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| /**
* Copyright 2017 Google Inc.
*
* 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.
*/
import { assert, fail } from './assert';
import { AnyJs } from './misc';
/*
* Implementation of an immutable SortedMap using a Left-leaning
* Red-Black Tree, adapted from the implementation in Mugs
* (http://mads379.github.com/mugs/) by Mads Hartmann Jensen
* (mads379@gmail.com).
*
* Original paper on Left-leaning Red-Black Trees:
* http://www.cs.princeton.edu/~rs/talks/LLRB/LLRB.pdf
*
* Invariant 1: No red node has a red child
* Invariant 2: Every leaf path has the same number of black nodes
* Invariant 3: Only the left child can be red (left leaning)
*/
export type Comparator<K> = (key1: K, key2: K) => number;
export interface Entry<K, V> {
key: K;
value: V;
}
// An immutable sorted map implementation, based on a Left-leaning Red-Black
// tree.
export class SortedMap<K, V> {
// visible for testing
root: LLRBNode<K, V> | LLRBEmptyNode<K, V>;
constructor(
public comparator: Comparator<K>,
root?: LLRBNode<K, V> | LLRBEmptyNode<K, V>
) {
this.root = root ? root : LLRBNode.EMPTY;
}
// Returns a copy of the map, with the specified key/value added or replaced.
insert(key: K, value: V): SortedMap<K, V> {
return new SortedMap<K, V>(
this.comparator,
this.root
.insert(key, value, this.comparator)
.copy(null, null, LLRBNode.BLACK, null, null)
);
}
// Returns a copy of the map, with the specified key removed.
remove(key: K): SortedMap<K, V> {
return new SortedMap<K, V>(
this.comparator,
this.root
.remove(key, this.comparator)
.copy(null, null, LLRBNode.BLACK, null, null)
);
}
// Returns the value of the node with the given key, or null.
get(key: K): V | null {
let node = this.root;
while (!node.isEmpty()) {
const cmp = this.comparator(key, node.key);
if (cmp === 0) {
return node.value;
} else if (cmp < 0) {
node = node.left;
} else Eif (cmp > 0) {
node = node.right;
}
}
return null;
}
// Returns the index of the element in this sorted map, or -1 if it doesn't
// exist.
indexOf(key: K): number {
// Number of nodes that were pruned when descending right
let prunedNodes = 0;
let node = this.root;
while (!node.isEmpty()) {
const cmp = this.comparator(key, node.key);
if (cmp === 0) {
return prunedNodes + node.left.size;
} else if (cmp < 0) {
node = node.left;
} else {
// Count all nodes left of the node plus the node itself
prunedNodes += node.left.size + 1;
node = node.right;
}
}
// Node not found
return -1;
}
isEmpty(): boolean {
return this.root.isEmpty();
}
// Returns the total number of nodes in the map.
get size(): number {
return this.root.size;
}
// Returns the minimum key in the map.
minKey(): K | null {
return this.root.minKey();
}
// Returns the maximum key in the map.
maxKey(): K | null {
return this.root.maxKey();
}
// Traverses the map in key order and calls the specified action function
// for each key/value pair. If action returns true, traversal is aborted.
// Returns the first truthy value returned by action, or the last falsey
// value returned by action.
inorderTraversal<T>(action: (k: K, v: V) => T): T {
return (this.root as LLRBNode<K, V>).inorderTraversal(action);
}
forEach(fn: (k: K, v: V) => void) {
this.inorderTraversal((k, v) => {
fn(k, v);
return false;
});
}
// Traverses the map in reverse key order and calls the specified action
// function for each key/value pair. If action returns true, traversal is
// aborted.
