{
/*前面构造一个根节点*/
tree = new BTree;
cout << "请输入一个元素" << endl;
elementype c;
cin >> c;
tree->lef_child = NULL;
tree->rig_child = NULL;
if (c != 65535)
{
tree->data = c;
}
//后面用递归排序 输入元素
while (c != 65535)
{
cin >> c;
if (c != 65535)
{
InSerChild(tree, c);
}
}
}
void InSerChild(T_NODE &tree, elementype c)
{
if (c<tree->data)
{
//如果小于根节点元素 则先判断左孩子是否存在
if (tree->lef_child == NULL)//如果左孩子不存在
{
tree->lef_child = new BTree;
tree->lef_child->lef_child = NULL;
tree->lef_child->rig_child = NULL;
tree->lef_child->data = c;
}
else//左孩子存在
{
InSerChild(tree->lef_child, c);
}
}
else
{
if (tree->rig_child == NULL)
{
tree->rig_child = new BTree;
tree->rig_child->lef_child = NULL;
tree->rig_child->rig_child = NULL;
tree->rig_child->data = c;
}
else
{
InSerChild(tree->rig_child, c);
}
}
}
Status OutputTree_mid(T_NODE &tree)
{
if (tree == NULL)
{
return 0;
}
else
{
if (tree->lef_child != NULL)
{
OutputTree_mid(tree->lef_child);
//cout << tree->lef_child->data << endl;
}
cout << tree->data << endl;
if (tree->rig_child != NULL)
{
OutputTree_mid(tree->rig_child);
//cout<<tree->rig_child->data << endl;
}
}
}
/*二叉排序树的查找*/
void FindBTree(T_NODE &tree, elementype x)
{
if (x<tree->data)
{
if (tree->lef_child != NULL)
{
FindBTree(tree->lef_child, x);
}
else
{
cout << "此内容小于根节点元素，且树中无此元素" << endl;
}
}
else if (x>tree->data)
{
if (tree->rig_child != NULL)
{
FindBTree(tree->rig_child, x);
}
else
{
cout << "此内容大于根节点元素，且树中无此元素" << endl;
}
}
else
{
cout << "存在" << endl;
}
}
/*二叉树的删除*/
//首先得先进行查找
void Del_Fin_BT(T_NODE &tree, elementype x)
{
if (x<tree->data)
{
if (tree->lef_child != NULL)
{
Del_Fin_BT(tree->lef_child, x);
}
else
{
cout << "此内容小于根节点元素，且树中无此元素" << endl;
}
}
else if (x>tree->data)
{
if (tree->rig_child != NULL)
{
Del_Fin_BT(tree->rig_child, x);
}
else
{
cout << "此内容大于根节点元素，且树中无此元素" << endl;
}
}
else
{
Del_BT(tree);
}
}
void Del_BT(T_NODE &tree)
{
//删除该节点内容，然后为了保持二叉排序树的结构
//应该，寻找该结点的前序和后继元素，取其一替代该节点
T_NODE q, s;
q = new BTree;
s= new BTree;
if (tree->lef_child == NULL)
{
q = tree;//先将其用q表示
tree = tree->rig_child;//柚子树替代 这里就是关键了 如果柚子树存在则直接取代，否则的话 还存在，右子树原本就是NULL 取代之后也是NULL 所以也删除了
free(q);//释放该节点
}
else if (tree->rig_child==NULL)
{
q = tree;
tree = tree->rig_child;
free(q);
}
else//如果都不为空，那么就要选择了
{
/*q->lef_child = tree->lef_child;
q->rig_child = tree->rig_child;
q->data = tree->data;*/
q = tree;
s = tree->lef_child;//选择该结点t的左子树最大的一个，也就是最接近它的一个
while (s->rig_child)//最大的在结点柚子树 所以寻找右侧的
{
q = s;//用q记录最大柚子树的 根结点
s = s->rig_child;//最大柚子树
}
tree->data = s->data;//直接赋值进去
if (q != tree)//有树状结构时，直接使得最大柚子树的左子树取代其位置
{
q->rig_child = s->lef_child;
}
else//只有一个元素时
{
q->lef_child = s->lef_child;
}
free(s);
}
}
void main()
{
T_NODE tree;
CreatBTree(tree);
OutputTree_mid(tree);
elementype x;
cout << "请输入一个需要查找的树元素" << endl;
cin >> x;
FindBTree(tree,x);
cout << "删除该元素" << endl;
Del_Fin_BT(tree,x);
OutputTree_mid(tree);
system("pause");
}