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export type NumericValue = number | bigint;
/**
* Represents an interval number
* isClosed is optional and defaults to true.
* isClosed represents if the number is included in the interval.
*/
export class IntervalNumber {
readonly number: NumericValue;
readonly isClosed: boolean;
constructor(number: NumericValue, isClosed: boolean = true) {
this.number = number;
this.isClosed = isClosed;
}
/**
* Returns true if the given IntervalNumber is equal to this IntervalNumber.
*/
equals(x: IntervalNumber | NumericValue): boolean {
if (typeof x === 'number' || typeof x === 'bigint') {
x = new IntervalNumber(x);
}
return this.number === x.number && this.isClosed === x.isClosed;
}
}
/**
* Represents an interval.
* To not be opinionated, we use a and b to represent the interval, where either a or b can be greater than the other.
* name is optional, but can be useful for keeping track of the interval.
* @example
* const interval: IInterval = { a: new IntervalNumber(1, false), b: new IntervalNumber(10), name: 'Interval 1' };
*/
export type IInterval = { a: IntervalNumber, b: IntervalNumber, name?: string };
/**
* Represents an interval.
* To not be opinionated, we use a and b to represent the interval, where either a or b can be greater than the other.
* name is optional, but can be useful for keeping track of the interval.
* @example
* const interval: Interval = new Interval({ a: new IntervalNumber(1, false), b: new IntervalNumber(10), name: 'Interval 1' });
* console.log(interval.toString()); // (1, 10]
*/
export class Interval implements IInterval {
private _a: IntervalNumber;
private _b: IntervalNumber;
public name?: string;
constructor(interval: IInterval | string) {
if (typeof interval === 'string') {
interval = Interval.toInterval(interval);
}
if (!Interval.validInterval(interval)) {
throw new Error(
`Invalid interval: Cannot exclude either minimum (${interval.a.number}) or maximum (${interval.b.number}) values if they are equal.`
);
}
this._a = interval.a;
this._b = interval.b;
this.name = interval.name;
}
get a(): IntervalNumber {
// return a copy of the interval number
return new IntervalNumber(this._a.number, this._a.isClosed);
}
set a(value: IntervalNumber | NumericValue) {
value = Interval.toIntervalNumber(value);
if (this._b.number === value.number && !this._b.isClosed && !value.isClosed) {
throw new Error('Invalid interval. Cannot exclude either minimum and maximum values if they are equal.');
}
this._a = value;
}
get b(): IntervalNumber {
// return a copy of the interval number
return new IntervalNumber(this._b.number, this._b.isClosed);
}
set b(value: IntervalNumber | NumericValue) {
value = Interval.toIntervalNumber(value);
if (this._a.number === value.number && !this._a.isClosed && !value.isClosed) {
throw new Error('Invalid interval. Cannot exclude either minimum and maximum values if they are equal.');
}
this._b = value;
}
get min(): IntervalNumber {
return this._a.number < this._b.number ? this._a : this._b;
}
set min(value: IntervalNumber | NumericValue) {
value = Interval.toIntervalNumber(value);
if (this._a.number === this.min.number) {
this.a = value;
} else {
this.b = value;
}
}
get max(): IntervalNumber {
return this._a.number > this._b.number ? this._a : this._b;
}
set max(value: IntervalNumber | NumericValue) {
value = Interval.toIntervalNumber(value);
if (this._a.number === this.max.number) {
this.a = value;
} else {
this.b = value;
}
}
/**
* Returns true if the interval contains the given number.
*/
containsNumber(x: NumericValue): boolean {
const isAboveMin = this.min.number < x || (this.min.number === x && this.min.isClosed);
const isBelowMax = this.max.number > x || (this.max.number === x && this.max.isClosed);
return isAboveMin && isBelowMax;
}
/**
* Returns true if the interval contains the given IntervalNumber that represents a minimum value.
*/
containsMin(x: IntervalNumber): boolean {
let containsMinValue = false;
// there's directionality when the number passed in is open and a minimum
if (!x.isClosed) {
containsMinValue = this.min.number <= x.number && this.max.number > x.number;
} else {
containsMinValue = (this.min.number < x.number || (this.min.number === x.number && this.min.isClosed)) &&
(this.max.number > x.number || (this.max.number === x.number && this.max.isClosed));
}
return containsMinValue;
}
/**
* Returns true if the interval contains the given IntervalNumber that represents a maximum value.
*/
containsMax(x: IntervalNumber): boolean {
let containsMaxValue = false;
// there's directionality when the number passed in is open and a maximum
if (!x.isClosed) {
containsMaxValue = this.min.number < x.number && this.max.number >= x.number;
} else {
containsMaxValue = (this.min.number < x.number || (this.min.number === x.number && this.min.isClosed)) &&
(this.max.number > x.number || (this.max.number === x.number && this.max.isClosed));
}
return containsMaxValue;
}
/**
* Returns true if the interval contains the given IntervalNumber or Interval.
