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‎assets/output/1494.md‎

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Return _the**minimum** number of semesters needed to take all courses_. The
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testcases will be generated such that it is possible to take every course.
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**Example 1:**
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![](https://assets.leetcode.com/uploads/2020/05/22/leetcode_parallel_courses_1.png)
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> Input: n = 4, relations = [[2,1],[3,1],[1,4]], k = 2
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> Output: 3
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> Explanation: The figure above represents the given graph.
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> In the first semester, you can take courses 2 and 3.
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> In the second semester, you can take course 1.
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> In the third semester, you can take course 4.
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**Example 2:**
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![](https://assets.leetcode.com/uploads/2020/05/22/leetcode_parallel_courses_2.png)
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> Input: n = 5, relations = [[2,1],[3,1],[4,1],[1,5]], k = 2
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> Output: 4
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> Explanation: The figure above represents the given graph.
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>
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> In the first semester, you can only take courses 2 and 3 since you cannot take more than two per semester.
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>
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> In the second semester, you can take course 4.
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> In the third semester, you can take course 1.
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> In the fourth semester, you can take course 5.
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**Constraints:**
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* `1 <= n <= 15`
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* `1 <= k <= n`
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* `0 <= relations.length <= n * (n-1) / 2`
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* `relations[i].length == 2`
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* `1 <= prevCoursei, nextCoursei <= n`
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* `prevCoursei != nextCoursei`
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* All the pairs `[prevCoursei, nextCoursei]` are **unique**.
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* The given graph is a directed acyclic graph.
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- `1 <= n <= 15`
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- `1 <= k <= n`
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- `0 <= relations.length <= n * (n-1) / 2`
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- `relations[i].length == 2`
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- `1 <= prevCoursei, nextCoursei <= n`
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- `prevCoursei != nextCoursei`
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- All the pairs `[prevCoursei, nextCoursei]` are **unique**.
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- The given graph is a directed acyclic graph.
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## 题目大意
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给你一个整数 `n` 表示某所大学里课程的数目，编号为 `1` 到 `n` ，数组 `relations` 中， `relations[i] = [xi,
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yi]` 表示一个先修课的关系，也就是课程 `xi` 必须在课程 `yi` 之前上。同时你还有一个整数 `k` 。
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yi]` 表示一个先修课的关系，也就是课程 `xi` 必须在课程 `yi` 之前上。同时你还有一个整数 `k` 。
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在一个学期中，你 **最多** 可以同时上 `k` 门课，前提是这些课的先修课在之前的学期里已经上过了。
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在一个学期中，你 **最多** 可以同时上 `k` 门课，前提是这些课的先修课在之前的学期里已经上过了。
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请你返回上完所有课最少需要多少个学期。题目保证一定存在一种上完所有课的方式。
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**示例 1：**
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**![](https://assets.leetcode-cn.com/aliyun-lc-
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upload/uploads/2020/06/27/leetcode_parallel_courses_1.png)**
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> **输入：** n = 4, relations = [[2,1],[3,1],[1,4]], k = 2
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> **输出：** 3
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> **输出：** 3
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> **解释：** 上图展示了题目输入的图。在第一个学期中，我们可以上课程 2 和课程 3 。然后第二个学期上课程 1 ，第三个学期上课程 4 。
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**示例 2：**
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**![](https://assets.leetcode-cn.com/aliyun-lc-
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upload/uploads/2020/06/27/leetcode_parallel_courses_2.png)**
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> **输入：** n = 5, relations = [[2,1],[3,1],[4,1],[1,5]], k = 2
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> **输出：** 4
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> **输出：** 4
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> **解释：** 上图展示了题目输入的图。一个最优方案是：第一学期上课程 2 和 3，第二学期上课程 4 ，第三学期上课程 1 ，第四学期上课程 5 。
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**示例 3：**
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> **输入：** n = 11, relations = [], k = 2
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> **输出：** 6
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**提示：**
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* `1 <= n <= 15`
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* `1 <= k <= n`
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* `0 <= relations.length <= n * (n-1) / 2`
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* `relations[i].length == 2`
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* `1 <= xi, yi <= n`
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* `xi != yi`
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* 所有先修关系都是不同的，也就是说 `relations[i] != relations[j]` 。
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* 题目输入的图是个有向无环图。
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- `1 <= n <= 15`
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- `1 <= k <= n`
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- `0 <= relations.length <= n * (n-1) / 2`
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- `relations[i].length == 2`
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- `1 <= xi, yi <= n`
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- `xi != yi`
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- 所有先修关系都是不同的，也就是说 `relations[i] != relations[j]` 。
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- 题目输入的图是个有向无环图。
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## 解题思路
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<!-- prettier-ignore -->
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| 题号 | 标题 | 题解 | 标签 | 难度 | 力扣 |
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| :------: | :------ | :------: | :------ | :------: | :------: |
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| 1136 | 并行课程 🔒 | | [`图`](/tag/graph.md) [`拓扑排序`](/tag/topological-sort.md) | 🟠 | [🀄️](https://leetcode.cn/problems/parallel-courses) [🔗](https://leetcode.com/problems/parallel-courses) |
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| 1136 | 并行课程 🔒 | | [`图`](/tag/graph.md) [`拓扑排序`](/tag/topological-sort.md) | 🟠 | [🀄️](https://leetcode.cn/problems/parallel-courses) [🔗](https://leetcode.com/problems/parallel-courses) |