// Returns the first truthy value returned by action, or the last falsey
// value returned by action.
reverseTraversal<T>(action: (k: K, v: V) => T): T {
return (this.root as LLRBNode<K, V>).reverseTraversal(action);
}
// Returns an iterator over the SortedMap.
getIterator(): SortedMapIterator<K, V> {
return new SortedMapIterator<K, V>(this.root, null, this.comparator, false);
}
getIteratorFrom(key: K): SortedMapIterator<K, V> {
return new SortedMapIterator<K, V>(this.root, key, this.comparator, false);
}
getReverseIterator(): SortedMapIterator<K, V> {
return new SortedMapIterator<K, V>(this.root, null, this.comparator, true);
}
getReverseIteratorFrom(key: K): SortedMapIterator<K, V> {
return new SortedMapIterator<K, V>(this.root, key, this.comparator, true);
}
} // end SortedMap
// An iterator over an LLRBNode.
export class SortedMapIterator<K, V> {
private isReverse: boolean;
private nodeStack: Array<LLRBNode<K, V> | LLRBEmptyNode<K, V>>;
constructor(
node: LLRBNode<K, V> | LLRBEmptyNode<K, V>,
startKey: K | null,
comparator: Comparator<K>,
isReverse: boolean
) {
this.isReverse = isReverse;
this.nodeStack = [];
let cmp = 1;
while (!node.isEmpty()) {
cmp = startKey ? comparator(node.key, startKey) : 1;
// flip the comparison if we're going in reverse
Iif (isReverse) cmp *= -1;
if (cmp < 0) {
// This node is less than our start key. ignore it
Iif (this.isReverse) {
node = node.left;
} else {
node = node.right;
}
} else if (cmp === 0) {
// This node is exactly equal to our start key. Push it on the stack,
// but stop iterating;
this.nodeStack.push(node);
break;
} else {
// This node is greater than our start key, add it to the stack and move
// to the next one
this.nodeStack.push(node);
Iif (this.isReverse) {
node = node.right;
} else {
node = node.left;
}
}
}
}
getNext(): Entry<K, V> {
assert(
this.nodeStack.length > 0,
'getNext() called on iterator when hasNext() is false.'
);
let node = this.nodeStack.pop()!;
const result = { key: node.key, value: node.value };
Iif (this.isReverse) {
node = node.left;
while (!node.isEmpty()) {
this.nodeStack.push(node);
node = node.right;
}
} else {
node = node.right;
while (!node.isEmpty()) {
this.nodeStack.push(node);
node = node.left;
}
}
return result;
}
hasNext(): boolean {
return this.nodeStack.length > 0;
}
peek(): Entry<K, V> {
if (this.nodeStack.length === 0) return null;
const node = this.nodeStack[this.nodeStack.length - 1];
return { key: node.key, value: node.value };
}
} // end SortedMapIterator
// Represents a node in a Left-leaning Red-Black tree.
export class LLRBNode<K, V> {
readonly color: boolean;
readonly left: LLRBNode<K, V> | LLRBEmptyNode<K, V>;
readonly right: LLRBNode<K, V> | LLRBEmptyNode<K, V>;
readonly size: number;
// tslint:disable-next-line:no-any Empty node is shared between all LLRB trees.
static EMPTY: LLRBEmptyNode<any, any> = null as any;
static RED = true;
static BLACK = false;
constructor(
public key: K,
public value: V,
color?: boolean,
left?: LLRBNode<K, V> | LLRBEmptyNode<K, V>,
right?: LLRBNode<K, V> | LLRBEmptyNode<K, V>
) {
this.color = color != null ? color : LLRBNode.RED;
this.left = left != null ? left : LLRBNode.EMPTY;
this.right = right != null ? right : LLRBNode.EMPTY;
this.size = this.left.size + 1 + this.right.size;
}
// Returns a copy of the current node, optionally replacing pieces of it.
copy(
key: K | null,
value: V | null,
color: boolean | null,
left: LLRBNode<K, V> | LLRBEmptyNode<K, V> | null,
right: LLRBNode<K, V> | LLRBEmptyNode<K, V> | null
): LLRBNode<K, V> {
return new LLRBNode<K, V>(
key != null ? key : this.key,
value != null ? value : this.value,
color != null ? color : this.color,
left != null ? left : this.left,
right != null ? right : this.right
);
}
isEmpty(): boolean {
return false;
}
// Traverses the tree in key order and calls the specified action function
// for each node. If action returns true, traversal is aborted.
