Tone.js/Tone/core/util/IntervalTimeline.ts

import { Tone } from "../Tone";
import { isDefined } from "./TypeCheck";

/**
 * An IntervalTimeline event must have a time and duration
 */
export interface IntervalTimelineEvent {
	time: number;
	duration: number;
	[propName: string]: any;
}

type IteratorCallback = (event: IntervalTimelineEvent) => void;

/**
 * Similar to Tone.Timeline, but all events represent
 * intervals with both "time" and "duration" times. The
 * events are placed in a tree structure optimized
 * for querying an intersection point with the timeline
 * events. Internally uses an [Interval Tree](https://en.wikipedia.org/wiki/Interval_tree)
 * to represent the data.
 */
export class IntervalTimeline extends Tone {

	readonly name: string = "IntervalTimeline";

	/**
	 * The root node of the inteval tree
	 */
	private _root: IntervalNode | null = null;

	/**
	 * Keep track of the length of the timeline.
	 */
	private _length = 0;

	/**
	 * The event to add to the timeline. All events must
	 * have a time and duration value
	 * @param  event  The event to add to the timeline
	 */
	add(event: IntervalTimelineEvent): this {
		this.assert(isDefined(event.time), "Events must have a time property");
		this.assert(isDefined(event.duration), "Events must have a duration parameter");

		event.time = event.time.valueOf();
		let node: IntervalNode | null = new IntervalNode(event.time, event.time + event.duration, event);
		if (this._root === null) {
			this._root = node;
		} else {
			this._root.insert(node);
		}
		this._length++;
		// Restructure tree to be balanced
		while (node !== null) {
			node.updateHeight();
			node.updateMax();
			this._rebalance(node);
			node = node.parent;
		}
		return this;
	}

	/**
	 * Remove an event from the timeline.
	 * @param  event  The event to remove from the timeline
	 */
	remove(event: IntervalTimelineEvent): this {
		if (this._root !== null) {
			const results: IntervalNode[] = [];
			this._root.search(event.time, results);
			for (const node of results) {
				if (node.event === event) {
					this._removeNode(node);
					this._length--;
					break;
				}
			}
		}
		return this;
	}

	/**
	 * The number of items in the timeline.
	 * @readOnly
	 */
	get length(): number {
		return this._length;
	}

	/**
	 * Remove events whose time time is after the given time
	 * @param  after  The time to query.
	 */
	cancel(after: number): this {
		this.forEachFrom(after, event => this.remove(event));
		return this;
	}

	/**
	 * Set the root node as the given node
	 */
	private _setRoot(node: IntervalNode | null): void {
		this._root = node;
		if (this._root !== null) {
			this._root.parent = null;
		}
	}

	/**
	 * Replace the references to the node in the node's parent
	 * with the replacement node.
	 */
	private _replaceNodeInParent(node: IntervalNode, replacement: IntervalNode | null): void {
		if (node.parent !== null) {
			if (node.isLeftChild()) {
				node.parent.left = replacement;
			} else {
				node.parent.right = replacement;
			}
			this._rebalance(node.parent);
		} else {
			this._setRoot(replacement);
		}
	}

	/**
	 * Remove the node from the tree and replace it with
	 * a successor which follows the schema.
	 */
	private _removeNode(node: IntervalNode): void {
		if (node.left === null && node.right === null) {
			this._replaceNodeInParent(node, null);
		} else if (node.right === null) {
			this._replaceNodeInParent(node, node.left);
		} else if (node.left === null) {
			this._replaceNodeInParent(node, node.right);
		} else {
			const balance = node.getBalance();
			let replacement: IntervalNode;
			let temp: IntervalNode | null = null;
			if (balance > 0) {
				if (node.left.right === null) {
					replacement = node.left;
					replacement.right = node.right;
					temp = replacement;
				} else {
					replacement = node.left.right;
					while (replacement.right !== null) {
						replacement = replacement.right;
					}
					if (replacement.parent) {
						replacement.parent.right = replacement.left;
						temp = replacement.parent;
						replacement.left = node.left;
						replacement.right = node.right;
					}
				}
			} else if (node.right.left === null) {
				replacement = node.right;
				replacement.left = node.left;
				temp = replacement;
			} else {
				replacement = node.right.left;
				while (replacement.left !== null) {
					replacement = replacement.left;
				}
				if (replacement.parent) {
					replacement.parent.left = replacement.right;
					temp = replacement.parent;
					replacement.left = node.left;
					replacement.right = node.right;
				}
			}
			if (node.parent !== null) {
				if (node.isLeftChild()) {
					node.parent.left = replacement;
				} else {
					node.parent.right = replacement;
				}
			} else {
				this._setRoot(replacement);
			}
			if (temp) {
				this._rebalance(temp);
			}
		}
		node.dispose();
	}

