✨ feat: implemented '@algorithm.ts/gcd'

Author: guanghechen

Diff for: README.md

@@ -60,6 +60,7 @@ Package                             | Description
 [@algorithm.ts/dinic][]             | Dinic algorithm. #MaxFlow, #NetworkFlow.
 [@algorithm.ts/dlx][]               | DLX algorithm.
 [@algorithm.ts/findset][]           | Find set.
+[@algorithm.ts/gcd][]               | Greatest Common Divisor (GCD) and extended Euclidean algorithm.
 [@algorithm.ts/isap][]              | ISAP algorithm. #MaxFlow, #NetworkFlow.
 [@algorithm.ts/knuth-shuffle][]     | Knuth-Shuffle algorithm.
 [@algorithm.ts/mcmf][]              | MCMF algorithm. #MinCostMaxFlow, #NetworkFlow.
@@ -80,6 +81,7 @@ algorithm.ts is [MIT licensed](https://github.com/guanghechen/algorithm.ts/blob/
 [@algorithm.ts/dinic]: ./packages/dinic
 [@algorithm.ts/dlx]: ./packages/dlx
 [@algorithm.ts/findset]: ./packages/findset
+[@algorithm.ts/gcd]: ./packages/gcd
 [@algorithm.ts/isap]: ./packages/isap
 [@algorithm.ts/knuth-shuffle]: ./packages/knuth-shuffle
 [@algorithm.ts/mcmf]: ./packages/mcmf

Diff for: package.json

@@ -28,6 +28,7 @@
     "postinstall:dev": "is-ci || husky install",
     "postpublish": "pinst --enable",
     "rebuild": "run-s clean build",
+    "run:ts": "node -r ts-node/register -r tsconfig-paths/register",
     "test": "lerna exec 'echo && pwd && yarn test' --concurrency 1",
     "test:coverage": "lerna exec 'echo && pwd && yarn test --coverage' --concurrency 1",
     "test:update": "lerna exec 'echo && pwd && yarn test -u' --concurrency 1",

Diff for: packages/gcd/README.md

@@ -0,0 +1,106 @@
+<header>
+  <h1 align="center">
+    <a href="https://github.com/guanghechen/algorithm.ts/tree/main/packages/gcd#readme">@algorithm.ts/gcd</a>
+  </h1>
+  <div align="center">
+    <a href="https://www.npmjs.com/package/@algorithm.ts/gcd">
+      <img
+        alt="Npm Version"
+        src="https://img.shields.io/npm/v/@algorithm.ts/gcd.svg"
+      />
+    </a>
+    <a href="https://www.npmjs.com/package/@algorithm.ts/gcd">
+      <img
+        alt="Npm Download"
+        src="https://img.shields.io/npm/dm/@algorithm.ts/gcd.svg"
+      />
+    </a>
+    <a href="https://www.npmjs.com/package/@algorithm.ts/gcd">
+      <img
+        alt="Npm License"
+        src="https://img.shields.io/npm/l/@algorithm.ts/gcd.svg"
+      />
+    </a>
+    <a href="#install">
+      <img
+        alt="Module Formats: cjs, esm"
+        src="https://img.shields.io/badge/module_formats-cjs%2C%20esm-green.svg"
+      />
+    </a>
+    <a href="https://github.com/nodejs/node">
+      <img
+        alt="Node.js Version"
+        src="https://img.shields.io/node/v/@algorithm.ts/gcd"
+      />
+    </a>
+    <a href="https://github.com/facebook/jest">
+      <img
+        alt="Tested with Jest"
+        src="https://img.shields.io/badge/tested_with-jest-9c465e.svg"
+      />
+    </a>
+    <a href="https://github.com/prettier/prettier">
+      <img
+        alt="Code Style: prettier"
+        src="https://img.shields.io/badge/code_style-prettier-ff69b4.svg?style=flat-square"
+      />
+    </a>
+  </div>
+</header>
+<br/>
+
+
+A typescript implementation of the **gcd** and **Extended Euclidean** algorithm.
+
+* gcd: The Greatest Common Divisor.
+
+* Extended Euclidean algorithm: For solving the smallest
+  integer solution (|x| + |y| smallest) of the equation `Ax + By = gcd(x,y)`.
+
+
+## Install
+
+* npm
+
+  ```bash
+  npm install --save @algorithm.ts/gcd
+  ```
+
+* yarn
+
+  ```bash
+  yarn add @algorithm.ts/gcd
+  ```
+
+
+## Usage
+
+
+* gcd
+
+  ```typescript
+  import { gcd, gcdBigint } from '@algorithm.ts/gcd'
+
+  gcd(3, 4) // => 1
+  gcdBigint(3n, 6n) // => 3n
+  ```
+
+* Extended Euclidean algorithm
+
+  ```typescript
+  import { euclidean, euclideanBigint } from '@algorithm.ts/gcd'
+
+  // 3x + 4y = gcd(3, 4)
+  euclidean(3, 4) // => [-1, 1, 1]
+  euclidean(3, 8) // => [3, -1, 1]
+  euclideanBigint(6, 8) // => [-1n, 1n, 2n]
+  ```
+
+## Related
+
+
+* [数论基础之模方程初步][gcd]
+
+
+[homepage]: https://github.com/guanghechen/algorithm.ts/tree/main/packages/gcd#readme
+[gcd]: https://me.guanghechen.com/post/math/number-theory/%E6%A8%A1%E6%96%B9%E7%A8%8B/basic/

