AVL树

AVL树相比较红黑树而言，是一种更加严格的平衡树，在插入和删除的时候，需要通过旋转来实现平衡。具体实现比红黑树简单。

代码：

#include<iostream>

using namespace std;

struct TNode
{
int value;
int h;
TNode * left;
TNode * right;
TNode * parent;
TNode()
{
left = NULL;
right = NULL;
parent = NULL;
h = 1;
}
};
struct Tree
{
TNode * root;
Tree()
{
root = NULL;
}
};

void avl_insert(Tree & t,int value);
void avl_fixup(Tree&t,TNode *x);
int tnodeh(TNode *x);
void refreshnode(Tree&t,TNode *x);
int mymax (int a,int b);
void left_rotate(Tree&t,TNode*x);
void right_rotate(Tree&t,TNode*x);
void printT(TNode *x);
void avl_delete(Tree &t,TNode*x);
void tp(int i)
{
// cout << i << endl;
}
int main ()
{
Tree t;
for (int i = 1; i < 5;i ++)
{
avl_insert(t,i);
}

for (int i = 10; i > 6;i --)
{
avl_insert(t,i);
}
printT(t.root);

}
void avl_insert(Tree&t,int value)
{
TNode * p = t.root;
TNode * q = NULL;
TNode * s = new TNode();
s->value = value;
if (NULL == t.root)
{
t.root = s;
}
else
{
while (p != NULL)
{
q = p;
if (p->value < value)
{
p = p->right;
}
else
{
p = p->left;
}
}
if (q->value < value)
{
q->right = s;
}
else
{
q->left = s;
}
s->parent = q;
avl_fixup(t,s);
}

}

void avl_fixup(Tree&t,TNode *x)
{
TNode * p = x->parent;
while (p!= NULL)
{
refreshnode(t,p);
p = p->parent;
}
}
int tnodeh(TNode *x)
{
int h = 0;
if (NULL != x)
{
h = x->h;
}
return h;
}
void refreshnode(Tree&t,TNode *x)
{
int lh = tnodeh(x->left);
int rh = tnodeh(x->right);
int tmp = lh-rh;
tp(1);
if (tmp> 2)
{
tp(2);
right_rotate(t,x);
refreshnode(t,x);
// refreshnode(t,x->parent);
}
else if (tmp < -2)
{
tp(3);
left_rotate(t,x);
refreshnode(t,x);
// refreshnode(t,x->parent);
}
else
{

x->h = mymax(lh,rh)+1;
}
}
int mymax(int a,int b)
{
return a>b?a:b;
}
void left_rotate(Tree&t,TNode*x)
{
tp(10);
TNode * y =x->right;
if (t.root == x)
{
t.root = y;
}
else if (x->parent->left == x)
{
x->parent->left = y;
}
else
{
x->parent->right = y;
}
y->parent = x->parent;
x->right = y->left;
if ( NULL != x->right)
{
x->right->parent = x;
}
x->parent = y;
y->left = x;
tp(10);
}

void right_rotate(Tree&t,TNode*x)
{
TNode * y =x->left;
if (t.root == x)
{
t.root = y;
}
else if (x->parent->left == x)
{
x->parent->left = y;
}
else
{
x->parent->right = y;
}
y->parent = x->parent;
x->left = y->right;
if ( NULL != x->left)
{
x->left->parent = x;
}
x->parent = y;
y->right = x;
}
void printT(TNode *x)
{
if (x != NULL)
{
cout << x->value << " "<< x->h << endl;
printT(x->left);
printT(x->right);
}
}

void avl_delete(Tree &t,TNode*x)
{

}