--avl Tree of data structure

• AVL Tree

The AVL tree, also known as a highly balanced two-fork search tree, keeps the height of the binary tree balanced, minimizing the height of the two-fork tree, and reducing the average search length of the tree;

• The nature of the AVL tree

1. The absolute value of the height difference of the right subtree of Saozi does not exceed 1

2. Each Saozi right subtree in the tree is an AVL tree

The following implementation of an AVL tree, the main implementation of its insertion part:

#pragma  oncetemplate <class K, class V>struct AVLTreeNode{K _key; v _val; avltreenode<k, v>* _left; avltreenode<k, v>* _right; avltreenode<k, v>* _parent;int _bf;//balance factor Avltreenode (const k& key,  Const k& val): _key (Key), _val (Val), _left (null), _right (null), _parent (null), _BF (0) {}};template  <class K, class V>class AVLTree{typedef AVLTreeNode<K, V>  node;public:avltree (): _root (NULL) {}~avltree () {_clear (_root);} Bool insert (Const k& key, const v& val) {if (_root == NULL)// If the root node is null, a node is created that returns true {_root = new node (key, val); return true;} node* cur = _root; Node* prev = null;while (Cur != null)//Find the right place to insert {if (Cur->_key == key)// If the node already exists, it returns false Return false;else if (Cur->_key > key)//IFTo insert a value less than the current node, go to the left subtree to find {prev = cur;cur = cur->_left;} else//If the insertion value is greater than the current node, go to the right subtree to find {prev = cur;cur = cur->_right;}} The end of the loop indicates that a suitable position has been found and that the left or right node* tmp = new node (key, val) should be inserted; if (key <  Prev->_key) prev->_left = tmp;elseprev->_right = tmp;tmp->_parent =  prev;//Insert a node, you need to determine whether the current tree satisfies the rules of the AVL tree, if not satisfied, make the appropriate adjustment while (Prev != null) {//Balance factor is the right height minus the left height if (prev->_left &NBSP;==&NBSP;TMP)--(PREV-&GT;_BF); else++ (PREV-&GT;_BF); if (prev->_bf == 0)//If the balance factor is 0, it must be balanced, Because it can be seen as inserting a node at the same level, there is no effect on height break;else if (prev->_bf == 1 | | &NBSP;PREV-&GT;_BF&NBSP;==&NBSP;-1)//If the balance factor is 1/-1, it indicates a change in height and needs to continue upward adjustment {tmp = prev;prev =  Prev->_parent;} else//shows that the absolute value of the balance factor is greater than 1, then this time does not satisfy the nature of the AVL tree, need to adjust {if (prev->_bf == 2) {if (tmp->_bf == 1) _ Rotatel (prev); Else{_rotater (TMP); _rotatel (prev);}} Else{if (tmp->_bf == -1) _rotater (prev); Else{_roTatel (TMP); _rotater (prev);}} Break;}} Return true;} Void inorder () {_inorder (_root); Cout<<endl;} Protected:void _clear (node* root) {if (root != null) {_clear (root->_left); _Clear (root-> _right);d Elete root;root = null;}} Zodan Void _rotatel (node* parent) {node* subr = parent->_right; Node* subrl = subr->_left;parent->_right = subrl;if (SubRL != NULL) subrl->_parent = parent;subr->_left = parent; Node* ppnode = parent->_parent;parent->_parent = subr;if (ppNode ==  NULL) _root = subr;else{if (ppnode->_left == parent) ppnode->_left = subr; ELSEPPNODE-&GT;_RIGHT&NBSP;=&NBSP;SUBR;} subr->_parent = ppnode;parent->_bf = subr->_bf = 0;} Right paddle Void _rotater (node* parent) {node* subl = parent->_left; Node* sublr = subL->_right;parent->_left = sublr;if (sublr != null) sublr->_parent =  parent;subl->_right = parent; Node* ppnode = parent->_parent;parent->_parent = subl;if (ppNode ==  NULL) _root = subl;else{if (ppnode->_left == parent) ppnode->_left = subl; Elseppnode->_right = subl;} subl->_parent = ppnode;parent->_bf = subl->_bf = 0;} Void _inorder (node* root) {if (root != null) {_inorder (root->_left); cout<<root->_ key<< " "; _inorder (Root->_right);}} protected:node* _root;}; Void test () {int arr[] = {4, 2, 6, 1, 3, 5, 15, 7,  16,&NBSP;14};//INT&NBSP;ARR[]&NBSP;=&NBSP;{16,&NBSP;3,&NBSP;7,&NBSP;11,&NBSP;9,&NBSP;26,&NBSP;18,&NBSP;14,  15}; Avltree<int, int> t;for (int i = 0; i < sizeof(arr)/sizeof (arr[0]);  ++i) T.insert (arr[i], i); T.inorder ();} 

One of the left and right spins as shown:

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650) this.width=650; "src=" Http://s1.51cto.com/wyfs02/M02/85/4C/wKioL1efSuuQIZGYAAAlOi3AhdE399.png "style=" float: none; "Title=" right single-spin. png "alt=" Wkiol1efsuuqizgyaaaloi3ahde399.png "/>

To run the program:

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650) this.width=650; "src=" Http://s4.51cto.com/wyfs02/M02/85/4C/wKiom1efS3aS7KR9AAAlmwJ7LU4310.png "style=" float: none; "title=" Second.png "alt=" Wkiom1efs3as7kr9aaalmwj7lu4310.png "/>

Finish

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--avl Tree of data structure