怎么在C++中实现AVL树？相信很多没有经验的人对此束手无策，为此本文总结了问题出现的原因和解决方法，通过这篇文章希望你能解决这个问题。
AVL树的介绍
AVL树是一种自平衡的二叉搜索树，它通过单旋转（single rotate）和双旋转(double rotate)的方式实现了根节点的左子树与右子树的高度差不超过1,。这有效的降低了二叉搜索树的时间复杂度，为O（log n）。那么，下面小编将详细介绍C++实现AVL树的代码。最后一步提供可靠的代码实现
这里先粘贴代码
给大家的忠告，一定要及时去实现，不然之后再实现要花更多的时间
#ifndef _AVLTREE_
#define _AVLTREE_
#include<iostream>
#include<vector>
#include<queue>
#include<map>
using namespace std;
#define MAXFACTOR = 2;
template<class Key , class E>
class AVLNode
{
private:
Key key;
E value;
AVLNode<Key,E>* left;
AVLNode<Key,E>* right;
AVLNode<Key,E>* parent;
public:
AVLNode():left(nullptr),right(nullptr),parent(nullptr){}
AVLNode(Key _key,E _value , AVLNode<Key,E>* _parent = nullptr,AVLNode<Key,E>*_left = nullptr, AVLNode<Key,E>*_right = nullptr):
key(_key),value(_value),left(_left),right(_right),parent(_parent){}
bool isLeaf(){return left==nullptr && right == nullptr ;}
//元素设置
Key getKey() const { return key;}
void setKey(Key set) {key = set;}
E getValue() const { return value;}
void setValue(E set) {value = set;}
AVLNode<Key,E>* getLeft() { return left; }
void setLeft (AVLNode< Key,E >* set){ left = set;}
AVLNode<Key,E>* getRight() { return right;}
void setRight (AVLNode<Key,E>* set) {right = set ;}
AVLNode<Key,E>* getParent() {return parent;}
void setParent(AVLNode<Key,E>* set) { parent = set;}
};
template<class Key , class E>
class AVLTree
{
private:
AVLNode<Key,E>* root;
void clear(AVLNode<Key,E>* &r)
{
if(r==nullptr)return;
if(r->getLeft())clear(r->getLeft());
if(r->getRight())clear(r->getRight);
delete r;
}
void Init()
{
root = new AVLNode<Key,E>();
root=nullptr;
}
void preOrder(AVLNode<Key,E>* r,void(*visit) (AVLNode<Key,E> * node))
{
if(r==nullptr)return;
(*visit) (r);
preOrder(r->getLeft() , visit);
preOrder(r->getRight(), visit);
}
void inOrder(AVLNode<Key,E>* r , void(*visit)(AVLNode<Key,E>* node) )
{
if(r==nullptr)return;
inOrder(r->getLeft() , visit);
(*visit)(r);
inOrder(r->getRight(),visit);
}
void postOrder(AVLNode<Key,E>*r , void (*visit) (AVLNode<Key,E>* node))
{
if(r==nullptr)return;
postOrder(r->getLeft(),visit);
postOrder(r->getRight(),visit);
(*visit)(r);
}
void levelOrder(AVLNode<Key,E>*r , void (*visit) (AVLNode<Key,E>* node))
{
queue< AVLNode<Key,E>* > q;
if(r==nullptr)return;
q.push(r);
while( ! q.empty() )
{
AVLNode<Key,E>* tmp = q.front();
q.pop();
(*visit)(tmp);
if(tmp->getLeft() ) q.push(tmp->getLeft() );
if(tmp->getRight()) q.push(tmp->getRight());
}
}
AVLNode<Key,E>* find(AVLNode<Key,E>* r,Key k)
{
if(r==nullptr)return nullptr;
if(k == r->getKey() ) return r;
else if( k < r->getKey())
{
find(r->getLeft(),k);
}
else {
find(r->getRight(),k);
}
}
//Find the smallest element in the avl tree
AVLNode<Key,E>* getMin(AVLNode<Key,E>* r)
{
if(r->getLeft() == nullptr) return r;
else{
getMin(r->getLeft());
}
}
//Remove the smallest element
AVLNode<Key,E>* deleteMin(AVLNode<Key,E>* rt)
{
if(rt->getLeft() == nullptr) return rt->getRight();
else{
rt->setLeft(deleteMin(rt->getLeft()));
return rt;
}
}
AVLNode<Key,E>* leftRotate(AVLNode<Key,E>* node)
{
if( node == nullptr) return nullptr;
AVLNode<Key,E>* newHead = node->getRight();
node->setRight( newHead -> getLeft() );
newHead -> setLeft( node );
return newHead;
}
AVLNode<Key,E>* rightRotate(AVLNode<Key,E>* node)
{
if(node == nullptr)return nullptr;
AVLNode<Key,E>* newHead = node->getLeft();
node->setLeft( newHead->getRight() );
newHead ->setRight(node);
return newHead;
}
int getHeight(AVLNode<Key,E>*node)
{
if(node == nullptr)return 0;
if(node->isLeaf())return 1;
else return ( getHeight( node->getLeft() ) > getHeight( node->getRight() ) ?