	/**
	 * Rotate the tree to the left
	 */
	private _rotateLeft(node: IntervalNode): void {
		const parent = node.parent;
		const isLeftChild = node.isLeftChild();

		// Make node.right the new root of this sub tree (instead of node)
		const pivotNode = node.right;
		if (pivotNode) {
			node.right = pivotNode.left;
			pivotNode.left = node;
		}

		if (parent !== null) {
			if (isLeftChild) {
				parent.left = pivotNode;
			} else {
				parent.right = pivotNode;
			}
		} else {
			this._setRoot(pivotNode);
		}
	}

	/**
	 * Rotate the tree to the right
	 */
	private _rotateRight(node: IntervalNode): void {
		const parent = node.parent;
		const isLeftChild = node.isLeftChild();

		// Make node.left the new root of this sub tree (instead of node)
		const pivotNode = node.left;
		if (pivotNode) {
			node.left = pivotNode.right;
			pivotNode.right = node;
		}

		if (parent !== null) {
			if (isLeftChild) {
				parent.left = pivotNode;
			} else {
				parent.right = pivotNode;
			}
		} else {
			this._setRoot(pivotNode);
		}
	}

	/**
	 * Balance the BST
	 */
	private _rebalance(node: IntervalNode): void {
		const balance = node.getBalance();
		if (balance > 1 && node.left) {
			if (node.left.getBalance() < 0) {
				this._rotateLeft(node.left);
			} else {
				this._rotateRight(node);
			}
		} else if (balance < -1 && node.right) {
			if (node.right.getBalance() > 0) {
				this._rotateRight(node.right);
			} else {
				this._rotateLeft(node);
			}
		}
	}

	/**
	 * Get an event whose time and duration span the give time. Will
	 * return the match whose "time" value is closest to the given time.
	 * @return  The event which spans the desired time
	 */
	get(time: number): IntervalTimelineEvent | null {
		if (this._root !== null) {
			const results: IntervalNode[] = [];
			this._root.search(time, results);
			if (results.length > 0) {
				let max = results[0];
				for (let i = 1; i < results.length; i++) {
					if (results[i].low > max.low) {
						max = results[i];
					}
				}
				return max.event;
			}
		}
		return null;
	}

	/**
	 * Iterate over everything in the timeline.
	 * @param  callback The callback to invoke with every item
	 */
	forEach(callback: IteratorCallback): this {
		if (this._root !== null) {
			const allNodes: IntervalNode[] = [];
			this._root.traverse(node => allNodes.push(node));
			allNodes.forEach(node => {
				if (node.event) {
					callback(node.event);
				}
			});
		}
		return this;
	}

	/**
	 * Iterate over everything in the array in which the given time
	 * overlaps with the time and duration time of the event.
	 * @param  time The time to check if items are overlapping
	 * @param  callback The callback to invoke with every item
	 */
	forEachAtTime(time: number, callback: IteratorCallback): this {
		if (this._root !== null) {
			const results: IntervalNode[] = [];
			this._root.search(time, results);
			results.forEach(node => {
				if (node.event) {
					callback(node.event);
				}
			});
		}
		return this;
	}

	/**
	 * Iterate over everything in the array in which the time is greater
	 * than or equal to the given time.
	 * @param  time The time to check if items are before
	 * @param  callback The callback to invoke with every item
	 */
	forEachFrom(time: number, callback: IteratorCallback): this {
		if (this._root !== null) {
			const results: IntervalNode[] = [];
			this._root.searchAfter(time, results);
			results.forEach(node => {
				if (node.event) {
					callback(node.event);
				}
			});
		}
		return this;
	}

	/**
	 * Clean up
	 */
	dispose(): this {
		super.dispose();
		if (this._root !== null) {
			this._root.traverse(node => node.dispose());
		}
		this._root = null;
		return this;
	}
}

//-------------------------------------
// 	INTERVAL NODE HELPER
//-------------------------------------

/**
 * Represents a node in the binary search tree, with the addition
 * of a "high" value which keeps track of the highest value of
 * its children.
 * References:
 * https://brooknovak.wordpress.com/2013/12/07/augmented-interval-tree-in-c/
 * http://www.mif.vu.lt/~valdas/ALGORITMAI/LITERATURA/Cormen/Cormen.pdf
 * @param low
 * @param high
 */
class IntervalNode {

