wip rbtree

1 files changed, 421 insertions, 0 deletions

diff --git a/pkg/rbtree/rbtree.go b/pkg/rbtree/rbtree.go
new file mode 100644
index 0000000..d9249c8
--- /dev/null
+++ b/pkg/rbtree/rbtree.go
@@ -0,0 +1,421 @@
+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]) Delete(key K) {
+	nodeToDelete := t.Lookup(key)
+	if nodeToDelete == nil {
+		return
+	}
+
+	needsFixup := nodeToDelete.getColor() == Black
+
+	var nodeToFixup *Node[V]
+	switch {
+	case nodeToDelete.Left == nil:
+		nodeToFixup = nodeToDelete.Right
+		if nodeToDelete.Right != nil {
+			nodeToDelete.Right.Parent = nodeToDelete.Parent
+		}
+		*t.parentChild(nodeToDelete) = nodeToDelete.Right
+	case nodeToDelete.Right == nil:
+		nodeToFixup = nodeToDelete.Left
+		if nodeToDelete.Left != nil {
+			nodeToDelete.Left.Parent = nodeToDelete.Parent
+		}
+		*t.parentChild(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()
+		needsFixup = next.getColor() == Black
+		if next.Parent != nodeToDelete {
+			if next.Right != nil {
+				next.Right.Parent = next.Parent
+			}
+			*t.parentChild(next) = next.Right
+
+			next.Right = nodeToDelete.Right
+			next.Right.Parent = next
+		}
+		next.Parent = nodeToDelete.Parent
+		*t.parentChild(nodeToDelete) = next
+		next.Left = nodeToDelete.Left
+		next.Left.Parent = next
+		next.Color = nodeToDelete.Color
+	}
+
+	if needsFixup {
+		node := nodeToFixup
+		for node != nil && node != t.root && node.getColor() == Black {
+			if node == node.Parent.Left {
+				sibling := node.Parent.Right
+				if sibling.getColor() == Red {
+					sibling.Color = Black
+					node.Parent.Color = Red
+					t.leftRotate(node.Parent)
+					sibling = node.Parent.Right
+				}
+				if sibling.Left.getColor() == Black && sibling.Right.getColor() == Black {
+					sibling.Color = Red
+					node = node.Parent
+				} else {
+					if sibling.Right.getColor() == Black {
+						sibling.Left.Color = Black
+						sibling.Color = Red
+						t.rightRotate(sibling)
+						sibling = node.Parent.Right
+					}
+					sibling.Color = node.Parent.Color
+					node.Parent.Color = Black
+					sibling.Right.Color = Black
+					t.leftRotate(node.Parent)
+					node = t.root
+				}
+			} else {
+				sibling := node.Parent.Left
+				if sibling.getColor() == Red {
+					sibling.Color = Black
+					node.Parent.Color = Red
+					t.rightRotate(node.Parent)
+					sibling = node.Parent.Left
+				}
+				if sibling.Right.getColor() == Black && sibling.Left.getColor() == Black {
+					sibling.Color = Red
+					node = node.Parent
+				} else {
+					if sibling.Left.getColor() == Black {
+						sibling.Right.Color = Black
+						sibling.Color = Red
+						t.leftRotate(sibling)
+						sibling = node.Parent.Left
+					}
+					sibling.Color = node.Parent.Color
+					node.Parent.Color = Black
+					sibling.Left.Color = Black
+					t.rightRotate(node.Parent)
+					node = t.root
+				}
+			}
+		}
+		if node != nil {
+			node.Color = Black
+		}
+	}
+}