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|
package rbtree
import (
"fmt"
"golang.org/x/exp/constraints"
)
type Color bool
const (
Black = Color(false)
Red = Color(true)
)
type Node[V any] struct {
Parent, Left, Right *Node[V]
Color Color
Value V
}
func (node *Node[V]) getColor() Color {
if node == nil {
return Black
}
return node.Color
}
type Tree[K constraints.Ordered, V any] struct {
KeyFn func(V) K
root *Node[V]
}
func (t *Tree[K, V]) Walk(fn func(*Node[V])) {
t.root.walk(fn)
}
func (node *Node[V]) walk(fn func(*Node[V])) {
if node == nil {
return
}
node.Left.walk(fn)
fn(node)
node.Right.walk(fn)
}
// Search the tree for a value that satisfied the given callbackk
// function. A return value of 0 means to to return this value; <0
// means to go left on the tree (the value is too high), >0 means to
// go right on th etree (the value is too low).
//
// +-----+
// | v=8 | == 0 : this is it
// +-----+
// / \
// / \
// <0 : go left >0 : go right
// / \
// +---+ +---+
// | 7 | | 9 |
// +---+ +---+
//
// Returns nil if no such value is found.
//
// Search is good for advanced lookup, like when a range of values is
// acceptable. For simple exact-value lookup, use Lookup.
func (t *Tree[K, V]) Search(fn func(V) int) *Node[V] {
ret, _ := t.root.search(fn)
return ret
}
func (node *Node[V]) search(fn func(V) int) (exact, nearest *Node[V]) {
var prev *Node[V]
for {
if node == nil {
return nil, prev
}
direction := fn(node.Value)
prev = node
switch {
case direction < 0:
node = node.Left
case direction == 0:
return node, nil
case direction > 0:
node = node.Right
}
}
}
func (t *Tree[K, V]) exactKey(key K) func(V) int {
return func(val V) int {
valKey := t.KeyFn(val)
switch {
case key < valKey:
return -1
case key > valKey:
return 1
default: // key == valKey:
return 0
}
}
}
// Lookup looks up the value for an exact key. If no such value
// exists, nil is returned.
func (t *Tree[K, V]) Lookup(key K) *Node[V] {
return t.Search(t.exactKey(key))
}
// Min returns the minimum value stored in the tree, or nil if the
// tree is empty.
func (t *Tree[K, V]) Min() *Node[V] {
return t.root.min()
}
func (node *Node[V]) min() *Node[V] {
if node == nil {
return nil
}
for {
if node.Left == nil {
return node
}
node = node.Left
}
}
// Max returns the maximum value stored in the tree, or nil if the
// tree is empty.
func (t *Tree[K, V]) Max() *Node[V] {
return t.root.max()
}
func (node *Node[V]) max() *Node[V] {
if node == nil {
return nil
}
for {
if node.Right == nil {
return node
}
node = node.Right
}
}
func (t *Tree[K, V]) Next(cur *Node[V]) *Node[V] {
return cur.next()
}
func (cur *Node[V]) next() *Node[V] {
if cur.Right != nil {
return cur.Right.min()
}
child, parent := cur, cur.Parent
for parent != nil && child == parent.Right {
child, parent = parent, parent.Parent
}
return parent
}
func (t *Tree[K, V]) Prev(cur *Node[V]) *Node[V] {
return cur.prev()
}
func (cur *Node[V]) prev() *Node[V] {
if cur.Left != nil {
return cur.Left.max()
}
child, parent := cur, cur.Parent
for parent != nil && child == parent.Left {
child, parent = parent, parent.Parent
}
return parent
}
func (t *Tree[K, V]) parentChild(node *Node[V]) **Node[V] {
switch {
case node.Parent == nil:
return &t.root
case node.Parent.Left == node:
return &node.Parent.Left
case node.Parent.Right == node:
return &node.Parent.Right
default:
panic(fmt.Errorf("node %p is not a child of its parent %p", node, node.Parent))
}
}
func (t *Tree[K, V]) leftRotate(x *Node[V]) {
// p p
// | |
// +---+ +---+
// | x | | y |
// +---+ +---+
// / \ => / \
// a +---+ +---+ c
// | y | | x |
// +---+ +---+
// / \ / \
// b c a b
// Define 'p', 'x', 'y', and 'b' per the above diagram.
p := x.Parent
pChild := t.parentChild(x)
y := x.Right
b := y.Left
// Move things around
y.Parent = p
*pChild = y
x.Parent = y
y.Left = x
if b != nil {
b.Parent = x
}
x.Right = b
}
func (t *Tree[K, V]) rightRotate(y *Node[V]) {
// | |
// +---+ +---+
// | y | | x |
// +---+ +---+
// / \ => / \
// +---+ c a +---+
// | x | | y |
// +---+ +---+
// / \ / \
// a b b c
// Define 'p', 'x', 'y', and 'b' per the above diagram.