	// the event container
	event: IntervalTimelineEvent | null;
	// the low value
	low: number;
	// the high value
	high: number;
	// the high value for this and all child nodes
	max: number;
	// the nodes to the left
	private _left: IntervalNode | null = null;
	// the nodes to the right
	private _right: IntervalNode | null = null;
	// the parent node
	parent: IntervalNode | null = null;
	// the number of child nodes
	height = 0;

	constructor(low: number, high: number, event: IntervalTimelineEvent) {
		this.event = event;
		// the low value
		this.low = low;
		// the high value
		this.high = high;
		// the high value for this and all child nodes
		this.max = this.high;
	}

	/**
	 * Insert a node into the correct spot in the tree
	 */
	insert(node: IntervalNode): void {
		if (node.low <= this.low) {
			if (this.left === null) {
				this.left = node;
			} else {
				this.left.insert(node);
			}
		} else if (this.right === null) {
			this.right = node;
		} else {
			this.right.insert(node);
		}
	}

	/**
	 * Search the tree for nodes which overlap
	 * with the given point
	 * @param  point  The point to query
	 * @param  results  The array to put the results
	 */
	search(point: number, results: IntervalNode[]): void {
		// If p is to the right of the rightmost point of any interval
		// in this node and all children, there won't be any matches.
		if (point > this.max) {
			return;
		}
		// Search left children
		if (this.left !== null) {
			this.left.search(point, results);
		}
		// Check this node
		if (this.low <= point && this.high > point) {
			results.push(this);
		}
		// If p is to the left of the time of this interval,
		// then it can't be in any child to the right.
		if (this.low > point) {
			return;
		}
		// Search right children
		if (this.right !== null) {
			this.right.search(point, results);
		}
	}

	/**
	 * Search the tree for nodes which are less
	 * than the given point
	 * @param  point  The point to query
	 * @param  results  The array to put the results
	 */
	searchAfter(point: number, results: IntervalNode[]): void {
		// Check this node
		if (this.low >= point) {
			results.push(this);
			if (this.left !== null) {
				this.left.searchAfter(point, results);
			}
		}
		// search the right side
		if (this.right !== null) {
			this.right.searchAfter(point, results);
		}
	}

	/**
	 * Invoke the callback on this element and both it's branches
	 * @param  {Function}  callback
	 */
	traverse(callback: (self: IntervalNode) => void): void {
		callback(this);
		if (this.left !== null) {
			this.left.traverse(callback);
		}
		if (this.right !== null) {
			this.right.traverse(callback);
		}
	}

	/**
	 * Update the height of the node
	 */
	updateHeight(): void {
		if (this.left !== null && this.right !== null) {
			this.height = Math.max(this.left.height, this.right.height) + 1;
		} else if (this.right !== null) {
			this.height = this.right.height + 1;
		} else if (this.left !== null) {
			this.height = this.left.height + 1;
		} else {
			this.height = 0;
		}
	}

	/**
	 * Update the height of the node
	 */
	updateMax(): void {
		this.max = this.high;
		if (this.left !== null) {
			this.max = Math.max(this.max, this.left.max);
		}
		if (this.right !== null) {
			this.max = Math.max(this.max, this.right.max);
		}
	}

	/**
	 * The balance is how the leafs are distributed on the node
	 * @return  Negative numbers are balanced to the right
	 */
	getBalance(): number {
		let balance = 0;
		if (this.left !== null && this.right !== null) {
			balance = this.left.height - this.right.height;
		} else if (this.left !== null) {
			balance = this.left.height + 1;
		} else if (this.right !== null) {
			balance = -(this.right.height + 1);
		}
		return balance;
	}

	/**
	 * @returns true if this node is the left child of its parent
	 */
	isLeftChild(): boolean {
		return this.parent !== null && this.parent.left === this;
	}

	/**
	 * get/set the left node
	 */
	get left(): IntervalNode | null {
		return this._left;
	}

	set left(node: IntervalNode | null) {
		this._left = node;
		if (node !== null) {
			node.parent = this;
		}
		this.updateHeight();
		this.updateMax();
	}

	/**
	 * get/set the right node
	 */
	get right(): IntervalNode | null {
		return this._right;
	}

	set right(node: IntervalNode | null) {
		this._right = node;
		if (node !== null) {
			node.parent = this;
		}
		this.updateHeight();
		this.updateMax();
	}

	/**
	 * null out references.
	 */
	dispose(): void {
		this.parent = null;
		this._left = null;
		this._right = null;
		this.event = null;
	}
}