Two-Three Tree
定义接口
树接口
interface TTTree<K : Comparable<K>, V> : KVOperation<K, V>, DataStructurePrintable {
fun getRoot(): TTNode<K, V>?
/**
* 中序遍历
*/
fun inorder(action: (K, V) -> Unit)
}
节点定义
class TTNode<K : Comparable<K>, V> {
var parent: TTNode<K, V>? = null
val keys = mutableListOf<KVPair<K, V>>()
val children = mutableListOf<TTNode<K, V>>()
fun isLeaf(): Boolean = children.isEmpty()
fun isTwoNode(): Boolean = keys.size == 1
fun isThreeNode(): Boolean = keys.size == 2
}
data class KVPair<K, V>(val key: K, val value: V) {
override fun toString(): String = "($key, $value)"
}
二三树的实现
class TTTreeImpl<K : Comparable<K>, V> : TTTree<K, V> {
companion object {
val log = getLogger(TTTreeImpl::class.java)
}
private var root: TTNode<K, V>? = null
private var count = 0
override fun getRoot(): TTNode<K, V>? = this.root
override fun size(): Int = this.count
override fun contains(key: K): Boolean = get(key) != null
override fun get(key: K): V? {
return get(this.root, key)
}
private fun get(node: TTNode<K, V>?, key: K): V? {
if (node == null) return null
if (node.isTwoNode()) {
return when {
key < node.keys[0].key -> get(node.children[0], key)
key == node.keys[0].key -> node.keys[0].value
else -> get(node.children[1], key)
}
} else if (node.isThreeNode()) {
return when {
key < node.keys[0].key -> get(node.children[0], key)
key == node.keys[0].key -> node.keys[0].value
key < node.keys[1].key -> get(node.children[1], key)
key == node.keys[1].key -> node.keys[1].value
else -> get(node.children[2], key)
}
} else {
throw IllegalStateException("Invalid Node")
}
}
override fun insert(key: K, value: V) {
if (this.root == null) {
this.root = TTNode<K, V>().apply { add(key, value) }
this.count++
return
}
findLeaf(this.root!!, key, value)?.apply {
// 不为空，说明没有替换值，添加新键值对
this.add(key, value)
count++
// 如果当前节点的键值对数量超过2，进行分裂
if (this.keys.size > 2) {
splitAndRebalance(this)
}
}
}
private fun TTNode<K, V>.add(key: K, value: V) {
when {
keys.isEmpty() || key < keys[0].key -> keys.add(0, KVPair(key, value))
keys.size == 1 || key < keys[1].key -> keys.add(1, KVPair(key, value))
else -> keys.add(2, KVPair(key, value))
}
}
// 如果在查找叶子节点的过程中发现值相同，替换值返回null
private fun findLeaf(node: TTNode<K, V>, key: K, value: V): TTNode<K, V>? {
var current = node
while (!current.isLeaf()) {
when {
current.isTwoNode() ->
when {
key < current.keys[0].key -> current = current.children[0]
key == current.keys[0].key -> {
current.keys[0] = KVPair(key, value)
return null // 替换值返回null
}
else -> current = current.children[1]
}
current.isThreeNode() ->
when {
key < current.keys[0].key -> current = current.children[0]
key == current.keys[0].key -> {
current.keys[0] = KVPair(key, value)
return null // 替换值返回null
}
key < current.keys[1].key -> current = current.children[1]
key == current.keys[1].key -> {
current.keys[1] = KVPair(key, value)
return null // 替换值返回null
}
else -> current = current.children[2]
}
else -> throw IllegalStateException("Invalid Node")
}
}
return current
}
// 一定是3节点分裂
private fun splitAndRebalance(node: TTNode<K, V>) {
log.debug("split and rebalance node: [${node.keys.map { it -> it.key }.joinToString(" ")}]")
/*
case1:
x y z y
/ \
x z
case2:
x y z y
/ | \ \ / \
a b c d x z
/ \ / \
a b c d
*/
val midKV = node.keys[1]
// 创建两个新节点
val leftNode = TTNode<K, V>()
val rightNode = TTNode<K, V>()
leftNode.add(node.keys[0].key, node.keys[0].value)
rightNode.add(node.keys[2].key, node.keys[2].value)
// 向上递归会遇到叶子节点
if (!node.isLeaf()) {
// 子节点重新分配
// 左子节点包含原节点的前两个子节点
// 右子节点包含原节点的后两个子节点
leftNode.children.addAll(listOf(node.children[0], node.children[1]))
rightNode.children.addAll(listOf(node.children[2], node.children[3]))
// 设置子节点的父节点
leftNode.children.forEach { it.parent = leftNode }
rightNode.children.forEach { it.parent = rightNode }
}
val curParent = node.parent
if (curParent == null) {
this.root = TTNode<K, V>().apply {
this.add(midKV.key, midKV.value)
this.children.add(leftNode)
this.children.add(rightNode)
}
// parent指向的形成
leftNode.parent = this.root
rightNode.parent = this.root
} else {
val index = curParent.children.indexOf(node)
curParent.children.removeAt(index)
// 这里parent可能会形成4节点
curParent.children.add(index, rightNode)
curParent.children.add(index, leftNode)
leftNode.parent = curParent
rightNode.parent = curParent
curParent.add(midKV.key, midKV.value)
if (curParent.keys.size > 2) {
splitAndRebalance(curParent)
}
}
}
override fun remove(key: K): V? {
TODO("Not yet implemented")
}
override fun inorder(action: (K, V) -> Unit) {
inorder(this.root, action)
}
private fun inorder(node: TTNode<K, V>?, action: (K, V) -> Unit) {
if (node == null) return
when {
node.isLeaf() -> node.keys.forEach { action(it.key, it.value) }
node.isTwoNode() -> {
val left = node.children[0]
val right = node.children[1]
inorder(left, action)
node.keys.forEach { action(it.key, it.value) }
inorder(right, action)
}
node.isThreeNode() -> {
val left = node.children[0]
val middle = node.children[1]
val right = node.children[2]
inorder(left, action)
action(node.keys[0].key, node.keys[0].value)
inorder(middle, action)
action(node.keys[1].key, node.keys[1].value)
inorder(right, action)
}
else -> throw IllegalStateException("Invalid Node")
}
}
override fun clear() {
this.root == null
this.count = 0
}
override fun print() {
if (this.root == null) return println("Empty Tree")
println("2-3 Tree Structure:")
printTreeHelper(root, "", true)
}
private fun printTreeHelper(node: TTNode<K, V>?, prefix: String, isLast: Boolean) {
if (node == null) return
// 打印当前节点
val connector = if (isLast) "└── " else "├── "
val nodeContent = if (node.keys.isEmpty()) "[]" else node.keys.joinToString(", ") { "${it.key}" }
println("$prefix$connector$nodeContent")
// 如果不是叶子节点，递归打印子节点
if (!node.isLeaf()) {
val childPrefix = prefix + if (isLast) " " else "│ "
for (i in node.children.indices) {
val isLastChild = (i == node.children.size - 1)
printTreeHelper(node.children[i], childPrefix, isLastChild)
}
}
}
}
27 January 2026