Adelson, Velski, and Landis pioneered the AVL tree data structure and hence it is named after them.

The AVL tree consists of height adjusting binary search trees. The balance factor is obtained by finding the difference between the heights of the left and right sub-trees.

Golang AVL Tree with Example

Let's create a file named "avl_tree.go" and add the following source code to it:

package main

// importing fmt package
import (
	"encoding/json"
	"fmt"
)

// KeyValue type
type KeyValue interface {
	LessThan(KeyValue) bool
	EqualTo(KeyValue) bool
}

// TreeNode class
type TreeNode struct {
	KeyValue     KeyValue
	BalanceValue int
	LinkedNodes  [2]*TreeNode
}

//opposite method
func opposite(nodeValue int) int {
	return 1 - nodeValue
}

// single rotation method
func singleRotation(rootNode *TreeNode, nodeValue int) *TreeNode {

	var saveNode *TreeNode
	saveNode = rootNode.LinkedNodes[opposite(nodeValue)]
	rootNode.LinkedNodes[opposite(nodeValue)] = saveNode.LinkedNodes[nodeValue]
	saveNode.LinkedNodes[nodeValue] = rootNode
	return saveNode
}

// double rotation method
func doubleRotation(rootNode *TreeNode, nodeValue int) *TreeNode {

	var saveNode *TreeNode
	saveNode = rootNode.LinkedNodes[opposite(nodeValue)].LinkedNodes[nodeValue]

	rootNode.LinkedNodes[opposite(nodeValue)].LinkedNodes[nodeValue] = saveNode.LinkedNodes[opposite(nodeValue)]
	saveNode.LinkedNodes[opposite(nodeValue)] = rootNode.LinkedNodes[opposite(nodeValue)]
	rootNode.LinkedNodes[opposite(nodeValue)] = saveNode

	saveNode = rootNode.LinkedNodes[opposite(nodeValue)]
	rootNode.LinkedNodes[opposite(nodeValue)] = saveNode.LinkedNodes[nodeValue]
	saveNode.LinkedNodes[nodeValue] = rootNode
	return saveNode
}

// adjust balance method
func adjustBalance(rootNode *TreeNode, nodeValue int, balanceValue int) {

	var node *TreeNode
	node = rootNode.LinkedNodes[nodeValue]
	var oppNode *TreeNode
	oppNode = node.LinkedNodes[opposite(nodeValue)]
	switch oppNode.BalanceValue {
	case 0:
		rootNode.BalanceValue = 0
		node.BalanceValue = 0
	case balanceValue:
		rootNode.BalanceValue = -balanceValue
		node.BalanceValue = 0
	default:
		rootNode.BalanceValue = 0
		node.BalanceValue = balanceValue
	}
	oppNode.BalanceValue = 0
}

// balanceTree method
func BalanceTree(rootNode *TreeNode, nodeValue int) *TreeNode {
	var node *TreeNode
	node = rootNode.LinkedNodes[nodeValue]
	var balance int
	balance = 2*nodeValue - 1
	if node.BalanceValue == balance {
		rootNode.BalanceValue = 0
		node.BalanceValue = 0
		return singleRotation(rootNode, opposite(nodeValue))
	}
	adjustBalance(rootNode, nodeValue, balance)
	return doubleRotation(rootNode, opposite(nodeValue))
}

//insertRNode method
func insertRNode(rootNode *TreeNode, key KeyValue) (*TreeNode, bool) {
	if rootNode == nil {
		return &TreeNode{KeyValue: key}, false
	}
	var dir int
	dir = 0
	if rootNode.KeyValue.LessThan(key) {
		dir = 1
	}
	var done bool
	rootNode.LinkedNodes[dir], done = insertRNode(rootNode.LinkedNodes[dir], key)
	if done {
		return rootNode, true
	}
	rootNode.BalanceValue = rootNode.BalanceValue + (2*dir - 1)
	switch rootNode.BalanceValue {
	case 0:
		return rootNode, true
	case 1, -1:
		return rootNode, false
	}
	return BalanceTree(rootNode, dir), true
}

// InsertNode method
func InsertNode(treeNode **TreeNode, key KeyValue) {
	*treeNode, _ = insertRNode(*treeNode, key)
}

// RemoveNode method
func RemoveNode(treeNode **TreeNode, key KeyValue) {
	*treeNode, _ = removeRNode(*treeNode, key)
}

