feat: leetcode 313

Author: deweyou

README.md

@@ -2,7 +2,7 @@
 
 <p align="center">
 <!-- TOPICS COUNT START -->
-<img src="https://img.shields.io/badge/-进度:332-green" alt="进度:332">
+<img src="https://img.shields.io/badge/-进度:333-green" alt="进度:333">
 <!-- 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

@@ -1129,6 +1129,12 @@
         "path": "./problemset/burst-balloons/README.md",
         "difficulty": "困难"
       },
+      {
+        "id": "313",
+        "title": "超级丑数",
+        "path": "./problemset/super-ugly-number/README.md",
+        "difficulty": "中等"
+      },
       {
         "id": "688",
         "title": "骑士在棋盘上的概率",

assets/data/topics.json

@@ -2479,6 +2479,16 @@
     "url": "https://leetcode-cn.com/problems/burst-balloons/",
     "path": "./problemset/burst-balloons/README.md"
   },
+  {
+    "id": "313",
+    "title": {
+      "cn": "超级丑数",
+      "en": "super-ugly-number"
+    },
+    "difficulty": "中等",
+    "url": "https://leetcode-cn.com/problems/super-ugly-number/",
+    "path": "./problemset/super-ugly-number/README.md"
+  },
   {
     "id": "342",
     "title": {
@@ -3319,4 +3329,4 @@
     "url": "https://leetcode-cn.com/problems/sum-of-subarray-ranges/",
     "path": "./problemset/sum-of-subarray-ranges/README.md"
   }
-]
+]

assets/docs/CATEGORIES.md

@@ -221,6 +221,7 @@
 | 300. [最长递增子序列](../../problemset/longest-increasing-subsequence/README.md) | 中等 |
 | 309. [最佳买卖股票时机含冷冻期](../../problemset/best-time-to-buy-and-sell-stock-with-cooldown/README.md) | 中等 |
 | 312. [戳气球](../../problemset/burst-balloons/README.md) | 困难 |
+| 313. [超级丑数](../../problemset/super-ugly-number/README.md) | 中等 |
 | 688. [骑士在棋盘上的概率](../../problemset/knight-probability-in-chessboard/README.md) | 中等 |
 | 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 |

assets/docs/TOPICS.md

@@ -496,6 +496,8 @@
 
 [312. 戳气球](../../problemset/burst-balloons/README.md)
 
+[313. 超级丑数](../../problemset/super-ugly-number/README.md)
+
 [342. 4的幂](../../problemset/power-of-four/README.md)
 
 [355. 设计推特](../../problemset/design-twitter/README.md)

problemset/super-ugly-number/README.md

@@ -0,0 +1,72 @@
+# 超级丑数
+
+> 难度：中等
+>
+> https://leetcode-cn.com/problems/super-ugly-number/
+
+## 题目
+
+**超级丑数** 是一个正整数，并满足其所有质因数都出现在质数数组 `primes` 中。
+
+给你一个整数 `n` 和一个整数数组 `primes` ，返回第 `n` 个 **超级丑数** 。
+
+题目数据保证第 `n` 个 **超级丑数** 在 `32-bit` 带符号整数范围内。
+
+### 示例
+
+#### 示例 1：
+
+```
+输入：n = 12, primes = [2,7,13,19]
+输出：32 
+解释：给定长度为 4 的质数数组 primes = [2,7,13,19]，前 12 个超级丑数序列为：[1,2,4,7,8,13,14,16,19,26,28,32] 。
+```
+
+#### 示例 2：
+
+```
+输入：n = 1, primes = [2,3,5]
+输出：1
+解释：1 不含质因数，因此它的所有质因数都在质数数组 primes = [2,3,5] 中。
+```
+
+
+### 提示：
+
+- `1 <= n <= 106`
+- `1 <= primes.length <= 100`
+- `2 <= primes[i] <= 1000`
+- 题目数据 **保证** `primes[i]` 是一个质数
+- `primes` 中的所有值都 **互不相同** ，且按 **递增顺序** 排列
+
+## 解题
+
+```ts
+/**
+ * 动态规划
+ * @desc 时间复杂度 O(MN)  空间复杂度 O(N+M)
+ * @param n
+ * @param primes
+ * @returns
+ */
+export function nthSuperUglyNumber(n: number, primes: number[]): number {
+  const dp = new Array(n + 1).fill(0)
+  const len = primes.length
+  const pointers = new Array(len).fill(0)
+  const nums = new Array(len).fill(1)
+  for (let i = 1; i <= n; i++) {
+    let minNum = Number.MAX_SAFE_INTEGER
+    for (let j = 0; j < len; j++)
+      minNum = Math.min(minNum, nums[j])
+
+    dp[i] = minNum
+    for (let j = 0; j < len; j++) {
+      if (nums[j] === minNum) {
+        pointers[j]++
+        nums[j] = dp[pointers[j]] * primes[j]
+      }
+    }
+  }
+  return dp[n]
+}
+```

problemset/super-ugly-number/index.spec.ts

@@ -0,0 +1,15 @@
+import { describe, expect, it } from 'vitest'
+import { nthSuperUglyNumber } from '.'
+
+describe('超级丑数', () => {
+  testCase(nthSuperUglyNumber)
+})
+
+function testCase(fn: (n: number, primes: number[]) => number) {
+  it.each([
+    [12, [2, 7, 13, 19], 32],
+    [1, [2, 3, 5], 1],
+  ])('示例%#', (n, primes, expected) => {
+    expect(fn(n, primes)).toBe(expected)
+  })
+}

problemset/super-ugly-number/index.ts

@@ -0,0 +1,27 @@
+/**
+ * 动态规划
+ * @desc 时间复杂度 O(MN)  空间复杂度 O(N+M)
+ * @param n
+ * @param primes
+ * @returns
+ */
+export function nthSuperUglyNumber(n: number, primes: number[]): number {
+  const dp = new Array(n + 1).fill(0)
+  const len = primes.length
+  const pointers = new Array(len).fill(0)
+  const nums = new Array(len).fill(1)
+  for (let i = 1; i <= n; i++) {
+    let minNum = Number.MAX_SAFE_INTEGER
+    for (let j = 0; j < len; j++)
+      minNum = Math.min(minNum, nums[j])
+
+    dp[i] = minNum
+    for (let j = 0; j < len; j++) {
+      if (nums[j] === minNum) {
+        pointers[j]++
+        nums[j] = dp[pointers[j]] * primes[j]
+      }
+    }
+  }
+  return dp[n]
+}