// Returns the first truthy value returned by action, or the last falsey
// value returned by action.
inorderTraversal<T>(action: (k: K, v: V) => T): T {
return (
(this.left as LLRBNode<K, V>).inorderTraversal(action) ||
action(this.key, this.value) ||
(this.right as LLRBNode<K, V>).inorderTraversal(action)
);
}
// Traverses the tree in reverse key order and calls the specified action
// function for each node. If action returns true, traversal is aborted.
// Returns the first truthy value returned by action, or the last falsey
// value returned by action.
reverseTraversal<T>(action: (k: K, v: V) => T): T {
return (
(this.right as LLRBNode<K, V>).reverseTraversal(action) ||
action(this.key, this.value) ||
(this.left as LLRBNode<K, V>).reverseTraversal(action)
);
}
// Returns the minimum node in the tree.
private min(): LLRBNode<K, V> {
if (this.left.isEmpty()) {
return this;
} else {
return (this.left as LLRBNode<K, V>).min();
}
}
// Returns the maximum key in the tree.
minKey(): K | null {
return this.min().key;
}
// Returns the maximum key in the tree.
maxKey(): K | null {
if (this.right.isEmpty()) {
return this.key;
} else {
return this.right.maxKey();
}
}
// Returns new tree, with the key/value added.
insert(key: K, value: V, comparator: Comparator<K>): LLRBNode<K, V> {
let n: LLRBNode<K, V> = this;
const cmp = comparator(key, n.key);
if (cmp < 0) {
n = n.copy(null, null, null, n.left.insert(key, value, comparator), null);
} else if (cmp === 0) {
n = n.copy(null, value, null, null, null);
} else {
n = n.copy(
null,
null,
null,
null,
n.right.insert(key, value, comparator)
);
}
return n.fixUp();
}
private removeMin(): LLRBNode<K, V> | LLRBEmptyNode<K, V> {
if (this.left.isEmpty()) {
return LLRBNode.EMPTY;
}
let n: LLRBNode<K, V> = this;
if (!n.left.isRed() && !n.left.left.isRed()) n = n.moveRedLeft();
n = n.copy(null, null, null, (n.left as LLRBNode<K, V>).removeMin(), null);
return n.fixUp();
}
// Returns new tree, with the specified item removed.
remove(
key: K,
comparator: Comparator<K>
): LLRBNode<K, V> | LLRBEmptyNode<K, V> {
let smallest: LLRBNode<K, V>;
let n: LLRBNode<K, V> = this;
if (comparator(key, n.key) < 0) {
if (!n.left.isEmpty() && !n.left.isRed() && !n.left.left.isRed()) {
n = n.moveRedLeft();
}
n = n.copy(null, null, null, n.left.remove(key, comparator), null);
} else {
if (n.left.isRed()) n = n.rotateRight();
if (!n.right.isEmpty() && !n.right.isRed() && !n.right.left.isRed()) {
n = n.moveRedRight();
}
if (comparator(key, n.key) === 0) {
if (n.right.isEmpty()) {
return LLRBNode.EMPTY;
} else {
smallest = (n.right as LLRBNode<K, V>).min();
n = n.copy(
smallest.key,
smallest.value,
null,
null,
(n.right as LLRBNode<K, V>).removeMin()
);
}
}
n = n.copy(null, null, null, null, n.right.remove(key, comparator));
}
return n.fixUp();
}
isRed(): boolean {
return this.color;
}
// Returns new tree after performing any needed rotations.
