C++ 程序实现自平衡二叉搜索树
c++programmingserver side programming
AVL 树是一种自平衡二叉搜索树，其中所有节点的左子树和右子树的高度差不能超过 1。
这是一个 C++ 程序实现自平衡二叉搜索树。
开始 类 avl_tree 声明以下函数: balance() = 通过获取平衡因子来平衡树。将 差异放入 bal_factor 中。如果 bal_factor > 1，则平衡 左子树。 如果 bal_factor < -1，则平衡右子树。 insert() = 在树中插入元素: 如果树为空，则将数据插入为根。 如果树不为空且数据 > 根 将数据插入为左子节点。 否则 将数据插入为右子节点。 结束。
示例代码
#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)//计算左右树之间的差异
{
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)//右旋转
{
avl *t;
t = parent→r;
parent→r = t→l;
t->l = parent;
cout<<"右-右旋转";
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<<"左-左旋转";
return t;
}
avl *avl_tree::lr_rotat(avl *parent)//左右旋转
{
avl *t;
t = parent→l;
parent->l = rr_rotat(t);
cout<<"左右旋转";
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 << "Enter your Choice: ";
cin >> c;
switch ©//perform switch operation
{
case 1:
cout << "Enter value to be inserted: ";
cin >> i;
r= avl.insert(r, i);
break;
case 2:
if (r == NULL)
{
cout << "Tree is Empty" << endl;
continue;
}
cout << "Balanced AVL Tree:" << endl;
avl.show(r, 1);
cout<<endl;
break;
case 3:
cout << "Inorder Traversal:" << endl;
avl.inorder(r);
cout << endl;
break;
case 4:
cout << "Preorder Traversal:" << endl;
avl.preorder(r);
cout << endl;
break;
case 5:
cout << "Postorder Traversal:" << endl;
avl.postorder(r);
cout << endl;
break;
case 6:
exit(1);
break;
default:
cout << "Wrong Choice" << endl;
}
}
return 0;
}
输出
1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 13 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 10 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 15 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 5 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 11 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 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 Enter your Choice: 1 Enter value to be inserted: 8 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 16 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 3 Inorder Traversal: 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 Enter your Choice: 4 Preorder Traversal: 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 Enter your Choice: 5 Postorder Traversal: 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 Enter your Choice: 1 Enter value to be inserted: 14 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 3 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 7 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 9 1.Insert Element into the tree 2.show Balanced AVL Tree 3.InOrder traversal 4.PreOrder traversal 5.PostOrder traversal 6.Exit Enter your Choice: 1 Enter value to be inserted: 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 Enter your Choice: 6