getHeight( node->getLeft() ) : getHeight( node->getRight() ) ) + 1;
}
int getBalanceFactor(AVLNode<Key,E>* node)
{
return getHeight(node->getLeft()) - getHeight(node->getRight() );
}
AVLNode<Key,E>* balance(AVLNode<Key,E>* node)
{
if(!node) return nullptr;
else if ( getBalanceFactor( node ) == 2)
{
if(getBalanceFactor( node ->getLeft() ) == 1)
{
node = rightRotate(node);
}
else
{
node->setLeft(leftRotate( node->getLeft() ) );
node = rightRotate(node);
}
}
else if(getBalanceFactor( node ) == -2)
{
if(getBalanceFactor( node->getRight()) == -1)
{
node = leftRotate(node);
}
else
{
node->setRight( rightRotate( node->getRight() ) );
node = leftRotate(node);
}
}
return node;
}
AVLNode<Key,E>* insert( AVLNode<Key,E>* root ,const pair<Key,E>& it)
{
if(root == nullptr)
{
return new AVLNode<Key,E>(it.first , it.second,NULL,NULL,NULL);
}
else if (it.first < root->getKey() )
{
root ->setLeft( insert(root->getLeft() , it) ) ;
}
else{
root ->setRight( insert(root->getRight() , it) );
}
root = balance(root);
return root;
}
AVLNode<Key,E>* remove(AVLNode<Key,E>* node , const Key k)
{
if(node == nullptr) return nullptr;
if(node->getKey() > k)
{
node->setLeft( remove(node->getLeft() , k) );
node = balance(node);
}
else if(node->getKey() < k)
{
node->setRight( remove(node->getRight(), k) );
node = balance(node);
}
else if(node->getKey() == k)
{
if(! node->isLeaf() )
{
AVLNode<Key,E>* tmp = getMin(node->getRight() );
node->setKey( tmp->getKey() );
node->setValue( tmp->getValue() );
node->setRight( deleteMin(node->getRight() ) );
delete tmp;
}
else {
AVLNode<Key,E>* tmp = node;
node = (node->getLeft() != nullptr) ? node->getLeft() : node->getRight() ;
delete tmp;
}
}
return node;
}
public:
~AVLTree(){clear(root);}
AVLTree(){/*Init();*/ root = nullptr; }
//四种遍历方式
void preOrder( void (*visit)(AVLNode<Key,E>* r))
{
preOrder(root,visit);
}
void inOrder(void (*visit)(AVLNode<Key,E>* r))
{
inOrder(root,visit);
}
void postOrder(void (*visit)(AVLNode<Key,E>* r))
{
postOrder(root,visit);
}
void levelOrder( void(*visit)(AVLNode<Key,E>*r) )
{
levelOrder(root,visit);
}
//插入
void insert(const pair<Key,E> &it)
{
root = insert(root,it);
}
//删除
void remove(const Key& k)
{
remove(root,k);
}
bool find(const Key&k)
{
return find(root,k);
}
};
#endif//AVLtest.cpp
#include"NewAvl.h"
#include<iostream>
using namespace std;
template<typename Key,typename E>
void traverse(AVLNode<Key,E>* root)
{
cout<<root->getKey()<<" "<<root->getValue()<<" ";
cout<<endl;
}
int main()
{
AVLTree<int,int>* tree = new AVLTree<int ,int>;
for(int i = 0 ; i < 5 ; i ++)
{
tree->insert(make_pair(i,i));
}
tree->remove(1);
cout<<"PreOrder: "<<endl;
tree->preOrder(traverse);
cout<<endl;
cout<<"LevelOrder: "<<endl;
tree->levelOrder(traverse);
cout<<endl;
cout<<"InOrder: "<<endl;
tree->inOrder(traverse);
cout<<endl;
cout<<"PostOrder: "<<endl;
tree->postOrder(traverse);
cout<<endl;
cout<<tree->find(2)<<endl;
tree->insert(make_pair(9,9));
tree->levelOrder(traverse);
}运行结果
看完上述内容，你们掌握怎么在C++中实现AVL树的方法了吗？如果还想学到更多技能或想了解更多相关内容，欢迎关注亿速云行业资讯频道，感谢各位的阅读！
免责声明：本站发布的内容（图片、视频和文字）以原创、转载和分享为主，文章观点不代表本网站立场，如果涉及侵权请联系站长邮箱：is@yisu.com进行举报，并提供相关证据，一经查实，将立刻删除涉嫌侵权内容。
