feat: leetcode 面试题 17.09

Author: deweyou

README.md

@@ -2,7 +2,7 @@
 
 <p align="center">
 <!-- TOPICS COUNT START -->
-<img src="https://img.shields.io/badge/-进度:506-green" alt="进度:506">
+<img src="https://img.shields.io/badge/-进度:507-green" alt="进度:507">
 <!-- TOPICS COUNT END -->
 <a href="./assets/docs/TOPICS.md"><img src="https://img.shields.io/badge/-题库目录-blue" alt="题库目录"></a>
 <a href="./assets/docs/CATEGORIES.md"><img src="https://img.shields.io/badge/-题库分类-red" alt="题库分类"></a>

assets/data/categories.json

@@ -1632,6 +1632,12 @@
         "title": "粉刷房子",
         "path": "./problemset/paint-house/README.md",
         "difficulty": "中等"
+      },
+      {
+        "id": "面试题 17.09",
+        "title": "第 k 个数",
+        "path": "./problemset/get-kth-magic-number-lcci/README.md",
+        "difficulty": "中等"
       }
     ]
   },

assets/data/topics.json

@@ -5058,5 +5058,15 @@
     "difficulty": "简单",
     "url": "https://leetcode.cn/problems/check-permutation-lcci/",
     "path": "./problemset/check-permutation-lcci/README.md"
+  },
+  {
+    "id": "面试题 17.09",
+    "title": {
+      "cn": "第 k 个数",
+      "en": "get-kth-magic-number-lcci"
+    },
+    "difficulty": "中等",
+    "url": "https://leetcode.cn/problems/get-kth-magic-number-lcci/",
+    "path": "./problemset/get-kth-magic-number-lcci/README.md"
   }
 ]

assets/docs/CATEGORIES.md

@@ -305,6 +305,7 @@
 | 1994. [好子集的数目](../../problemset/the-number-of-good-subsets/README.md) | 困难 |
 | 2100. [适合打劫银行的日子](../../problemset/find-good-days-to-rob-the-bank/README.md) | 中等 |
 | 剑指 Offer II 091. [粉刷房子](../../problemset/paint-house/README.md) | 中等 |
+| 面试题 17.09. [第 k 个数](../../problemset/get-kth-magic-number-lcci/README.md) | 中等 |
 
 ## 双指针
 

assets/docs/TOPICS.md

@@ -1010,4 +1010,6 @@
 
 [面试题 17.19. 消失的两个数字](../../problemset/missing-two-lcci/README.md)
 
-[面试题 01.02. 判定是否互为字符重排](../../problemset/check-permutation-lcci/README.md)
+[面试题 01.02. 判定是否互为字符重排](../../problemset/check-permutation-lcci/README.md)
+
+[面试题 17.09. 第 k 个数](../../problemset/get-kth-magic-number-lcci/README.md)

problemset/get-kth-magic-number-lcci/README.md

@@ -0,0 +1,45 @@
+# 第 k 个数
+
+> 难度：中等
+>
+> https://leetcode.cn/problems/get-kth-magic-number-lcci/
+
+## 题目
+
+有些数的素因子只有 3，5，7，请设计一个算法找出第 `k` 个数。注意，不是必须有这些素因子，而是必须不包含其他的素因子。例如，前几个数按顺序应该是 1，3，5，7，9，15，21。
+
+### 示例 1:
+
+```
+输入: k = 5
+
+输出: 9
+```
+
+## 解题
+
+```ts 
+/**
+ * 动态规划
+ * @desc 时间复杂度 O(N)  空间复杂度 O(N)
+ * @param k
+ * @returns
+ */
+export function getKthMagicNumber(k: number): number {
+  const dp = new Array(k + 1).fill(0)
+  dp[1] = 1
+  let p3 = 1
+  let p5 = 1
+  let p7 = 1
+  for (let i = 2; i <= k; i++) {
+    const num3 = dp[p3] * 3
+    const num5 = dp[p5] * 5
+    const num7 = dp[p7] * 7
+    dp[i] = Math.min(Math.min(num3, num5), num7)
+    if (dp[i] === num3) p3++
+    if (dp[i] === num5) p5++
+    if (dp[i] === num7) p7++
+  }
+  return dp[k]
+}
+```

problemset/get-kth-magic-number-lcci/index.spec.ts

@@ -0,0 +1,14 @@
+import { describe, expect, it } from 'vitest'
+import { getKthMagicNumber } from '.'
+
+describe('第 k 个数', () => {
+  testCase(getKthMagicNumber)
+})
+
+function testCase(fn: (k: number) => number) {
+  it.each([
+    [5, 9],
+  ])('示例%#', (k, expected) => {
+    expect(fn(k)).toBe(expected)
+  })
+}

problemset/get-kth-magic-number-lcci/index.ts

@@ -0,0 +1,23 @@
+/**
+ * 动态规划
+ * @desc 时间复杂度 O(N)  空间复杂度 O(N)
+ * @param k
+ * @returns
+ */
+export function getKthMagicNumber(k: number): number {
+  const dp = new Array(k + 1).fill(0)
+  dp[1] = 1
+  let p3 = 1
+  let p5 = 1
+  let p7 = 1
+  for (let i = 2; i <= k; i++) {
+    const num3 = dp[p3] * 3
+    const num5 = dp[p5] * 5
+    const num7 = dp[p7] * 7
+    dp[i] = Math.min(Math.min(num3, num5), num7)
+    if (dp[i] === num3) p3++
+    if (dp[i] === num5) p5++
+    if (dp[i] === num7) p7++
+  }
+  return dp[k]
+}