‎src/.vuepress/sidebar.ts‎

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"1089",
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{
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"2777",
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"2779",
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"2796",

‎src/book/dynamic_programming.md‎

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| 403 | 青蛙过河 | | [`数组`](/tag/array.md) [`动态规划`](/tag/dynamic-programming.md) | 🔴 | [🀄️](https://leetcode.cn/problems/frog-jump) [🔗](https://leetcode.com/problems/frog-jump) |
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| 552 | 学生出勤记录 II | | [`动态规划`](/tag/dynamic-programming.md) | 🔴 | [🀄️](https://leetcode.cn/problems/student-attendance-record-ii) [🔗](https://leetcode.com/problems/student-attendance-record-ii) |
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| 913 | 猫和老鼠 | | [`图`](/tag/graph.md) [`拓扑排序`](/tag/topological-sort.md) [`记忆化搜索`](/tag/memoization.md) `3+` | 🔴 | [🀄️](https://leetcode.cn/problems/cat-and-mouse) [🔗](https://leetcode.com/problems/cat-and-mouse) |
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| 329 | 矩阵中的最长递增路径 | | [`深度优先搜索`](/tag/depth-first-search.md) [`广度优先搜索`](/tag/breadth-first-search.md) [`图`](/tag/graph.md) `5+` | 🔴 | [🀄️](https://leetcode.cn/problems/longest-increasing-path-in-a-matrix) [🔗](https://leetcode.com/problems/longest-increasing-path-in-a-matrix) |
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| 329 | 矩阵中的最长递增路径 | [[✓]](/problem/0329.md) | [`深度优先搜索`](/tag/depth-first-search.md) [`广度优先搜索`](/tag/breadth-first-search.md) [`图`](/tag/graph.md) `5+` | 🔴 | [🀄️](https://leetcode.cn/problems/longest-increasing-path-in-a-matrix) [🔗](https://leetcode.com/problems/longest-increasing-path-in-a-matrix) |
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#### 线性 DP
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| 213 | 打家劫舍 II | [[✓]](/problem/0213.md) | [`数组`](/tag/array.md) [`动态规划`](/tag/dynamic-programming.md) | 🟠 | [🀄️](https://leetcode.cn/problems/house-robber-ii) [🔗](https://leetcode.com/problems/house-robber-ii) |
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| 740 | 删除并获得点数 | [[✓]](/problem/0740.md) | [`数组`](/tag/array.md) [`哈希表`](/tag/hash-table.md) [`动态规划`](/tag/dynamic-programming.md) | 🟠 | [🀄️](https://leetcode.cn/problems/delete-and-earn) [🔗](https://leetcode.com/problems/delete-and-earn) |
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| 1388 | 3n 块披萨 | | [`贪心`](/tag/greedy.md) [`数组`](/tag/array.md) [`动态规划`](/tag/dynamic-programming.md) `1+` | 🔴 | [🀄️](https://leetcode.cn/problems/pizza-with-3n-slices) [🔗](https://leetcode.com/problems/pizza-with-3n-slices) |
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| 873 | 最长的斐波那契子序列的长度 | | [`数组`](/tag/array.md) [`哈希表`](/tag/hash-table.md) [`动态规划`](/tag/dynamic-programming.md) | 🟠 | [🀄️](https://leetcode.cn/problems/length-of-longest-fibonacci-subsequence) [🔗](https://leetcode.com/problems/length-of-longest-fibonacci-subsequence) |