// removeBalance method
func removeBalance(rootNode *TreeNode, nodeValue int) (*TreeNode, bool) {
	var node *TreeNode
	node = rootNode.LinkedNodes[opposite(nodeValue)]
	var balance int
	balance = 2*nodeValue - 1
	switch node.BalanceValue {
	case -balance:
		rootNode.BalanceValue = 0
		node.BalanceValue = 0
		return singleRotation(rootNode, nodeValue), false
	case balance:
		adjustBalance(rootNode, opposite(nodeValue), -balance)
		return doubleRotation(rootNode, nodeValue), false
	}
	rootNode.BalanceValue = -balance
	node.BalanceValue = balance
	return singleRotation(rootNode, nodeValue), true
}
// removeRNode method
func removeRNode(rootNode *TreeNode, key KeyValue) (*TreeNode, bool) {
	if rootNode == nil {
		return nil, false
	}
	if rootNode.KeyValue.EqualTo(key) {
		switch {
		case rootNode.LinkedNodes[0] == nil:
			return rootNode.LinkedNodes[1], false
		case rootNode.LinkedNodes[1] == nil:
			return rootNode.LinkedNodes[0], false
		}
		var heirNode *TreeNode
		heirNode = rootNode.LinkedNodes[0]
		for heirNode.LinkedNodes[1] != nil {
			heirNode = heirNode.LinkedNodes[1]
		}
		rootNode.KeyValue = heirNode.KeyValue
		key = heirNode.KeyValue
	}
	var dir int
	dir = 0
	if rootNode.KeyValue.LessThan(key) {
		dir = 1
	}
	var done bool
	rootNode.LinkedNodes[dir], done = removeRNode(rootNode.LinkedNodes[dir], key)
	if done {
		return rootNode, true
	}
	rootNode.BalanceValue = rootNode.BalanceValue + (1 - 2*dir)
	switch rootNode.BalanceValue {
	case 1, -1:
		return rootNode, true
	case 0:
		return rootNode, false
	}
	return removeBalance(rootNode, dir)
}

type integerKey int

func (k integerKey) LessThan(k1 KeyValue) bool { return k < k1.(integerKey) }
func (k integerKey) EqualTo(k1 KeyValue) bool  { return k == k1.(integerKey) }

//main method
func main() {
	var treeNode *TreeNode
	fmt.Println("Tree is empty")
	var avlTree []byte
	avlTree, _ = json.MarshalIndent(treeNode, "", "   ")
	fmt.Println(string(avlTree))

	fmt.Println("\n Add Tree")
	InsertNode(&treeNode, integerKey(5))
	InsertNode(&treeNode, integerKey(3))
	InsertNode(&treeNode, integerKey(8))
	InsertNode(&treeNode, integerKey(7))
	InsertNode(&treeNode, integerKey(6))
	InsertNode(&treeNode, integerKey(10))
	avlTree, _ = json.MarshalIndent(treeNode, "", "   ")
	fmt.Println(string(avlTree))

	fmt.Println("\n Delete Tree")
	RemoveNode(&treeNode, integerKey(3))
	RemoveNode(&treeNode, integerKey(7))
	avlTree, _ = json.MarshalIndent(treeNode, "", "   ")
	fmt.Println(string(avlTree))
}

Output:

G:\GoLang\examples>go run avl_tree.go
Tree is empty
null

 Add Tree
{
   "KeyValue": 7,
   "BalanceValue": 0,
   "LinkedNodes": [
      {
         "KeyValue": 5,
         "BalanceValue": 0,
         "LinkedNodes": [
            {
               "KeyValue": 3,
               "BalanceValue": 0,
               "LinkedNodes": [
                  null,
                  null
               ]
            },
            {
               "KeyValue": 6,
               "BalanceValue": 0,
               "LinkedNodes": [
                  null,
                  null
               ]
            }
         ]
      },
      {
         "KeyValue": 8,
         "BalanceValue": 1,
         "LinkedNodes": [
            null,
            {
               "KeyValue": 10,
               "BalanceValue": 0,
               "LinkedNodes": [
                  null,
                  null
               ]
            }
         ]
      }
   ]
}

 Delete Tree
{
   "KeyValue": 6,
   "BalanceValue": 1,
   "LinkedNodes": [
      {
         "KeyValue": 5,
         "BalanceValue": 0,
         "LinkedNodes": [
            null,
            null
         ]
      },
      {
         "KeyValue": 8,
         "BalanceValue": 1,
         "LinkedNodes": [
            null,
            {
               "KeyValue": 10,
               "BalanceValue": 0,
               "LinkedNodes": [
                  null,
                  null
               ]
            }
         ]
      }
   ]
}

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