AVL- tree
AVL- tree
In computer science, an AVL tree (Adelson-Velskii and Landis' tree, named after the inventors) is a self-balancing binary search tree. It was the first such data structure to be invented.In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Lookup, insertion, and deletion all take O(log n) time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or moretree rotations.
The AVL tree is named after its two Soviet inventors, G. M. Adelson-Velskii and E. M. Landis, who published it in their 1962 paper "An algorithm for the organization of information".
AVL trees are often compared with red-black trees because both support the same set of operations and take O(log n) time for the basic operations. For lookup-intensive applications, AVL trees are faster than red-black trees because they are more rigidly balanced. Similar to red-black trees, AVL trees are height-balanced. Both are in general not weight-balanced nor μ-balanced for any ; That is, sibling nodes can have hugely differing numbers of descendants.
我的代码实现：
avl_tree.h
#ifndef _avl_TREE_H
#define _avl_TREE_H 1
//declaration for node
struct node
{
int data;
int height;
int balance_factor;
struct node* parent;
struct node* rightchild;
struct node* leftchild;
};
#include "avl_insert_node.h"
#include "avl_height.h"
#include "print_tree.h"
#include "single_rotation_with_left.h"
#include "single_rotation_with_right.h"
#include "double_rotation_with_left.h"
#include "double_rotation_with_right.h"
#endif
avl_tree.c
/***************************************************************************************** code writer : EOF code date : 2014.03.01 e-mail: [email protected] code purpose: This is the main functin of this program. Just modify a avl-tree and print out the data we writed in. If something could be changed into better situation, please touch me by e-mail. Thank you! ******************************************************************************************/ #include <stdio.h> #include "avl_tree.h" #define ARRAY_SIZE 10 int main() { int array[ARRAY_SIZE] = {2,4,23,15,98,34,66,75,41,17}; int temp = 0; struct node* root; root = NULL; for(temp = 0;temp < ARRAY_SIZE;temp++) { root = avl_insert_node(&root,NULL,array[temp]); } if(root == NULL) { printf("insert failed!\nProcess end!\n"); } print_tree(root); return 0; }
avl_height.c
/************************************************************************
code writer :EOF
data : 2014.02.28
code purpose:
My implementation for avl_height function
This function would return current node's height and if current
node is NULL, -1 would be returned.
If this node is not NULL ,return height of the node,else return -1.
*************************************************************************/
#include "avl_tree.h"
#include "stdio.h"
int avl_height(struct node* p_node)
{
if(p_node != NULL)
{
return p_node->height; //If current node is not NULL, we return the height of current node.
}
else
{
return -1;// If current node is NULL, we assume that the height of current node is -1.
}
}
avl_insert_node.c
/***************************************************************************************** code writer : EOF code date : 2014.03.01 e-mail: [email protected] code purpose: implementation of function avl_insert_node If something could be changed into better situation, please touch me by e-mail. Thank you! ******************************************************************************************/ #include <stdio.h> #include <math.h> #include <stdlib.h> #include "avl_tree.h" struct node* avl_insert_node(struct node** pp_node, struct node* p_parent,int number) { if((*pp_node) == NULL) { (*pp_node) = (struct node*)malloc(sizeof(struct node)); if((*pp_node) == NULL) { printf("malloc faild!\n"); return 0; } //initilization for new node (*pp_node)->data = number; (*pp_node)->height = 0; (*pp_node)->parent = p_parent; (*pp_node)->rightchild = NULL; (*pp_node)->leftchild = NULL; } else if((*pp_node)->data > number)//right_rotation { (*pp_node)->leftchild = avl_insert_node(&((*pp_node)->leftchild),(*pp_node),number); //Now, we have inserted a node and interrupt the balance of the tree. So, we should rebalance the tree.What we should do is rotation. (*pp_node)->height = (avl_height((*pp_node)->leftchild) > avl_height((*pp_node)->rightchild) ?\ avl_height((*pp_node)->leftchild) : avl_height((*pp_node)->rightchild))+1; if(abs(avl_height((*pp_node)->rightchild) - avl_height((*pp_node)->leftchild)) == 2) { if((*pp_node)->leftchild->data > number) { (*pp_node) = single_rotation_with_right(*pp_node); } else if((*pp_node)->leftchild->data < number) { (*pp_node) = double_rotation_with_right(*pp_node); } } } else if((*pp_node)->data < number)//left_rotation { (*pp_node)->rightchild = avl_insert_node(&((*pp_node)->rightchild),(*pp_node),number); (*pp_node)->height = (avl_height((*pp_node)->leftchild) > avl_height((*pp_node)->rightchild) ?\ avl_height((*pp_node)->leftchild) : avl_height((*pp_node)->rightchild))+1; if(abs(avl_height((*pp_node)->rightchild) - avl_height((*pp_node)->leftchild)) == 2) { if((*pp_node)->rightchild->data < number) { (*pp_node) = single_rotation_with_left(*pp_node); } else if((*pp_node)->rightchild->data > number) { (*pp_node) = double_rotation_with_left(*pp_node); } } } return (*pp_node); }double_rotation_with_left.c