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| 873 | 最长的斐波那契子序列的长度 | [[✓]](/problem/0873.md) | [`数组`](/tag/array.md) [`哈希表`](/tag/hash-table.md) [`动态规划`](/tag/dynamic-programming.md) | 🟠 | [🀄️](https://leetcode.cn/problems/length-of-longest-fibonacci-subsequence) [🔗](https://leetcode.com/problems/length-of-longest-fibonacci-subsequence) |
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| 1027 | 最长等差数列 | [[✓]](/problem/1027.md) | [`数组`](/tag/array.md) [`哈希表`](/tag/hash-table.md) [`二分查找`](/tag/binary-search.md) `1+` | 🟠 | [🀄️](https://leetcode.cn/problems/longest-arithmetic-subsequence) [🔗](https://leetcode.com/problems/longest-arithmetic-subsequence) |
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| 1055 | 形成字符串的最短路径 🔒 | | [`贪心`](/tag/greedy.md) [`双指针`](/tag/two-pointers.md) [`字符串`](/tag/string.md) `1+` | 🟠 | [🀄️](https://leetcode.cn/problems/shortest-way-to-form-string) [🔗](https://leetcode.com/problems/shortest-way-to-form-string) |
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| 368 | 最大整除子集 | [[✓]](/problem/0368.md) | [`数组`](/tag/array.md) [`数学`](/tag/math.md) [`动态规划`](/tag/dynamic-programming.md) `1+` | 🟠 | [🀄️](https://leetcode.cn/problems/largest-divisible-subset) [🔗](https://leetcode.com/problems/largest-divisible-subset) |
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| 518 | 零钱兑换 II | [[✓]](/problem/0518.md) | [`数组`](/tag/array.md) [`动态规划`](/tag/dynamic-programming.md) | 🟠 | [🀄️](https://leetcode.cn/problems/coin-change-ii) [🔗](https://leetcode.com/problems/coin-change-ii) |
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| 139 | 单词拆分 | [[✓]](/problem/0139.md) | [`字典树`](/tag/trie.md) [`记忆化搜索`](/tag/memoization.md) [`数组`](/tag/array.md) `3+` | 🟠 | [🀄️](https://leetcode.cn/problems/word-break) [🔗](https://leetcode.com/problems/word-break) |
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| 377 | 组合总和 Ⅳ | [[✓]](/problem/0377.md) | [`数组`](/tag/array.md) [`动态规划`](/tag/dynamic-programming.md) | 🟠 | [🀄️](https://leetcode.cn/problems/combination-sum-iv) [🔗](https://leetcode.com/problems/combination-sum-iv) |
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| 638 | 大礼包 | | [`位运算`](/tag/bit-manipulation.md) [`记忆化搜索`](/tag/memoization.md) [`数组`](/tag/array.md) `3+` | 🟠 | [🀄️](https://leetcode.cn/problems/shopping-offers) [🔗](https://leetcode.com/problems/shopping-offers) |
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| 638 | 大礼包 | [[✓]](/problem/0638.md) | [`位运算`](/tag/bit-manipulation.md) [`记忆化搜索`](/tag/memoization.md) [`数组`](/tag/array.md) `3+` | 🟠 | [🀄️](https://leetcode.cn/problems/shopping-offers) [🔗](https://leetcode.com/problems/shopping-offers) |
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| 1449 | 数位成本和为目标值的最大数字 | | [`数组`](/tag/array.md) [`动态规划`](/tag/dynamic-programming.md) | 🔴 | [🀄️](https://leetcode.cn/problems/form-largest-integer-with-digits-that-add-up-to-target) [🔗](https://leetcode.com/problems/form-largest-integer-with-digits-that-add-up-to-target) |
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| 1681 | 最小不兼容性 | | [`位运算`](/tag/bit-manipulation.md) [`数组`](/tag/array.md) [`动态规划`](/tag/dynamic-programming.md) `1+` | 🔴 | [🀄️](https://leetcode.cn/problems/minimum-incompatibility) [🔗](https://leetcode.com/problems/minimum-incompatibility) |
