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// Derived from https://github.com/vadimg/js_bintrees. MIT Licensed.
import { assert } from "./util.ts";
class RBNode<T> {
public left: this | null;
public right: this | null;
public red: boolean;
constructor(public data: T) {
this.left = null;
this.right = null;
this.red = true;
}
getChild(dir: boolean | number): this | null {
return dir ? this.right : this.left;
}
setChild(dir: boolean | number, val: this | null): void {
if (dir) {
this.right = val;
} else {
this.left = val;
}
}
}
export class RBTree<T> {
#comparator: (a: T, b: T) => number;
#root: RBNode<T> | null;
constructor(comparator: (a: T, b: T) => number) {
this.#comparator = comparator;
this.#root = null;
}
/** Returns `null` if tree is empty. */
min(): T | null {
let res = this.#root;
if (res === null) {
return null;
}
while (res.left !== null) {
res = res.left;
}
return res.data;
}
/** Returns node `data` if found, `null` otherwise. */
find(data: T): T | null {
let res = this.#root;
while (res !== null) {
const c = this.#comparator(data, res.data);
if (c === 0) {
return res.data;
} else {
res = res.getChild(c > 0);
}
}
return null;
}
/** returns `true` if inserted, `false` if duplicate. */
insert(data: T): boolean {
let ret = false;
if (this.#root === null) {
// empty tree
this.#root = new RBNode(data);
ret = true;
} else {
const head = new RBNode((null as unknown) as T); // fake tree root
let dir = 0;
let last = 0;
// setup
let gp = null; // grandparent
let ggp = head; // grand-grand-parent
let p: RBNode<T> | null = null; // parent
let node: RBNode<T> | null = this.#root;
ggp.right = this.#root;
// search down
while (true) {
if (node === null) {
// insert new node at the bottom
node = new RBNode(data);
p!.setChild(dir, node);
ret = true;
} else if (isRed(node.left) && isRed(node.right)) {
// color flip
node.red = true;
node.left!.red = false;
node.right!.red = false;
}
// fix red violation
if (isRed(node) && isRed(p)) {
const dir2 = ggp.right === gp;
assert(gp);
if (node === p!.getChild(last)) {
ggp.setChild(dir2, singleRotate(gp, !last));
} else {
ggp.setChild(dir2, doubleRotate(gp, !last));
}
}
const cmp = this.#comparator(node.data, data);
// stop if found
if (cmp === 0) {
break;
}
last = dir;
dir = Number(cmp < 0); // Fix type
// update helpers
if (gp !== null) {
ggp = gp;
}
gp = p;
p = node;
node = node.getChild(dir);
}
// update root
this.#root = head.right;
}
// make root black
this.#root!.red = false;
return ret;
}
/** Returns `true` if removed, `false` if not found. */
remove(data: T): boolean {
if (this.#root === null) {
return false;
}
const head = new RBNode((null as unknown) as T); // fake tree root
let node = head;
node.right = this.#root;
let p = null; // parent
let gp = null; // grand parent
let found = null; // found item
let dir: boolean | number = 1;
while (node.getChild(dir) !== null) {
const last = dir;
// update helpers
gp = p;
p = node;
node = node.getChild(dir)!;
const cmp = this.#comparator(data, node.data);
dir = cmp > 0;
// save found node
if (cmp === 0) {
found = node;
}
// push the red node down
if (!isRed(node) && !isRed(node.getChild(dir))) {
if (isRed(node.getChild(!dir))) {
const sr = singleRotate(node, dir);
p.setChild(last, sr);
p = sr;
} else if (!isRed(node.getChild(!dir))) {
const sibling = p.getChild(!last);
if (sibling !== null) {
if (
!isRed(sibling.getChild(!last)) &&
!isRed(sibling.getChild(last))
) {
// color flip
p.red = false;
sibling.red = true;
node.red = true;
} else {
assert(gp);
const dir2 = gp.right === p;
if (isRed(sibling.getChild(last))) {
gp!.setChild(dir2, doubleRotate(p, last));
} else if (isRed(sibling.getChild(!last))) {
gp!.setChild(dir2, singleRotate(p, last));
}
// ensure correct coloring
const gpc = gp.getChild(dir2);
assert(gpc);
gpc.red = true;
node.red = true;
assert(gpc.left);
gpc.left.red = false;
assert(gpc.right);
gpc.right.red = false;
}
}
}
}
}
// replace and remove if found
if (found !== null) {
found.data = node.data;
assert(p);
p.setChild(p.right === node, node.getChild(node.left === null));
}
// update root and make it black
this.#root = head.right;
if (this.#root !== null) {
this.#root.red = false;
}
return found !== null;
}
}
function isRed<T>(node: RBNode<T> | null): boolean {
return node !== null && node.red;
}
function singleRotate<T>(root: RBNode<T>, dir: boolean | number): RBNode<T> {
const save = root.getChild(!dir);
assert(save);
root.setChild(!dir, save.getChild(dir));
save.setChild(dir, root);
root.red = true;
save.red = false;
return save;
}
function doubleRotate<T>(root: RBNode<T>, dir: boolean | number): RBNode<T> {
root.setChild(!dir, singleRotate(root.getChild(!dir)!, !dir));
return singleRotate(root, dir);
}
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