feat: lcm

docs/.vuepress/config.js

@@ -37,10 +37,10 @@ module.exports = {
       anchor: {
         permalink: true,
       },
-      // toc: {
-      //   includeLevel: [1, 2],
-      // },
-      config: md => {
+      toc: {
+        includeLevel: [1, 2],
+      },
+      extendMarkdown: md => {
         md.use(require('markdown-it-task-lists'));
         md.use(require('markdown-it-imsize'), { autofill: true });
         md.set({ html: true });

src/Math/gcd/__tests__.ts

@@ -2,10 +2,10 @@
  * @Author: Rainy
  * @Date: 2020-01-30 11:42:57
  * @LastEditors  : Rainy
- * @LastEditTime : 2020-01-30 13:49:59
+ * @LastEditTime : 2020-01-31 13:28:09
  */
 
-import { gcd_enumeration, gcd_division_recursive, gcd_sub_recursive, gcd_best, } from '.';
+import { gcd_enumeration, gcd_division_recursive, gcd_sub_recursive, gcd_optimal, } from '.';
 
 test('gcd_enumeration(5, 10) should be 5', () => {
   expect(gcd_enumeration(5, 10)).toEqual(5);
@@ -19,6 +19,6 @@ test('gcd_sub_recursive(5, 10) should be 5', () => {
   expect(gcd_sub_recursive(5, 10)).toEqual(5);
 });
 
-test('gcd_best(5, 10) should be 5', () => {
-  expect(gcd_best(5, 10)).toEqual(5);
+test('gcd_optimal(5, 10) should be 5', () => {
+  expect(gcd_optimal(5, 10)).toEqual(5);
 });

src/Math/gcd/index.ts

@@ -2,9 +2,10 @@
  * @Author: Rainy
  * @Date: 2020-01-30 11:42:57
  * @LastEditors  : Rainy
- * @LastEditTime : 2020-01-30 14:18:01
+ * @LastEditTime : 2020-01-31 13:28:43
  */
 
+// the greatest common divisor
 export function gcd_enumeration(a: number, b: number): number {
   let gcd = 1;
 
@@ -35,20 +36,20 @@ export function gcd_sub_recursive(a: number, b: number): number {
   return a > b ? gcd_sub_recursive(a - b, b) : gcd_sub_recursive(a, b - a);
 }
 
-export function gcd_best(a: number, b: number): number {
+export function gcd_optimal(a: number, b: number): number {
   if (a === b) {
     return a;
   }
 
   if ((a & 1) === 0 && (b & 1) === 0) {
-    return gcd_best(a >> 1, b >> 1);
+    return gcd_optimal(a >> 1, b >> 1);
   } else if ((a & 1) === 0 && (b & 1) !== 0) {
-    return gcd_best(a >> 1, b);
+    return gcd_optimal(a >> 1, b);
   } else if ((a & 1) !== 0 && (b & 1) === 0) {
-    return gcd_best(a, b >> 1);
+    return gcd_optimal(a, b >> 1);
   } else {
     const max = Math.max(a, b);
     const min = Math.min(a, b);
-    return gcd_best(max - min, min);
+    return gcd_optimal(max - min, min);
   }
 }

src/Math/lcm/README.md

@@ -0,0 +1,13 @@
+### 最小公倍数
+
+#### 定义
+
+若有一个数 `X`, 可以被另外两个数 `A` 、 `B` 整除, 且 `X` 大于（或等于） `A` 和 `B`, 则 `X` 为 `A` 和 `B` 的公倍数。 `A` 和 `B` 的公倍数有无限个, 而所有的公倍数中, 最小的公倍数就叫做最小公倍数。
+
+**Note**
+
+$$ lcm(a, b) = \frac{gcm(a, b)}{|a * b|} $$
+
+### 参考资料
+
+[最小公倍数 - wiki](https://zh.wikipedia.org/zh-cn/%E6%9C%80%E5%B0%8F%E5%85%AC%E5%80%8D%E6%95%B8)

src/Math/lcm/__tests__.ts

@@ -0,0 +1,12 @@
+/*
+ * @Author: Rainy
+ * @Date: 2020-01-30 11:42:57
+ * @LastEditors  : Rainy
+ * @LastEditTime : 2020-01-31 13:23:08
+ */
+
+import { lcm } from '.';
+
+test('lcm(5, 10) should be 10', () => {
+  expect(lcm(5, 10)).toEqual(10);
+});

src/Math/lcm/index.ts

@@ -0,0 +1,13 @@
+/*
+ * @Author: Rainy
+ * @Date: 2020-01-31 12:33:43
+ * @LastEditors  : Rainy
+ * @LastEditTime : 2020-01-31 13:25:56
+ */
+
+import { gcd_optimal } from '../gcd';
+
+// the least common multiple
+export function lcm(a: number, b: number): number {
+  return ((a === 0) || (b === 0)) ? 0 : Math.abs(a * b) / gcd_optimal(a, b);
+}