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| 526 | 优美的排列 | | [`位运算`](/tag/bit-manipulation.md) [`数组`](/tag/array.md) [`动态规划`](/tag/dynamic-programming.md) `2+` | 🟠 | [🀄️](https://leetcode.cn/problems/beautiful-arrangement) [🔗](https://leetcode.com/problems/beautiful-arrangement) |
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| 351 | 安卓系统手势解锁 🔒 | | [`位运算`](/tag/bit-manipulation.md) [`动态规划`](/tag/dynamic-programming.md) [`回溯`](/tag/backtracking.md) `1+` | 🟠 | [🀄️](https://leetcode.cn/problems/android-unlock-patterns) [🔗](https://leetcode.com/problems/android-unlock-patterns) |
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| 464 | 我能赢吗 | | [`位运算`](/tag/bit-manipulation.md) [`记忆化搜索`](/tag/memoization.md) [`数学`](/tag/math.md) `3+` | 🟠 | [🀄️](https://leetcode.cn/problems/can-i-win) [🔗](https://leetcode.com/problems/can-i-win) |
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| 464 | 我能赢吗 | [[✓]](/problem/0464.md) | [`位运算`](/tag/bit-manipulation.md) [`记忆化搜索`](/tag/memoization.md) [`数学`](/tag/math.md) `3+` | 🟠 | [🀄️](https://leetcode.cn/problems/can-i-win) [🔗](https://leetcode.com/problems/can-i-win) |
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| 847 | 访问所有节点的最短路径 | | [`位运算`](/tag/bit-manipulation.md) [`广度优先搜索`](/tag/breadth-first-search.md) [`图`](/tag/graph.md) `2+` | 🔴 | [🀄️](https://leetcode.cn/problems/shortest-path-visiting-all-nodes) [🔗](https://leetcode.com/problems/shortest-path-visiting-all-nodes) |
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| 638 | 大礼包 | | [`位运算`](/tag/bit-manipulation.md) [`记忆化搜索`](/tag/memoization.md) [`数组`](/tag/array.md) `3+` | 🟠 | [🀄️](https://leetcode.cn/problems/shopping-offers) [🔗](https://leetcode.com/problems/shopping-offers) |
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| 638 | 大礼包 | [[✓]](/problem/0638.md) | [`位运算`](/tag/bit-manipulation.md) [`记忆化搜索`](/tag/memoization.md) [`数组`](/tag/array.md) `3+` | 🟠 | [🀄️](https://leetcode.cn/problems/shopping-offers) [🔗](https://leetcode.com/problems/shopping-offers) |
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| 1994 | 好子集的数目 | | [`位运算`](/tag/bit-manipulation.md) [`数组`](/tag/array.md) [`数学`](/tag/math.md) `2+` | 🔴 | [🀄️](https://leetcode.cn/problems/the-number-of-good-subsets) [🔗](https://leetcode.com/problems/the-number-of-good-subsets) |
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| 1349 | 参加考试的最大学生数 | | [`位运算`](/tag/bit-manipulation.md) [`数组`](/tag/array.md) [`动态规划`](/tag/dynamic-programming.md) `2+` | 🔴 | [🀄️](https://leetcode.cn/problems/maximum-students-taking-exam) [🔗](https://leetcode.com/problems/maximum-students-taking-exam) |
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| 698 | 划分为k个相等的子集 | | [`位运算`](/tag/bit-manipulation.md) [`记忆化搜索`](/tag/memoization.md) [`数组`](/tag/array.md) `3+` | 🟠 | [🀄️](https://leetcode.cn/problems/partition-to-k-equal-sum-subsets) [🔗](https://leetcode.com/problems/partition-to-k-equal-sum-subsets) |