private fixUp(): LLRBNode<K, V> {
let n: LLRBNode<K, V> = this;
if (n.right.isRed() && !n.left.isRed()) n = n.rotateLeft();
if (n.left.isRed() && n.left.left.isRed()) n = n.rotateRight();
if (n.left.isRed() && n.right.isRed()) n = n.colorFlip();
return n;
}
private moveRedLeft(): LLRBNode<K, V> {
let n = this.colorFlip();
if (n.right.left.isRed()) {
n = n.copy(
null,
null,
null,
null,
(n.right as LLRBNode<K, V>).rotateRight()
);
n = n.rotateLeft();
n = n.colorFlip();
}
return n;
}
private moveRedRight(): LLRBNode<K, V> {
let n = this.colorFlip();
if (n.left.left.isRed()) {
n = n.rotateRight();
n = n.colorFlip();
}
return n;
}
private rotateLeft(): LLRBNode<K, V> {
const nl = this.copy(null, null, LLRBNode.RED, null, this.right.left);
return (this.right as LLRBNode<K, V>).copy(
null,
null,
this.color,
nl,
null
);
}
private rotateRight(): LLRBNode<K, V> {
const nr = this.copy(null, null, LLRBNode.RED, this.left.right, null);
return (this.left as LLRBNode<K, V>).copy(null, null, this.color, null, nr);
}
private colorFlip(): LLRBNode<K, V> {
const left = this.left.copy(null, null, !this.left.color, null, null);
const right = this.right.copy(null, null, !this.right.color, null, null);
return this.copy(null, null, !this.color, left, right);
}
// For testing.
checkMaxDepth(): boolean {
const blackDepth = this.check();
Eif (Math.pow(2.0, blackDepth) <= this.size + 1) {
return true;
} else {
return false;
}
}
// In a balanced RB tree, the black-depth (number of black nodes) from root to
// leaves is equal on both sides. This function verifies that or asserts.
protected check(): number {
Iif (this.isRed() && this.left.isRed()) {
throw fail('Red node has red child(' + this.key + ',' + this.value + ')');
}
Iif (this.right.isRed()) {
throw fail('Right child of (' + this.key + ',' + this.value + ') is red');
}
const blackDepth = (this.left as LLRBNode<K, V>).check();
Iif (blackDepth !== (this.right as LLRBNode<K, V>).check()) {
throw fail('Black depths differ');
} else {
return blackDepth + (this.isRed() ? 0 : 1);
}
}
} // end LLRBNode
// Represents an empty node (a leaf node in the Red-Black Tree).
export class LLRBEmptyNode<K, V> {
key: K;
value: V;
color: boolean;
left: LLRBNode<K, V>;
right: LLRBNode<K, V>;
size = 0;
constructor() {}
// Returns a copy of the current node.
copy(
key: K | null,
value: V | null,
color: boolean | null,
left: LLRBNode<K, V> | LLRBEmptyNode<K, V> | null,
right: LLRBNode<K, V> | LLRBEmptyNode<K, V> | null
): LLRBEmptyNode<K, V> {
return this;
}
// Returns a copy of the tree, with the specified key/value added.
insert(key: K, value: V, comparator: Comparator<K>): LLRBNode<K, V> {
return new LLRBNode<K, V>(key, value);
}
// Returns a copy of the tree, with the specified key removed.
remove(key: K, comparator: Comparator<K>): LLRBEmptyNode<K, V> {
return this;
}
isEmpty(): boolean {
return true;
}
inorderTraversal(action: (k: K, v: V) => boolean): boolean {
return false;
}
reverseTraversal(action: (k: K, v: V) => boolean): boolean {
return false;
}
minKey(): K | null {
return null;
}
maxKey(): K | null {
return null;
}
isRed(): boolean {
return false;
}
// For testing.
checkMaxDepth(): boolean {
return true;
}
protected check() {
return 0;
}
} // end LLRBEmptyNode
LLRBNode.EMPTY = new LLRBEmptyNode<AnyJs, AnyJs>();
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