ts-combinatorics
Version:
Simple combinatorics like power set, combination, and permutation in JavaScript
294 lines • 24.7 kB
JavaScript
"use strict";
Object.defineProperty(exports, "__esModule", { value: true });
exports.CartesianProduct = exports.PowerSet = exports.BaseN = exports.Combination = exports.Permutation = exports.randomInteger = exports.combinadic = exports.factoradic = exports.factorial = exports.combination = exports.permutation = exports.version = void 0;
exports.version = "1.4.5";
const _BI = typeof BigInt == "function" ? BigInt : Number;
const _crop = (n) => (n <= Number.MAX_SAFE_INTEGER ? Number(n) : _BI(n));
function permutation(n, k) {
if (n < 0)
throw new RangeError(`negative n is not acceptable`);
if (k < 0)
throw new RangeError(`negative k is not acceptable`);
if (0 == k)
return 1;
if (n < k)
return 0;
[n, k] = [_BI(n), _BI(k)];
let p = _BI(1);
while (k--)
p *= n--;
return _crop(p);
}
exports.permutation = permutation;
function combination(n, k) {
if (0 == k)
return 1;
if (n == k)
return 1;
if (n < k)
return 0;
const P = permutation;
const c = _BI(P(n, k)) / _BI(P(k, k));
return _crop(c);
}
exports.combination = combination;
function factorial(n) {
return permutation(n, n);
}
exports.factorial = factorial;
function factoradic(n, l = 0) {
if (n < 0)
return undefined;
let [bn, bf] = [_BI(n), _BI(1)];
if (!l) {
for (l = 1; bf < bn; bf *= _BI(++l))
;
if (bn < bf)
bf /= _BI(l--);
}
else {
bf = _BI(factorial(l));
}
let digits = [0];
for (; l; bf /= _BI(l--)) {
digits[l] = Math.floor(Number(bn / bf));
bn %= bf;
}
return digits;
}
exports.factoradic = factoradic;
function combinadic(n, k) {
const count = combination(n, k);
return (m) => {
if (m < 0 || count <= m)
return undefined;
let digits = [];
let [a, b] = [n, k];
let x = _BI(count) - _BI(1) - _BI(m);
for (let i = 0; i < k; i++) {
a--;
while (x < combination(a, b))
a--;
digits.push(n - 1 - a);
x -= _BI(combination(a, b));
b--;
}
return digits;
};
}
exports.combinadic = combinadic;
const _crypto = typeof crypto !== "undefined" ? crypto : {};
const _randomBytes = typeof _crypto["randomBytes"] === "function"
? (len) => Uint8Array.from(_crypto["randomBytes"](len))
: typeof _crypto["getRandomValues"] === "function"
? (len) => _crypto["getRandomValues"](new Uint8Array(len))
: (len) => Uint8Array.from(Array(len), () => Math.random() * 256);
function randomInteger(min = 0, max = Math.pow(2, 53)) {
let ctor = min.constructor;
if (arguments.length === 0) {
return Math.floor(Math.random() * ctor(max));
}
if (arguments.length == 1) {
;
[min, max] = [ctor(0), min];
}
if (typeof min == "number") {
;
[min, max] = [Math.ceil(Number(min)), Math.ceil(Number(max))];
return Math.floor(Math.random() * (max - min)) + min;
}
const mag = ctor(max) - ctor(min);
const len = mag.toString(16).length;
const u8s = _randomBytes(len);
const rnd = u8s.reduce((a, v) => (a << ctor(8)) + ctor(v), ctor(0));
return ((ctor(rnd) * mag) >> ctor(len * 8)) + ctor(min);
}
exports.randomInteger = randomInteger;
class _CBase {
static of(...args) {
return new (Function.prototype.bind.apply(this, [null].concat(args)))();
}
static from(arg) {
return new (Function.prototype.bind.apply(this, [null].concat(arg)))();
}
[Symbol.iterator]() {
return (function* (it, len) {
for (let i = 0; i < len; i++)
yield it.nth(i);
})(this, this.length);
}
toArray() {
return [...this];
}
get isBig() {
return Number.MAX_SAFE_INTEGER < this.length;
}
get isSafe() {
return typeof BigInt !== "undefined" || !this.isBig;
}
_check(n) {
if (n < 0) {
if (this.length < -n)
