feat: leetcode 310

Author: deweyou

assets/data/category.json

@@ -1271,6 +1271,12 @@
         "path": "../../problemset/range-sum-query-mutable/README.md",
         "difficulty": "中等"
       },
+      {
+        "id": 310,
+        "title": "最小高度树",
+        "path": "../../problemset/minimum-height-trees/README.md",
+        "difficulty": "中等"
+      },
       {
         "id": 393,
         "title": "UTF-8 编码验证",

assets/data/problems.json

@@ -2009,6 +2009,16 @@
     "url": "https://leetcode-cn.com/problems/range-sum-query-mutable/",
     "path": "../../problemset/range-sum-query-mutable/README.md"
   },
+  {
+    "id": 310,
+    "title": {
+      "cn": "最小高度树",
+      "en": "minimum-height-trees"
+    },
+    "difficulty": "中等",
+    "url": "https://leetcode-cn.com/problems/minimum-height-trees/",
+    "path": "../../problemset/minimum-height-trees/README.md"
+  },
   {
     "id": 393,
     "title": {

assets/docs/CATEGORY.md

@@ -253,6 +253,7 @@
 | 218. [天际线问题](../../problemset/the-skyline-problem/README.md) | 困难 |
 | 258. [各位相加](../../problemset/add-digits/README.md) | 简单 |
 | 307. [ 区域和检索 - 数组可修改](../../problemset/range-sum-query-mutable/README.md) | 中等 |
+| 310. [最小高度树](../../problemset/minimum-height-trees/README.md) | 中等 |
 | 393. [UTF-8 编码验证](../../problemset/utf-8-validation/README.md) | 中等 |
 | 420. [强密码检验器](../../problemset/strong-password-checker/README.md) | 困难 |
 | 521. [最长特殊序列](../../problemset/longest-uncommon-subsequence/README.md) | 简单 |

assets/docs/PROBLEMS.md

@@ -402,6 +402,8 @@
 
 [307.  区域和检索 - 数组可修改](../../problemset/range-sum-query-mutable/README.md)
 
+[310. 最小高度树](../../problemset/minimum-height-trees/README.md)
+
 [393. UTF-8 编码验证](../../problemset/utf-8-validation/README.md)
 
 [420. 强密码检验器](../../problemset/strong-password-checker/README.md)

problemset/minimum-height-trees/README.md

@@ -0,0 +1,86 @@
+# 最小高度树
+
+> 难度：中等
+>
+> https://leetcode-cn.com/problems/minimum-height-trees/
+
+## 题目
+
+树是一个无向图，其中任何两个顶点只通过一条路径连接。 换句话说，一个任何没有简单环路的连通图都是一棵树。
+
+给你一棵包含 `n` 个节点的树，标记为 `0` 到 `n - 1` 。给定数字 n` 和一个有 `n - 1` 条无向边的 `edges` 列表（每一个边都是一对标签），其中 `edges[i] = [ai, bi]` 表示树中节点 `ai` 和 `bi` 之间存在一条无向边。
+
+可选择树中任何一个节点作为根。当选择节点 `x` 作为根节点时，设结果树的高度为 `h` 。在所有可能的树中，具有最小高度的树（即，`min(h)`）被称为 **最小高度树** 。
+
+请你找到所有的 **最小高度树** 并按 **任意顺序** 返回它们的根节点标签列表。
+
+树的 **高度** 是指根节点和叶子节点之间最长向下路径上边的数量。
+
+### 示例
+
+#### 示例 1：
+
+![minimum-height-trees-1](https://user-images.githubusercontent.com/54696834/161868696-47ec3e60-9a14-4f63-ad17-f8b9d79e97fa.jpg)
+
+```
+输入：n = 4, edges = [[1,0],[1,2],[1,3]]
+输出：[1]
+解释：如图所示，当根是标签为 1 的节点时，树的高度是 1 ，这是唯一的最小高度树。
+```
+
+#### 示例 2：
+
+![minimum-height-trees-2](https://user-images.githubusercontent.com/54696834/161868698-43b003b1-58d5-4fcc-8170-27d77b9b189d.jpg)
+
+```
+输入：n = 6, edges = [[3,0],[3,1],[3,2],[3,4],[5,4]]
+输出：[3,4]
+```
+
+## 解题
+
+```ts
+/**
+ * 拓扑排序
+ * @desc 时间复杂度 O(N)  空间复杂度 O(N)
+ * @param n
+ * @param edges
+ * @returns
+ */
+export function findMinHeightTrees(n: number, edges: number[][]): number[] {
+  if (n === 1) return [0]
+
+  const degree = new Array<number>(n).fill(0)
+  const adj = new Array(n).fill([]).map(() => [] as number[])
+  for (const edge of edges) {
+    adj[edge[0]].push(edge[1])
+    adj[edge[1]].push(edge[0])
+    degree[edge[0]]++
+    degree[edge[1]]++
+  }
+
+  const queue: number[] = []
+  // 将度为1的节点压入队列
+  for (let i = 0; i < n; i++) {
+    if (degree[i] === 1)
+      queue.push(i)
+  }
+
+  // 剩余节点
+  let remainNodes = n
+  while (remainNodes > 2) {
+    const sz = queue.length
+    remainNodes -= sz
+    for (let i = 0; i < sz; i++) {
+      const cur = queue.shift()!
+      for (const v of adj[cur]) {
+        degree[v]--
+        if (degree[v] === 1)
+          queue.push(v)
+      }
+    }
+  }
+
+  return queue
+}
+```

problemset/minimum-height-trees/index.spec.ts

@@ -0,0 +1,15 @@
+import { describe, expect, it } from 'vitest'
+import { findMinHeightTrees } from '.'
+
+describe('最小高度树', () => {
+  testCase(findMinHeightTrees)
+})
+
+function testCase(fn: (n: number, edges: number[][]) => number[]) {
+  it.each([
+    [4, [[1, 0], [1, 2], [1, 3]], [1]],
+    [6, [[3, 0], [3, 1], [3, 2], [3, 4], [5, 4]], [3, 4]],
+  ])('示例%#', (n, edges, expected) => {
+    expect(fn(n, edges)).toStrictEqual(expected)
+  })
+}

problemset/minimum-height-trees/index.ts

@@ -0,0 +1,43 @@
+/**
+ * 拓扑排序
+ * @desc 时间复杂度 O(N)  空间复杂度 O(N)
+ * @param n
+ * @param edges
+ * @returns
+ */
+export function findMinHeightTrees(n: number, edges: number[][]): number[] {
+  if (n === 1) return [0]
+
+  const degree = new Array<number>(n).fill(0)
+  const adj = new Array(n).fill([]).map(() => [] as number[])
+  for (const edge of edges) {
+    adj[edge[0]].push(edge[1])
+    adj[edge[1]].push(edge[0])
+    degree[edge[0]]++
+    degree[edge[1]]++
+  }
+
+  const queue: number[] = []
+  // 将度为1的节点压入队列
+  for (let i = 0; i < n; i++) {
+    if (degree[i] === 1)
+      queue.push(i)
+  }
+
+  // 剩余节点
+  let remainNodes = n
+  while (remainNodes > 2) {
+    const sz = queue.length
+    remainNodes -= sz
+    for (let i = 0; i < sz; i++) {
+      const cur = queue.shift()!
+      for (const v of adj[cur]) {
+        degree[v]--
+        if (degree[v] === 1)
+          queue.push(v)
+      }
+    }
+  }
+
+  return queue
+}