feat(count-primes): 枚举 | 埃氏筛

Author: oushihao

assets/data/category.json

@@ -603,6 +603,12 @@
         "path": "../../problemset/factorial-trailing-zeroes/README.md",
         "difficulty": "中等"
       },
+      {
+        "id": 204,
+        "title": "计数质数",
+        "path": "../../problemset/count-primes/README.md",
+        "difficulty": "中等"
+      },
       {
         "id": 258,
         "title": "各位相加",
@@ -1982,6 +1988,12 @@
   {
     "label": "枚举",
     "problems": [
+      {
+        "id": 204,
+        "title": "计数质数",
+        "path": "../../problemset/count-primes/README.md",
+        "difficulty": "中等"
+      },
       {
         "id": 1601,
         "title": "最多可达成的换楼请求数目",

assets/data/problems.json

@@ -1789,6 +1789,16 @@
     "url": "https://leetcode-cn.com/problems/remove-linked-list-elements/",
     "path": "../../problemset/remove-linked-list-elements/README.md"
   },
+  {
+    "id": 204,
+    "title": {
+      "cn": "计数质数",
+      "en": "count-primes"
+    },
+    "difficulty": "中等",
+    "url": "https://leetcode-cn.com/problems/count-primes/",
+    "path": "../../problemset/count-primes/README.md"
+  },
   {
     "id": 258,
     "title": {

assets/docs/CATEGORY.md

@@ -125,6 +125,7 @@
 | 169. [多数元素](../../problemset/majority-element/README.md) | 简单 |
 | 171. [Excel 表列序号](../../problemset/excel-sheet-column-number/README.md) | 简单 |
 | 172. [阶乘后的零](../../problemset/factorial-trailing-zeroes/README.md) | 中等 |
+| 204. [计数质数](../../problemset/count-primes/README.md) | 中等 |
 | 258. [各位相加](../../problemset/add-digits/README.md) | 简单 |
 | 504. [七进制数](../../problemset/base-7/README.md) | 简单 |
 | 553. [最优除法](../../problemset/optimal-division/README.md) | 中等 |
@@ -409,6 +410,7 @@
 
 | 题目 | 难度 |
 | ---- | ---- |
+| 204. [计数质数](../../problemset/count-primes/README.md) | 中等 |
 | 1601. [最多可达成的换楼请求数目](../../problemset/maximum-number-of-achievable-transfer-requests/README.md) | 困难 |
 
 ## 位运算

assets/docs/PROBLEMS.md

@@ -358,6 +358,8 @@
 
 [203. 移除链表元素](../../problemset/remove-linked-list-elements/README.md)
 
+[204. 计数质数](../../problemset/count-primes/README.md)
+
 [258. 各位相加](../../problemset/add-digits/README.md)
 
 [300. 最长递增子序列](../../problemset/longest-increasing-subsequence/README.md)

problemset/count-primes/README.md

@@ -0,0 +1,82 @@
+# 计数质数
+
+> 难度：中等
+>
+> https://leetcode-cn.com/problems/count-primes/
+
+## 题目
+
+给定整数 `n` ，**返回** 所有小于非负整数  `n`  的质数的数量 。
+
+### 示例
+
+#### 示例 1：
+
+```
+输入：n = 10
+输出：4
+解释：小于 10 的质数一共有 4 个, 它们是 2, 3, 5, 7 。
+```
+
+#### 示例 2：
+
+```
+输入：n = 0
+输出：0
+```
+
+#### 示例 3：
+
+```
+输入：n = 1
+输出：0
+```
+
+## 解题
+
+### 枚举
+
+```typescript
+/**
+ * 枚举
+ * @desc 时间复杂度 O(N√N)  空间复杂度 O(1)
+ * @param n
+ */
+export function countPrimes(n: number): number {
+  let ans = 0;
+  for (let i = 2; i < n; i++) isPrimes(i) && ans++;
+  return ans;
+
+  function isPrimes(x: number): boolean {
+    for (let i = 2; i * i <= x; i++) {
+      if (x % i === 0) return false;
+    }
+    return true;
+  }
+}
+```
+
+### 埃氏筛
+
+```typescript
+/**
+ * 埃氏筛
+ * @desc 时间复杂度 O(Nlog(logN))  空间复杂度 O(N)
+ * @param n
+ */
+export function countPrimes2(n: number): number {
+  const isPrime = new Array(n).fill(true);
+
+  let ans = 0;
+  for (let i = 2; i < n; i++) {
+    if (isPrime[i]) {
+      ans += 1;
+      for (let j = i * i; j < n; j += i) {
+        isPrime[j] = false;
+      }
+    }
+  }
+
+  return ans;
+}
+```

problemset/count-primes/index.spec.ts

@@ -0,0 +1,31 @@
+import { countPrimes, countPrimes2 } from '.';
+
+describe('计数质数', () => {
+  describe('枚举', () => {
+    testCase(countPrimes);
+  });
+
+  describe('埃氏筛', () => {
+    testCase(countPrimes2);
+  });
+});
+
+function testCase(fn: (n: number) => number) {
+  it('示例一', () => {
+    const n = 10;
+    const expected = 4;
+    expect(fn(n)).toBe(expected);
+  });
+
+  it('示例二', () => {
+    const n = 0;
+    const expected = 0;
+    expect(fn(n)).toBe(expected);
+  });
+
+  it('示例三', () => {
+    const n = 1;
+    const expected = 0;
+    expect(fn(n)).toBe(expected);
+  });
+}

problemset/count-primes/index.ts

@@ -0,0 +1,38 @@
+/**
+ * 枚举
+ * @desc 时间复杂度 O(N√N)  空间复杂度 O(1)
+ * @param n
+ */
+export function countPrimes(n: number): number {
+  let ans = 0;
+  for (let i = 2; i < n; i++) isPrimes(i) && ans++;
+  return ans;
+
+  function isPrimes(x: number): boolean {
+    for (let i = 2; i * i <= x; i++) {
+      if (x % i === 0) return false;
+    }
+    return true;
+  }
+}
+
+/**
+ * 埃氏筛
+ * @desc 时间复杂度 O(Nlog(logN))  空间复杂度 O(N)
+ * @param n
+ */
+export function countPrimes2(n: number): number {
+  const isPrime = new Array(n).fill(true);
+
+  let ans = 0;
+  for (let i = 2; i < n; i++) {
+    if (isPrime[i]) {
+      ans += 1;
+      for (let j = i * i; j < n; j += i) {
+        isPrime[j] = false;
+      }
+    }
+  }
+
+  return ans;
+}