return undefined;
return _crop(_BI(this.length) + _BI(n));
}
if (this.length <= n)
return undefined;
return n;
}
nth(n) {
return [];
}
sample() {
return this.nth(randomInteger(this.length));
}
samples() {
return (function* (it) {
while (true)
yield it.sample();
})(this);
}
}
class Permutation extends _CBase {
constructor(seed, size = 0) {
super();
this.seed = [...seed];
this.size = 0 < size ? size : this.seed.length;
this.length = permutation(this.seed.length, this.size);
Object.freeze(this);
}
nth(n) {
n = this._check(n);
if (n === undefined)
return undefined;
const offset = this.seed.length - this.size;
const skip = factorial(offset);
let digits = factoradic(_BI(n) * _BI(skip), this.seed.length);
let source = this.seed.slice();
let result = [];
for (let i = this.seed.length - 1; offset <= i; i--) {
result.push(source.splice(digits[i], 1)[0]);
}
return result;
}
}
exports.Permutation = Permutation;
class Combination extends _CBase {
constructor(seed, size = 0) {
super();
this.seed = [...seed];
this.size = 0 < size ? size : this.seed.length;
this.size = size;
this.length = combination(this.seed.length, this.size);
this.comb = combinadic(this.seed.length, this.size);
Object.freeze(this);
}
bitwiseIterator() {
const ctor = this.length.constructor;
const [zero, one, two] = [ctor(0), ctor(1), ctor(2)];
const inc = (x) => {
const u = x & -x;
const v = u + x;
return v + (((v ^ x) / u) >> two);
};
let x = (one << ctor(this.size)) - one;
return (function* (it, len) {
for (let i = 0; i < len; i++, x = inc(x)) {
var result = [];
for (let y = x, j = 0; zero < y; y >>= one, j++) {
if (y & one)
result.push(it.seed[j]);
}
yield result;
}
})(this, this.length);
}
nth(n) {
n = this._check(n);
if (n === undefined)
return undefined;
return this.comb(n).reduce((a, v) => a.concat(this.seed[v]), []);
}
}
exports.Combination = Combination;
class BaseN extends _CBase {
constructor(seed, size = 1) {
super();
this.seed = [...seed];
this.size = size;
let base = this.seed.length;
this.base = base;
let length = size < 1
? 0
: Array(size)
.fill(_BI(base))
.reduce((a, v) => a * v);
this.length = _crop(length);
Object.freeze(this);
}
nth(n) {
n = this._check(n);
if (n === undefined)
return undefined;
let bn = _BI(n);
const bb = _BI(this.base);
let result = [];
for (let i = 0; i < this.size; i++) {
var bd = bn % bb;
result.push(this.seed[Number(bd)]);
bn -= bd;
bn /= bb;
}
return result;
}
}
exports.BaseN = BaseN;
class PowerSet extends _CBase {
constructor(seed) {
super();
this.seed = [...seed];
const length = _BI(1) << _BI(this.seed.length);
this.length = _crop(length);
Object.freeze(this);
}
nth(n) {
n = this._check(n);
if (n === undefined)
return undefined;
let bn = _BI(n);
let result = [];
for (let bi = _BI(0); bn; bn >>= _BI(1), bi++)
if (bn & _BI(1))
result.push(this.seed[Number(bi)]);
return result;
}
}
exports.PowerSet = PowerSet;
class CartesianProduct extends _CBase {
constructor(...args) {
super();
this.seed = args.map((v) => [...v]);
this.size = this.seed.length;
const length = this.seed.reduce((a, v) => a * _BI(v.length), _BI(1));
this.length = _crop(length);
Object.freeze(this);
}
nth(n) {
n = this._check(n);
if (n === undefined)
return undefined;
let bn = _BI(n);
let result = [];
for (let i = 0; i < this.size; i++) {
const base = this.seed[i].length;
const bb = _BI(base);
const bd = bn % bb;
result.push(this.seed[i][Number(bd)]);
bn -= bd;
bn /= bb;
}
return result;
}
}
exports.CartesianProduct = CartesianProduct;
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