Diff for: packages/gcd/__test__/gcd.spec.ts

@@ -0,0 +1,51 @@
+import { euclidean, euclideanBigint, gcd, gcdBigint } from '../src'
+
+test('gcd', function () {
+  for (let i = 1; i < 50; ++i) {
+    expect(gcd(i, 0)).toBe(i)
+    expect(gcd(0, i)).toBe(i)
+    for (let j = 1; j < 50; ++j) {
+      const d = gcd(i, j)
+      expect(i % d).toBe(0)
+      expect(j % d).toBe(0)
+      expect(gcd(i / d, j / d)).toBe(1)
+    }
+  }
+})
+
+test('gcdBigint', function () {
+  for (let i = 1n; i < 50n; ++i) {
+    expect(gcdBigint(i, 0n)).toBe(i)
+    expect(gcdBigint(0n, i)).toBe(i)
+    for (let j = 1n; j < 50n; ++j) {
+      const d = gcdBigint(i, j)
+      expect(i % d).toBe(0n)
+      expect(j % d).toBe(0n)
+      expect(gcdBigint(i / d, j / d)).toBe(1n)
+    }
+  }
+})
+
+test('euclid', function () {
+  for (let i = 1; i < 50; ++i) {
+    for (let j = 1; j < 50; ++j) {
+      const [x, y, d] = euclidean(i, j)
+      expect(i % d).toBe(0)
+      expect(j % d).toBe(0)
+      expect(gcd(i / d, j / d)).toBe(1)
+      expect(i * x + j * y).toBe(d)
+    }
+  }
+})
+
+test('euclidBigint', function () {
+  for (let i = 1n; i < 50n; ++i) {
+    for (let j = 1n; j < 50n; ++j) {
+      const [x, y, d] = euclideanBigint(i, j)
+      expect(i % d).toBe(0n)
+      expect(j % d).toBe(0n)
+      expect(gcdBigint(i / d, j / d)).toBe(1n)
+      expect(i * x + j * y).toBe(d)
+    }
+  }
+})

Diff for: packages/gcd/package.json

@@ -0,0 +1,43 @@
+{
+  "name": "@algorithm.ts/gcd",
+  "version": "1.0.12",
+  "description": "GCD + Euclidean algorithm",
+  "author": {
+    "name": "guanghechen",
+    "url": "https://github.com/guanghechen/"
+  },
+  "repository": {
+    "type": "git",
+    "url": "https://github.com/guanghechen/algorithm.ts.git",
+    "directory": "packages/gcd"
+  },
+  "homepage": "https://github.com/guanghechen/algorithm.ts/tree/main/packages/gcd#readme",
+  "keywords": [
+    "algorithm",
+    "gcd",
+    "extended euclidean algorithm"
+  ],
+  "main": "lib/cjs/index.js",
+  "module": "lib/esm/index.js",
+  "types": "lib/types/index.d.ts",
+  "source": "src/index.ts",
+  "license": "MIT",
+  "engines": {
+    "node": ">= 14.15.0"
+  },
+  "files": [
+    "lib/",
+    "!lib/**/*.js.map",
+    "!lib/**/*.d.ts.map",
+    "package.json",
+    "CHANGELOG.md",
+    "LICENSE",
+    "README.md"
+  ],
+  "scripts": {
+    "build": "cross-env NODE_ENV=production rollup -c ../../rollup.config.js",
+    "prebuild": "rimraf lib/ && tsc -p tsconfig.src.json --emitDeclarationOnly",
+    "prepublishOnly": "cross-env ROLLUP_SHOULD_SOURCEMAP=false yarn build",
+    "test": "cross-env TS_NODE_FILES=true jest --config ../../jest.config.js --rootDir ."
+  }
+}