‎src/book/slide_window.md‎

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| 713 | 乘积小于 K 的子数组 | | [`数组`](/tag/array.md) [`二分查找`](/tag/binary-search.md) [`前缀和`](/tag/prefix-sum.md) `1+` | 🟠 | [🀄️](https://leetcode.cn/problems/subarray-product-less-than-k) [🔗](https://leetcode.com/problems/subarray-product-less-than-k) |
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| 904 | 水果成篮 | | [`数组`](/tag/array.md) [`哈希表`](/tag/hash-table.md) [`滑动窗口`](/tag/sliding-window.md) | 🟠 | [🀄️](https://leetcode.cn/problems/fruit-into-baskets) [🔗](https://leetcode.com/problems/fruit-into-baskets) |
592592
| 1358 | 包含所有三种字符的子字符串数目 | | [`哈希表`](/tag/hash-table.md) [`字符串`](/tag/string.md) [`滑动窗口`](/tag/sliding-window.md) | 🟠 | [🀄️](https://leetcode.cn/problems/number-of-substrings-containing-all-three-characters) [🔗](https://leetcode.com/problems/number-of-substrings-containing-all-three-characters) |
593-
| 467 | 环绕字符串中唯一的子字符串 | | [`字符串`](/tag/string.md) [`动态规划`](/tag/dynamic-programming.md) | 🟠 | [🀄️](https://leetcode.cn/problems/unique-substrings-in-wraparound-string) [🔗](https://leetcode.com/problems/unique-substrings-in-wraparound-string) |
593+
| 467 | 环绕字符串中唯一的子字符串 | [[✓]](/problem/0467.md) | [`字符串`](/tag/string.md) [`动态规划`](/tag/dynamic-programming.md) | 🟠 | [🀄️](https://leetcode.cn/problems/unique-substrings-in-wraparound-string) [🔗](https://leetcode.com/problems/unique-substrings-in-wraparound-string) |
594594
| 1438 | 绝对差不超过限制的最长连续子数组 | | [`队列`](/tag/queue.md) [`数组`](/tag/array.md) [`有序集合`](/tag/ordered-set.md) `3+` | 🟠 | [🀄️](https://leetcode.cn/problems/longest-continuous-subarray-with-absolute-diff-less-than-or-equal-to-limit) [🔗](https://leetcode.com/problems/longest-continuous-subarray-with-absolute-diff-less-than-or-equal-to-limit) |
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‎src/plan/codetop_list.md‎

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| 384 | 打乱数组 | [[✓]](/problem/0384.md) | [`数组`](/tag/array.md) [`数学`](/tag/math.md) [`随机化`](/tag/randomized.md) | 🟠 | [🀄️](https://leetcode.cn/problems/shuffle-an-array) [🔗](https://leetcode.com/problems/shuffle-an-array) | 28 |
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| 328 | 奇偶链表 | [[✓]](/problem/0328.md) | [`链表`](/tag/linked-list.md) | 🟠 | [🀄️](https://leetcode.cn/problems/odd-even-linked-list) [🔗](https://leetcode.com/problems/odd-even-linked-list) | 28 |
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| 91 | 解码方法 | [[✓]](/problem/0091.md) | [`字符串`](/tag/string.md) [`动态规划`](/tag/dynamic-programming.md) | 🟠 | [🀄️](https://leetcode.cn/problems/decode-ways) [🔗](https://leetcode.com/problems/decode-ways) | 28 |
162-
| 329 | 矩阵中的最长递增路径 | | [`深度优先搜索`](/tag/depth-first-search.md) [`广度优先搜索`](/tag/breadth-first-search.md) [`图`](/tag/graph.md) `5+` | 🔴 | [🀄️](https://leetcode.cn/problems/longest-increasing-path-in-a-matrix) [🔗](https://leetcode.com/problems/longest-increasing-path-in-a-matrix) | 28 |
162+
| 329 | 矩阵中的最长递增路径 | [[✓]](/problem/0329.md) | [`深度优先搜索`](/tag/depth-first-search.md) [`广度优先搜索`](/tag/breadth-first-search.md) [`图`](/tag/graph.md) `5+` | 🔴 | [🀄️](https://leetcode.cn/problems/longest-increasing-path-in-a-matrix) [🔗](https://leetcode.com/problems/longest-increasing-path-in-a-matrix) | 28 |
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| 208 | 实现 Trie (前缀树) | [[✓]](/problem/0208.md) | [`设计`](/tag/design.md) [`字典树`](/tag/trie.md) [`哈希表`](/tag/hash-table.md) `1+` | 🟠 | [🀄️](https://leetcode.cn/problems/implement-trie-prefix-tree) [🔗](https://leetcode.com/problems/implement-trie-prefix-tree) | 27 |
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| 9 | 回文数 | [[✓]](/problem/0009.md) | [`数学`](/tag/math.md) | 🟢 | [🀄️](https://leetcode.cn/problems/palindrome-number) [🔗](https://leetcode.com/problems/palindrome-number) | 27 |
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| 10 | 正则表达式匹配 | [[✓]](/problem/0010.md) | [`递归`](/tag/recursion.md) [`字符串`](/tag/string.md) [`动态规划`](/tag/dynamic-programming.md) | 🔴 | [🀄️](https://leetcode.cn/problems/regular-expression-matching) [🔗](https://leetcode.com/problems/regular-expression-matching) | 26 |

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