AVL平衡搜尋樹
阿新 • • 發佈：2018-11-26
AVL樹又稱高度平衡的二叉搜尋樹。
性質： 1. 左子樹和右子樹的高度之差的絕對值不超過1 2. 樹中的每個左子樹和右子樹都是AVL樹 3. 每個節點都有一個平衡因子(balance factor--bf),任一節點的平衡因子是-1,0,1。(每個節點的平衡因子等於右子樹的高度減去左子樹的高度 )
當插入一個節點時，如果這個節點的父節點的平衡因子不滿足AVL樹的特點，這時就需要對AVL樹進行調整，即旋轉。
1、左單旋轉
2、右單旋轉
3、左右旋轉
4、右左旋轉
實現程式碼如下： #pragma once
template<class K,class V> struct AVLTreeNode { AVLTreeNode<K,V>* _left; AVLTreeNode<K,V>* _right; AVLTreeNode<K,V>* _parent;
K _key; V _value;
int _bf;//平衡因子 AVLTreeNode(const K& key,const V& value) :_bf(0) ,_left(NULL) ,_right(NULL) ,_parent(NULL) ,_key(key) ,_value(value) { } };
template<class K,class V> class AVLTree { public: typedef AVLTreeNode<K,V> Node; AVLTree() :_root(NULL) { }
bool Insert(const K& key,V& value) { if(_root == NULL) { _root = new Node(key,value); return true; }
Node* cur = _root; Node* parent = NULL;
while (cur) { if(cur->_key < key) { parent = cur; cur = cur->_right; } else if(cur->_key > key) { parent = cur; cur = cur->_left; } else { return false; } }
cur = new Node(key,value); if(parent->_key < key) { parent->_right = cur; cur->_parent = parent; } else { parent->_left = cur; cur->_parent = parent; }
//檢查樹是否平衡 //更新平衡因子，不滿足條件時，進行旋轉 while (parent) { if(cur == parent->_left) parent->_bf--; else parent->_bf++; if(parent->_bf == 0) break; else if(parent->_bf == -1 || parent->_bf == 1)//回朔 { cur = parent; parent = cur->_parent; } else//平衡因子為2或-2 { if(cur->_bf == 1) { if(parent->_bf == 2) RotateL(parent); else//-2 RotateLR(parent); } else { if(parent->_bf == -2) RotateR(parent); else RotateRL(parent); } break; } } return true; }
Node* Find(const K& key) { if(_root == NULL) return NULL; Node* cur = _root; while (cur) { if(cur->_key < key) { cur = cur->_right; } else if(cur->_key > key) { cur = cur->_left; } else { return cur; } } return NULL; }
void InOrder() { _InOrder(_root); cout<<endl; }
bool IsBlance() { return _IsBlance(_root); }
~AVLTree() { _Destroy(_root); _root = NULL; }
protected: void RotateL(Node* parent) { Node* subR = parent->_right; Node* subRL = subR->_left;
parent->_right = subRL; if(subRL) subRL->_parent = parent;
subR->_left = parent;
Node* ppNode = parent->_parent; parent->_parent = subR; subR->_parent = ppNode; if(ppNode == NULL) { _root = subR; } else { if(ppNode->_left == parent) ppNode->_left = subR; else ppNode->_right = subR; } parent->_bf = subR->_bf = 0; }
void RotateR(Node* parent) { Node* subL = parent->_left; Node* subLR = subL->_right; parent->_left = subLR; if(subLR) subLR->_parent = parent; subL->_right = parent; Node* ppNode = parent->_parent; parent->_parent = subL; subL->_parent = ppNode;
if(ppNode == NULL) { _root = subL; } else { if(ppNode->_left == parent) ppNode->_left = subL; else ppNode->_right = subL; } parent->_bf = subL->_bf = 0; }
void RotateLR(Node* parent) { Node* subL = parent->_left; Node* subLR =subL->_right; int bf = subLR->_bf;
RotateL(parent->_left); RotateR(parent);
//根據subL的平衡因子修正其他節點的平衡因子 if(bf == -1) { subL->_bf = 0; parent->_bf = 1; } else if(bf == 1) { subL->_bf = -1; parent->_bf = 0; } else { subL->_bf = parent->_bf = 0; } }
void RotateRL(Node* parent) { Node* subR = parent->_right; Node* subRL = subR->_left; int bf = subRL->_bf; RotateR(parent->_right); RotateL(parent);
//根據subRL的平衡因子修正其它節點的平衡因子 if(bf == 1) { subR->_bf = 0; parent->_bf = -1; } else if(bf == -1) { subR->_bf = 1; parent->_bf = 0; } else { parent->_bf = subR->_bf = 0; } }
void _Destroy(Node* root) { if(root == NULL) return; _Destroy(root->_left); _Destroy(root->_right); delete root; }
void _InOrder(Node* root) { if(root == NULL) return; _InOrder(root->_left); cout<<root->_key<<" "; _InOrder(root->_right); }
int _Height(Node* root) { if(root == NULL) return 0; int Left = _Height(root->_left); int Right = _Height(root->_right); return (Left > Right) ? (Left + 1) : (Right + 1); }
bool _IsBlance(Node* root) { if(root == NULL) return true; int left = _Height(root->_left); int right = _Height(root->_right); if((right - left) != root->_bf || abs(right - left) > 1) { cout<<"該節點的平衡因子異常:"; cout<<root->_key<<" "<<endl; return false; } return _IsBlance(root->_left) && _IsBlance(root->_right); }
protected: Node* _root; };
void AVLTreeTest() { int a[] = {16, 3, 7, 11, 9, 26, 18, 14, 15}; AVLTree<int,int> tree; for(int i = 0;i < 9;i++) { tree.Insert(a[i],i); } tree.InOrder(); tree.Find(16); tree.IsBlance();
}
void TestTree_SP() { int a[] = {4, 2, 6, 1, 3, 5, 15, 7, 16, 14}; AVLTree<int, int> t;
for (int i = 0; i < sizeof(a)/sizeof(a[0]); ++i) { t.Insert(a[i], i); } t.InOrder(); t.IsBlance(); }