/****************************************************************************** code writer : EOF code date : 2014.03.01 e-mail : [email protected] code purpose : implementation of function double_rotation_with_left If something could be changed into a situation, please touch me. Thank you! *******************************************************************************/ #include "avl_tree.h" #include "stdio.h" struct node* double_rotation_with_left(struct node* p_node) { struct node* temp = NULL; p_node = single_rotation_with_left(p_node); return single_rotation_with_right(p_node); }
double_rotation_with_right.c
/************************************************************************************ code writer : EOF code date : 2014.03.01 e-mail : [email protected] code purpose : implementation of function double_rotation_with_right If something could be changed into a better situation, please touch me. Thank you! **********************************************************************************/ #include "avl_tree.h" struct node* double_rotation_with_right(struct node* p_node) { p_node = single_rotation_with_right(p_node); return single_rotation_with_left(p_node); }single_rotation_with_left.c
/********************************************************************* code writer: EOF code date: 2014.02.28 e-mail: [email protected] code purpose: implementation of function single_rotation_with_left If something could be changed into better situation, please touche me by e-mail **********************************************************************/ #include "avl_tree.h" struct node* single_rotation_with_left(struct node* p_node) { //when there are only three nodes in the tree, we make the middile node -- *p_node as the root-node. struct node* temp = p_node->rightchild; p_node->rightchild = temp->leftchild; temp->leftchild = p_node; p_node->height = (avl_height(p_node->rightchild) > avl_height(p_node->leftchild) ?\ avl_height(p_node->rightchild) : avl_height(p_node->leftchild))+1; temp->height = (avl_height(temp->rightchild) > avl_height(temp->leftchild) ?\ avl_height(temp->rightchild) : avl_height(temp->leftchild))+1; return temp;//new root }single_rotation_with_right.c
/********************************************************************************************* code writer : EOF code date : 2014.03.01 e-mail : [email protected] code purpose : implementation of function single_rotation_with_right If something could be changed into a better situation, please touch me. Thank you! *********************************************************************************************/ #include "avl_tree.h" struct node* single_rotation_with_right(struct node* p_node) { struct node* temp; temp = p_node->leftchild; p_node->leftchild = temp->rightchild; temp->rightchild = p_node; p_node->height = (avl_height(p_node->rightchild) > avl_height(p_node->leftchild) ? \ avl_height(p_node->rightchild) : avl_height(p_node->leftchild))+1; temp->height = (avl_height(temp->leftchild) > avl_height(temp->rightchild) ? \ avl_height(temp->leftchild) : avl_height(temp->rightchild))+1; return temp; }
print_tree.c
/******************************************************************************* * code writer: EOF * Date : 2014.02.20 * code purpose: This code is the definition for function -- print_tree *e-mail:[email protected] If there somthing wrong with my code, please touch me by e-mail.Thank you! *****************************************************************************/ #include "avl_tree.h" #include "stdio.h" int print_tree(struct node* p_node)// use recursion to print out the data in the binary tree { // print the left side of the binary tree if((p_node->leftchild) != NULL) { print_tree(p_node->leftchild); } printf("%d\n",p_node->data); // print the right side of the binary tree if((p_node->rightchild) != NULL) { print_tree(p_node->rightchild); } //printf("%d\n",p_node->data); we don't need this }
I don't want to show all the header files. It is meaningless. But here is a simple model：
#ifndef _SINGLE_ROTATION_WITH_LEFT_H #define _SINGLE_ROTATION_WITH_LEFT_H 1 extern struct node* single_rotation_with_left(struct node* p_node); #endifNamely, every source file has their own header file.
AVL- tree is here.