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| /*!
* Copyright 2018 Ron Buckton
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
// self-balancing AVL-tree for code-point ranges
import * as utils from "./tests/utils";
export class Range {
public readonly start: number;
public readonly end: number;
constructor(start: number, end: number = start) {
Iif (end < start) throw new RangeError("'end' may not come before 'start'");
this.start = start;
this.end = end;
}
public get size() {
return this.end - this.start;
}
public update(start: number, end: number) {
return start === this.start && end === this.end ? this : new Range(start, end);
}
public equals(value: Range) {
return this === value
|| this.start === value.start && this.end === value.end;
}
public contains(value: Range | number) {
return typeof value === "number"
? value >= this.start && value <= this.end
: value.start >= this.start && value.end <= this.end;
}
public clamp(value: number): number;
public clamp(value: Range): Range;
public clamp(value: Range | number): Range | number {
return typeof value === "number"
? Math.min(Math.max(this.start, value), this.end)
: value.update(this.clamp(value.start), this.clamp(value.end));
}
public overlaps(value: Range) {
return this.start <= value.end
&& this.end >= value.start;
}
public union(value: Range | null) {
return value === null
|| value.end < this.start - 1
|| value.start > this.end + 1 ? this :
this.update(Math.min(this.start, value.start), Math.max(this.end, value.end));
}
public intersect(value: Range | null) {
return value === null
|| value.end < this.start
|| value.start > this.end ? null :
this.update(Math.max(this.start, value.start), Math.min(this.end, value.end));
}
}
export class Node {
public readonly range: Range;
public readonly left: Node | null;
public readonly right: Node | null;
public readonly height: number;
public readonly leftmost: Node | null;
public readonly rightmost: Node | null;
constructor(left: Node | null, range: Range, right: Node | null) {
Iif (left !== null && left.max >= range.start - 1) throw new RangeError("Maximum end of left subtree must be less than range start - 1");
Iif (right !== null && right.min <= range.end + 1) throw new RangeError("Minimum start of right subtree must be greater than range end + 1");
this.range = range;
this.left = left;
this.right = right;
this.height = Math.max(height(left), height(right)) + 1;
this.leftmost = leftmost(left);
this.rightmost = rightmost(right);
}
public get min() {
return leftmost(this).range.start;
}
public get max() {
return rightmost(this).range.end;
}
}
function rotateLeft(node: Node) {
return new Node(new Node(node.left, node.range, node.right!.left), node.right!.range, node.right!.right);
}
function rotateRight(node: Node) {
return new Node(node.left!.left, node.left!.range, new Node(node.left!.right, node.range, node.right));
}
export function leftmost(T: Node): Node;
export function leftmost(T: Node | null): Node | null;
export function leftmost(T: Node | null) {
return T && T.leftmost || T;
}
export function rightmost(T: Node): Node;
export function rightmost(T: Node | null): Node | null;
export function rightmost(T: Node | null) {
return T && T.rightmost || T;
}
export function height(T: Node | null): number {
return T === null ? 0 : T.height;
}
function expose(T: Node): [Node | null, Range, Node | null] {
return [T.left, T.range, T.right];
}
export function join(Tl: Node, k: Range | null, Tr: Node | null): Node;
export function join(Tl: Node | null, k: Range, Tr: Node | null): Node;
export function join(Tl: Node | null, k: Range | null, Tr: Node): Node;
export function join(Tl: Node | null, k: Range | null, Tr: Node | null): Node | null;
export function join(Tl: Node | null, k: Range | null, Tr: Node | null): Node | null {
while (true) {
if (k === null) {
// inlined `join2`
if (Tl === null) return Tr;
[Tl, k] = splitLast(Tl);
}
// If `k` is immediately adjacent to the rightmost of Tl or the leftmost of Tr, we will
// merge the range rather than allowing adjacent ranges.
