AVL 树是一种自平衡二叉搜索树，其中所有节点的左右子树的高度差不能超过 1。
这是一个实现自平衡二叉搜索树的 C++ 程序。
Begin class avl_tree to declare following functions: balance() = Balance the tree by getting balance factor. Put the difference in bal_factor. If bal_factor > 1 then balance the left subtree. If bal_factor < -1 then balance the right subtree. insert() = To insert the elements in the tree: If tree is empty insert data as root. If tree is not empty and data > root Insert data as left child. Else Insert data as right child. End.
#include<iostream>
#include<cstdio>
#include<sstream>
#include<algorithm>
#define pow2(n) (1 << (n))
using namespace std;
struct avl//节点声明
{
int d;
struct avl *l;
struct avl *r;
}*r;
class avl_tree
{
public://declare functions
int height(avl *);
int difference(avl *);
avl * rr_rotat(avl *);
avl * ll_rotat(avl *);
avl * lr_rotat(avl*);
avl * rl_rotat(avl *);
avl * balance(avl *);
avl * insert(avl *, int);
void show(avl *, int);
void inorder(avl *);
void preorder(avl *);
void postorder(avl*);
avl_tree()
{
r = NULL;
}
};
int avl_tree::height(avl *t)
{
int h = 0;
if (t != NULL)
{
int l_height = height(t→l);
int r_height = height(t→r);
int max_height = max(l_height, r_height);
h = max_height + 1;
}
return h;
}
int avl_tree::difference(avl *t)//计算左和之间的差异
right tree
{
int l_height = height(t→l);
int r_height = height(t→r);
int b_factor = l_height - r_height;
return b_factor;
}
avl *avl_tree::rr_rotat(avl *parent)//右旋
{
avl *t;
t = parent→r;
parent→r = t→l;
t->l = parent;
cout<<"Right-Right Rotation";
return t;
}
avl *avl_tree::ll_rotat(avl *parent)//左左旋转
{
avl *t;
t = parent→l;
parent→l = t->r;
t->r = parent;
cout<<"Left-Left Rotation";
return t;
}
avl *avl_tree::lr_rotat(avl *parent)//左右旋转
{
avl *t;
t = parent→l;
parent->l = rr_rotat(t);
cout<<"Left-Right Rotation";
return ll_rotat(parent);
}
avl *avl_tree::rl_rotat(avl *parent)//左右旋转
{
avl *t;
t= parent→r;
parent->r = ll_rotat(t);
cout<<"Right-Left Rotation";
return rr_rotat(parent);
}
avl *avl_tree::balance(avl *t)
{
int bal_factor = difference(t);
if (bal_factor > 1)
{
if (difference(t->l) > 0)
t = ll_rotat(t);
else
t = lr_rotat(t);
}
else if (bal_factor < -1)
{
if (difference(t->r) > 0)
t = rl_rotat(t);
else
t = rr_rotat(t);
}
return t;
}
avl *avl_tree::insert(avl *r, int v)
{
if (r == NULL)
{
r = new avl;
r->d = v;
r->l = NULL;
r->r= NULL;
return r;
}
else if (v< r→d)
{
r->l= insert(r→l, v);
r = balance(r);
}
else if (v >= r→d)
{
r->r= insert(r→r, v);
r = balance(r);
}
return r;
}
void avl_tree::show(avl *p, int l)//显示树
{
int i;
if (p != NULL)
{
show(p->r, l+ 1);
cout<<" ";
if (p == r)
cout << "Root → ";
for (i = 0; i < l&& p != r; i++)
cout << " ";
cout << p→d;
show(p->l, l + 1);
}
}
void avl_tree::inorder(avl *t)//中序遍历
{
if (t == NULL)
return;
inorder(t->l);
cout << t->d << " ";
inorder(t->r);
}
void avl_tree::preorder(avl *t)//前序遍历
{
if (t == NULL)
return;
cout << t->d << " ";
preorder(t->l);
preorder(t->r);
}
void avl_tree::postorder(avl *t)//后序遍历
{
if (t == NULL)
return;
postorder(t ->l);
postorder(t ->r);
cout << t→d << " ";
}
int main()
{
int c, i;
avl_tree avl;
while (1)
{
cout << "1.Insert Element into the tree" << endl;
cout << "2.show Balanced AVL Tree" << endl;
cout << "3.InOrder traversal" << endl;
cout << "4.PreOrder traversal" << endl;
cout << "5.PostOrder traversal" << endl;
cout << "6.Exit" << endl;
cout << "输入您的选择： ";
cin >> c;
switch ©//执行开关操作
{
case 1:
cout << "输入要插入的值： ";
cin >> i;
r= avl.insert(r, i);
break;
case 2:
if (r == NULL)
{
cout << "Tree is Empty" << endl;
continue;
}
cout << "平衡 AVL 树：" << endl;
avl.show(r, 1);
cout<<endl;
break;
case 3:
cout << "中序遍历：" << endl;
avl.inorder(r);
cout << endl;
break;
case 4:
cout << "预序遍历：" << endl;
avl.preorder(r);
cout << endl;
break;
case 5:
cout << "后序遍历：" << endl;
avl.postorder(r);
cout << endl;
break;
case 6:
exit(1);
break;
default:
cout << "Wrong Choice" << endl;
}
}
return 0;
}输出结果1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit 输入您的选择： 1 输入要插入的值： 13 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit 输入您的选择： 1 输入要插入的值： 10 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit 输入您的选择： 1 输入要插入的值： 15 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit 输入您的选择： 1 输入要插入的值： 5 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit 输入您的选择： 1 输入要插入的值： 11 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit 输入您的选择： 1 输入要插入的值： 4 Left-Left Rotation1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit 输入您的选择： 1 输入要插入的值： 8 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit 输入您的选择： 1 输入要插入的值： 16 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit 输入您的选择： 3 中序遍历： 4 5 8 10 11 13 15 16 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit 输入您的选择： 4 预序遍历： 10 5 4 8 13 11 15 16 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit 输入您的选择： 5 后序遍历： 4 8 5 11 16 15 13 10 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit 输入您的选择： 1 输入要插入的值： 14 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit 输入您的选择： 1 输入要插入的值： 3 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit 输入您的选择： 1 输入要插入的值： 7 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit 输入您的选择： 1 输入要插入的值： 9 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit 输入您的选择： 1 输入要插入的值： 52 Right-Right Rotation 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit 输入您的选择： 6