*/
contains(x: IntervalNumber | Interval): boolean {
if (Interval.isIntervalNumber(x)) {
const isAboveMin = this.min.number < x.number || (this.min.number === x.number && this.min.isClosed && x.isClosed);
const isBelowMax = this.max.number > x.number || (this.max.number === x.number && this.max.isClosed && x.isClosed);
return isAboveMin && isBelowMax;
}
return this.containsMin(x.min) && this.containsMax(x.max);
}
/**
* Returns true if the interval overlaps with the given interval.
*/
overlaps(interval: Interval): boolean {
return this.containsMin(interval.min) || this.containsMax(interval.max);
}
/**
* Returns a string representation of the interval.
* @example
* const interval: Interval = new Interval({ a: new IntervalNumber(1, false), b: new IntervalNumber(10), name: 'Interval 1' });
* console.log(interval.toString()); // (1, 10]
*/
toString(): string {
const aIsClosedChar: string = this._a.isClosed ? '[' : '(';
const bIsClosedChar: string = this._b.isClosed ? ']' : ')';
return `${aIsClosedChar}${formatNumericValue(this._a.number)}, ${formatNumericValue(this._b.number)}${bIsClosedChar}`;
}
private static parseNumericString(str: string): NumericValue {
const trimmed = str.trim();
// Handle BigInt notation (ends with 'n')
if (trimmed.endsWith('n')) {
return BigInt(trimmed.slice(0, -1));
}
// Use Number() for everything else (handles hex, octal, binary automatically)
const num = Number(trimmed);
if (isNaN(num)) {
throw new Error(`Invalid numeric string: ${str}`);
}
return num;
}
/**
* Returns true if the given interval is valid.
*/
static validInterval(interval: IInterval): boolean {
const aIsValid = typeof interval.a.number === 'number' || typeof interval.a.number === 'bigint';
const bIsValid = typeof interval.b.number === 'number' || typeof interval.b.number === 'bigint';
return aIsValid && bIsValid &&
(interval.a.number !== interval.b.number || (interval.a.isClosed && interval.b.isClosed));
}
/**
* Returns true if the given string is a valid interval.
* Supports the use of -Infinity and Infinity.
* @param interval - The string representation of the interval.
* @example
* console.log(Interval.validIntervalString('(1, 10]')); // true
* console.log(Interval.validIntervalString('1, 10]')); // false
* @returns A boolean indicating if the string is a valid interval.
*/
static validIntervalString(interval: string): boolean {
try {
const intervalObj = Interval.toInterval(interval);
return Interval.validInterval(intervalObj);
} catch {
return false;
}
}
/**
* Takes a string representation of an interval and returns an Interval object.
* @param interval - The string representation of the interval.
* @returns An Interval object.
* @example
* const interval: Interval = Interval.toInterval('(1, 10]');
* console.log(interval.toString()); // (1, 10]
*/
static toInterval(interval: string): IInterval {
const intervalTrimmed = interval.trim();
const startSymbol = intervalTrimmed[0];
const endSymbol = intervalTrimmed[intervalTrimmed.length - 1];
if (startSymbol !== '(' && startSymbol !== '[' || endSymbol !== ')' && endSymbol !== ']') {
throw new Error(`Invalid interval string: ${interval}`);
}
const a = intervalTrimmed.slice(1, intervalTrimmed.indexOf(',')).trim();
const b = intervalTrimmed.slice(intervalTrimmed.indexOf(',') + 1, intervalTrimmed.length - 1).trim();
const aNum = Interval.parseNumericString(a);
const bNum = Interval.parseNumericString(b);
const aIsClosed = startSymbol === '[';
const bIsClosed = endSymbol === ']';
const iInterval: IInterval = {
a: new IntervalNumber(aNum, aIsClosed),
b: new IntervalNumber(bNum, bIsClosed)
};
if (!Interval.validInterval(iInterval)) {
throw new Error(`Invalid interval string: ${interval}`);
}
return iInterval;
}
private static toIntervalNumber(x: IntervalNumber | NumericValue, isClosed = true): IntervalNumber {
return Interval.isIntervalNumber(x) ? x : new IntervalNumber(x, isClosed);
}
static isIntervalNumber(x: any): x is IntervalNumber {
return x instanceof IntervalNumber;
}
}
export function formatNumericValue(v: NumericValue): string {
return typeof v === 'bigint' ? `${v}n` : `${v}`;
}
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