p := y.Parent
pChild := t.parentChild(y)
x := y.Left
b := x.Right
// Move things around
x.Parent = p
*pChild = x
y.Parent = x
x.Right = y
if b != nil {
b.Parent = y
}
y.Left = b
}
func (t *Tree[K, V]) Insert(val V) {
// Naive-insert
key := t.KeyFn(val)
exact, parent := t.root.search(t.exactKey(key))
if exact != nil {
exact.Value = val
return
}
node := &Node[V]{
Color: Red,
Parent: parent,
Value: val,
}
if parent == nil {
t.root = node
} else if key < t.KeyFn(parent.Value) {
parent.Left = node
} else {
parent.Right = node
}
// Re-balance
for node.Parent.getColor() == Red {
if node.Parent == node.Parent.Parent.Left {
uncle := node.Parent.Parent.Right
if uncle.getColor() == Red {
node.Parent.Color = Black
uncle.Color = Black
node.Parent.Parent.Color = Red
node = node.Parent.Parent
} else {
if node == node.Parent.Right {
node = node.Parent
t.leftRotate(node)
}
node.Parent.Color = Black
node.Parent.Parent.Color = Red
t.rightRotate(node.Parent.Parent)
}
} else {
uncle := node.Parent.Parent.Left
if uncle.getColor() == Red {
node.Parent.Color = Black
uncle.Color = Black
node.Parent.Parent.Color = Red
node = node.Parent.Parent
} else {
if node == node.Parent.Left {
node = node.Parent
t.rightRotate(node)
}
node.Parent.Color = Black
node.Parent.Parent.Color = Red
t.leftRotate(node.Parent.Parent)
}
}
}
t.root.Color = Black
}
func (t *Tree[K, V]) transplant(old, new *Node[V]) {
*t.parentChild(old) = new
if new != nil {
new.Parent = old.Parent
}
}
func (t *Tree[K, V]) Delete(key K) {
nodeToDelete := t.Lookup(key)
if nodeToDelete == nil {
return
}
var nodeToRebalance, nodeToRebalanceParent *Node[V]
needsRebalance := nodeToDelete.Color == Black
switch {
case nodeToDelete.Left == nil:
nodeToRebalance = nodeToDelete.Right
nodeToRebalanceParent = nodeToDelete.Parent
t.transplant(nodeToDelete, nodeToDelete.Right)
case nodeToDelete.Right == nil:
nodeToRebalance = nodeToDelete.Left
nodeToRebalanceParent = nodeToDelete.Parent
t.transplant(nodeToDelete, nodeToDelete.Left)
default:
// The node being deleted has a child on both sides,
// so we've go to reshuffle the parents a bit to make
// room for those children.
next := nodeToDelete.next()
if next.Parent == nodeToDelete {
// p p
// | |
// +-----+ +-----+
// | ntd | | nxt |
// +-----+ +-----+
// / \ => / \
// a +-----+ a b
// | nxt |
// +-----+
// / \
// nil b
nodeToRebalance = next.Right
nodeToRebalanceParent = next
*t.parentChild(nodeToDelete) = next
next.Parent = nodeToDelete.Parent
next.Left = nodeToDelete.Left
next.Left.Parent = next
} else {
// p p
// | |
// +-----+ +-----+
// | ntd | | nxt |
// +-----+ +-----+
// / \ / \
// a x a x
// / \ => / \
// y z y z
// / \ / \
// +-----+ c b c
// | nxt |
// +-----+
// / \
// nil b
y := next.Parent
b := next.Right
nodeToRebalance = b
nodeToRebalanceParent = y
*t.parentChild(nodeToDelete) = next
next.Parent = nodeToDelete.Parent
next.Left = nodeToDelete.Left
next.Left.Parent = next
next.Right = nodeToDelete.Right
next.Right.Parent = next
y.Left = b
if b != nil {
b.Parent = y
}
}
// idk
needsRebalance = next.Color == Black
next.Color = nodeToDelete.Color
}
if needsRebalance {
node := nodeToRebalance
nodeParent := nodeToRebalanceParent // in case 'node' is nil, which it can be
for node != t.root && node.getColor() == Black {
if node == nodeParent.Left {
sibling := nodeParent.Right
if sibling.getColor() == Red {
sibling.Color = Black
nodeParent.Color = Red
t.leftRotate(nodeParent)
sibling = nodeParent.Right
}
if sibling.Left.getColor() == Black && sibling.Right.getColor() == Black {
sibling.Color = Red
node, nodeParent = nodeParent, nodeParent.Parent
} else {
if sibling.Right.getColor() == Black {
sibling.Left.Color = Black
sibling.Color = Red
t.rightRotate(sibling)
sibling = nodeParent.Right
}
sibling.Color = nodeParent.Color
nodeParent.Color = Black
sibling.Right.Color = Black
t.leftRotate(nodeParent)
node, nodeParent = t.root, nil
}
} else {
sibling := nodeParent.Left
if sibling.getColor() == Red {
sibling.Color = Black
nodeParent.Color = Red
t.rightRotate(nodeParent)
sibling = nodeParent.Left
}
if sibling.Right.getColor() == Black && sibling.Left.getColor() == Black {
sibling.Color = Red
node, nodeParent = nodeParent, nodeParent.Parent
} else {
if sibling.Left.getColor() == Black {
sibling.Right.Color = Black
sibling.Color = Red
t.leftRotate(sibling)
sibling = nodeParent.Left
}
sibling.Color = nodeParent.Color
nodeParent.Color = Black
sibling.Left.Color = Black
t.rightRotate(nodeParent)
node, nodeParent = t.root, nil
}
}
}
if node != nil {
node.Color = Black
}
}
}
|