//
// As a result, instead of:
//
// { [1, 2], [3, 4] }
//
// We instead end up with:
//
// { [1, 4] }
//
const Tlmax = rightmost(Tl);
if (Tlmax && Tlmax.range.end === k.start - 1) {
Tl = replace(Tl, Tlmax.range, new Range(Tlmax.range.start, k.end));
k = null;
continue;
}
const Trmin = leftmost(Tr);
if (Trmin && Trmin.range.start === k.end + 1) {
Tr = replace(Tr, Trmin.range, new Range(k.start, Trmin.range.end));
k = null;
continue;
}
Iif (height(Tl) > height(Tr) + 1) return joinRight(Tl!, k, Tr);
Iif (height(Tr) > height(Tl) + 1) return joinLeft(Tl, k, Tr!);
return new Node(Tl, k, Tr);
}
}
function joinRight(Tl: Node, k: Range, Tr: Node | null): Node {
const [l, k_, c] = expose(Tl);
if (height(c) <= height(Tr) + 1) {
const T_ = new Node(c, k, Tr);
if (height(T_) <= height(l) + 1) return new Node(l, k_, T_);
return rotateLeft(new Node(l, k_, rotateRight(T_)));
}
else {
const T_ = joinRight(c!, k, Tr);
const T__ = new Node(l, k_, T_);
if (height(T_) <= height(l) + 1) return T__;
return rotateLeft(T__);
}
}
function joinLeft(Tl: Node | null, k: Range, Tr: Node): Node {
const [c, k_, r] = expose(Tr);
if (height(c) <= height(Tl) + 1) {
const T_ = new Node(Tl, k, c);
if (height(T_) <= height(r) + 1) return new Node(T_, k_, r);
return rotateRight(new Node(rotateLeft(T_), k_, r));
}
else {
const T_ = joinLeft(Tl, k, c!);
const T__ = new Node(T_, k_, r);
if (height(T_) <= height(r) + 1) return T__;
return rotateRight(T__);
}
}
export function split(T: Node | null, k: Range): [Node | null, Range | null, Node | null] {
if (T === null) { // range does not exist
return [null, null, null];
}
let [L, m, R] = expose(T);
if (k.end < m.start) { // k is entirely before m
const [Ll, b, Lr] = split(L, k);
return [Ll, b, join(Lr, m, R)];
}
if (k.start > m.end) { // k is entirely after m
const [Rl, b, Rr] = split(R, k);
return [join(L, m, Rl), b, Rr];
}
if (k.start < m.start) { // k overlaps m.start
L = remove(L, new Range(k.start, m.start - 1));
k = new Range(m.start, k.end);
}
if (k.end > m.end) { // k overlaps m.end
R = remove(R, new Range(m.end + 1, k.end));
k = new Range(k.start, m.end);
}
if (m.start < k.start) { // k.start bisects m
L = insert(L, new Range(m.start, k.start - 1));
m = new Range(k.start, m.end);
}
if (m.end > k.end) { // k.end bisects m
R = insert(R, new Range(k.end + 1, m.end));
m = new Range(m.start, k.end);
}
return [L, m, R];
}
function splitLast(T: Node): [Node | null, Range] {
const [L, k, R] = expose(T);
if (R === null) return [L, k];
const [T_, k_] = splitLast(R);
return [join(L, k, T_), k_];
}
export function search(T: Node | null, k: number): Node | null {
return T === null ? null :
k < T.range.start ? search(T.left, k) :
k > T.range.end ? search(T.right, k) :
T;
}
export function insert(T: Node | null, k: Range) {
const [Tl, , Tr] = split(T, k);
return join(Tl, k, Tr);
}
export function remove(T: Node | null, k: Range) {
const [Tl, , Tr] = split(T, k);
return join(Tl, null, Tr);
}
function replace(T: Node | null, k1: Range, k2: Range) {
const [Tl, , Tr] = split(T, k1);
return join(Tl, k2, Tr);
}
export function union(T1: Node | null, T2: Node | null): Node | null {
if (T1 === null) return T2;
if (T2 === null) return T1;
const [L2, k2, R2] = expose(T2);
const [L1, k1, R1] = split(T1, k2);
// If JS supported parallelism, the next two statements could
// be safely run in parallel.
const Tl = union(L1, L2);
const Tr = union(R1, R2);
return join(Tl, k2.union(k1), Tr);
}
function slice(T: Node | null, k: Range) {
const [,,Tr] = split(T, new Range(k.start - 1));
const [Trl] = split(Tr, new Range(k.end + 1));
return Trl;
}
export function intersect(T1: Node | null, T2: Node | null): Node | null {
if (T1 === null) return null;
if (T2 === null) return null;
const [L2, k2, R2] = expose(T2);
const [L1, k1, R1] = split(T1, k2);
// If JS supported parallelism, the next two statements could
// be safely run in parallel.