Diff for: packages/gcd/src/euclidean.ts

@@ -0,0 +1,71 @@
+/**
+ * Extended Euclidean algorithm for solving the smallest
+ * integer solution (|x| + |y| smallest) of the equation `Ax + By = gcd(x,y)`.
+ *
+ * @param a
+ * @param b
+ * @returns
+ * @see https://me.guanghechen.com/post/math/number-theory/%E6%A8%A1%E6%96%B9%E7%A8%8B/basic/
+ */
+export function euclidean(a: number, b: number): [number, number, number] {
+  let x: number
+  let y: number
+  let d: number
+  solve(a, b)
+  return [x!, y!, d!]
+
+  function solve(_a: number, _b: number): void {
+    if (_b === 0) {
+      x = 1
+      y = 0
+      d = _a
+    } else {
+      const A = _a % _b
+      const B = _b
+      solve(B, A)
+
+      const X = y
+      const Y = x
+
+      x = X
+      y = Y - Math.floor(_a / _b) * X
+    }
+  }
+}
+
+/**
+ * Bigint version.
+ *
+ * @param a
+ * @param b
+ * @returns
+ * @see https://me.guanghechen.com/post/math/number-theory/%E6%A8%A1%E6%96%B9%E7%A8%8B/basic/
+ */
+export function euclideanBigint(
+  a: bigint,
+  b: bigint,
+): [bigint, bigint, bigint] {
+  let x: bigint
+  let y: bigint
+  let d: bigint
+  solve(a, b)
+  return [x!, y!, d!]
+
+  function solve(_a: bigint, _b: bigint): void {
+    if (_b === 0n) {
+      x = 1n
+      y = 0n
+      d = _a
+    } else {
+      const A = _a % _b
+      const B = _b
+      solve(B, A)
+
+      const X = y
+      const Y = x
+
+      x = X
+      y = Y - (_a / _b) * X
+    }
+  }
+}

Diff for: packages/gcd/src/gcd.ts

@@ -0,0 +1,21 @@
+/**
+ * Find the greatest common divisor of x and y
+ *
+ * @param x
+ * @param y
+ * @returns
+ */
+export function gcd(x: number, y: number): number {
+  return y === 0 ? x : gcd(y, x % y)
+}
+
+/**
+ * Bigint version.
+ *
+ * @param x
+ * @param y
+ * @returns
+ */
+export function gcdBigint(x: bigint, y: bigint): bigint {
+  return y === 0n ? x : gcdBigint(y, x % y)
+}

Diff for: packages/gcd/src/index.ts

@@ -0,0 +1,2 @@
+export * from './gcd'
+export * from './euclidean'

Diff for: packages/gcd/tsconfig.json

@@ -0,0 +1,4 @@
+{
+  "extends": "../../tsconfig",
+  "include": ["src", "script", "__test__"]
+}

Diff for: packages/gcd/tsconfig.src.json

@@ -0,0 +1,8 @@
+{
+  "extends": "../../tsconfig.settings",
+  "compilerOptions": {
+    "declarationDir": "lib/types",
+    "rootDir": "src"
+  },
+  "include": ["src"]
+}

Diff for: tsconfig.json

@@ -11,6 +11,7 @@
       "@algorithm.ts/dinic": ["packages/dinic/src"],
       "@algorithm.ts/dlx": ["packages/dlx/src"],
       "@algorithm.ts/findset": ["packages/findset/src"],
+      "@algorithm.ts/gcd": ["packages/gcd/src"],
       "@algorithm.ts/isap": ["packages/isap/src"],
       "@algorithm.ts/knuth-shuffle": ["packages/knuth-shuffle/src"],
       "@algorithm.ts/mcmf": ["packages/mcmf/src"],