const Tl = intersect(L1, L2);
const Tr = intersect(R1, R2);
const Tm = slice(T1, k2);
return join(join(Tl, null, Tm), null, Tr);
}
export function difference(T1: Node | null, T2: Node | null): Node | null {
if (T1 === null) return null;
if (T2 === null) return T1;
const [L2, k2, R2] = expose(T2);
const [L1, , R1] = split(T1, k2);
// If JS supported parallelism, the next two statements could
// be safely run in parallel.
const Tl = difference(L1, L2);
const Tr = difference(R1, R2);
return join(Tl, null, Tr);
}
export function invert(T: Node | null, k: Range) {
return difference(new Node(null, k, null), T);
}
export function deserialize(array: ReadonlyArray<number>, bounds: Range = new Range(-Infinity, +Infinity)): Node | null {
Iif (array.length % 2 !== 0) throw new TypeError();
return deserializeRecursive(array, 0, (array.length >> 1) - 1, bounds);
}
function deserializeRecursive(array: ReadonlyArray<number>, start: number, end: number, bounds: Range): Node | null {
if (end < start || start > end) return null;
const mid = start + (end - start >> 1);
const index = mid << 1;
const range = new Range(array[index], array[index] + array[index + 1]);
Iif (!bounds.contains(range)) throw new RangeError();
const left = deserializeRecursive(array, start, mid - 1, bounds);
const right = deserializeRecursive(array, mid + 1, end, bounds);
return new Node(left, range, right);
}
export function serialize(T: Node | null): number[] {
const array: number[] = [];
const stack: Node[] = [];
while (T !== null) {
stack.push(T);
T = T.left;
}
while (T = stack.pop() || null) {
array.push(T.range.start, T.range.size);
Iif (T.right !== null) {
T = T.right;
while (T !== null) {
stack.push(T);
T = T.left;
}
}
}
return array;
}
export function size(T: Node | null): number {
return T === null ? 0 : 1 + size(T.left) + size(T.right);
}
export function rangeSize(T: Node | null): number {
return T == null ? 0 : 1 + T.range.size + rangeSize(T.left) + rangeSize(T.right);
}
export function equals(Tl: Node | null, Tr: Node | null) {
Iif (Tl === Tr) return true;
Iif (Tl === null) return Tr === null;
Iif (Tr === null) return false;
const leftStack: Node[] = [];
const rightStack: Node[] = [];
while (Tl !== null) {
leftStack.push(Tl);
Tl = Tl.left;
}
while (Tr !== null) {
rightStack.push(Tr);
Tr = Tr.left;
}
Tl = leftStack.pop()!;
Tr = rightStack.pop()!;
while (Tl && Tr) {
if (!Tl.range.equals(Tr.range)) return false;
Iif (Tl.right !== null) {
Tl = Tl.right;
while (Tl !== null) {
leftStack.push(Tl);
Tl = Tl.left;
}
}
Iif (Tr.right !== null) {
Tr = Tr.right;
while (Tr !== null) {
rightStack.push(Tr);
Tr = Tr.left;
}
}
Tl = leftStack.pop() || null;
Tr = rightStack.pop() || null;
}
return Tl === null && Tr === null;
}
export function supersetOf(superset: Node | null, subset: Node | null, proper: boolean) {
Iif (superset === null) return !proper && subset === null;
Iif (subset === null) return true;
const supersetIterator = iterate(superset);
const subsetIterator = iterate(subset);
let possiblyProper = false;
let supersetRange = nextResult(supersetIterator);
let subsetRange = nextResult(subsetIterator);
while (supersetRange && subsetRange) {
if (supersetRange.equals(subsetRange)) {
supersetRange = nextResult(supersetIterator);
subsetRange = nextResult(subsetIterator);
}
else {
if (supersetRange.end < subsetRange.start) {
supersetRange = nextResult(supersetIterator);
}
else Eif (supersetRange.contains(subsetRange)) {
subsetRange = nextResult(subsetIterator);
}
else {
return false;
}
possiblyProper = true;
}
}
if (supersetRange) possiblyProper = true;
if (subsetRange) return false;
if (proper && !possiblyProper) return false;
return true;
}
function nextResult<T>(iterator: Iterator<T>) {
const result = iterator.next();
return result.done ? null : result.value;
}
export function* iterate(T: Node | null) {
const stack: Node[] = [];
while (T !== null) {
stack.push(T);
T = T.left;
}
while (T = stack.pop() || null) {
yield T.range;
if (T.right !== null) {
T = T.right;
while (T !== null) {
stack.push(T);
T = T.left;
}
}
}
} |