feat: 715. Range Module : 动态开点线段树 / 区间合并

Author: upupming

.vscode/settings.json

@@ -115,12 +115,13 @@
   "cSpell.words": [
     "ACWing",
     "Kruskal",
-    "Manacher",
-    "SPFA",
-    "Treap",
     "lowbit",
+    "Manacher",
+    "pushdown",
     "readline",
-    "struct"
+    "SPFA",
+    "struct",
+    "Treap"
   ],
   // 好多地方只支持 4 的 indent，例如知乎和 AcWing
   "markdownlint.config": {
@@ -138,23 +139,23 @@
   // prettier is included by eslint
   "[javascript]": {
     "editor.formatOnSave": false,
-    "editor.tabSize": 2,
+    "editor.tabSize": 2
   },
   "[javascriptreact]": {
     "editor.formatOnSave": false,
-    "editor.tabSize": 2,
+    "editor.tabSize": 2
   },
   "[typescript]": {
     "editor.formatOnSave": false,
-    "editor.tabSize": 2,
+    "editor.tabSize": 2
   },
   "[typescriptreact]": {
     "editor.formatOnSave": false,
-    "editor.tabSize": 2,
+    "editor.tabSize": 2
   },
   "editor.codeActionsOnSave": {
     "source.fixAll.eslint": true
   },
   "eslint.packageManager": "yarn",
-  "typescript.tsdk": "node_modules\\typescript\\lib",
+  "typescript.tsdk": "node_modules\\typescript\\lib"
 }

leetcode/残酷刷题/715. Range Module.ts

@@ -0,0 +1,96 @@
+class RangeModule {
+  tree: SegmentTree
+  constructor () {
+    this.tree = new SegmentTree(0, 1e9)
+  }
+
+  addRange (left: number, right: number): void {
+    this.tree.modify(left, right - 1, true)
+  }
+
+  queryRange (left: number, right: number): boolean {
+    return this.tree.query(left, right - 1) === right - left
+  }
+
+  removeRange (left: number, right: number): void {
+    this.tree.modify(left, right - 1, false)
+  }
+}
+
+export declare const a: 1
+
+enum Tracked {
+  TRUE = 'TRUE',
+  FALSE = 'FALSE'
+}
+
+class Node {
+  start: number
+  end: number
+  val: number = 0
+  lazy: Tracked | null = null
+  left: null | Node = null
+  right: null | Node = null
+  constructor (start: number, end: number) {
+    this.start = start
+    this.end = end
+  }
+}
+
+// https://www.acwing.com/activity/content/code/content/167900/
+class SegmentTree {
+  root: Node
+  constructor (start: number, end: number) {
+    this.root = new Node(start, end)
+  }
+
+  modify (start: number, end: number, tracked: boolean) {
+    this.modifyNode(this.root, start, end, tracked)
+  }
+
+  modifyNode (node: Node, start: number, end: number, tracked: boolean) {
+    if (start <= node.start && end >= node.end) {
+      node.val = tracked ? (node.end - node.start + 1) : 0
+      node.lazy = tracked ? Tracked.TRUE : Tracked.FALSE
+    } else {
+      this.pushdown(node)
+      // pushdown 已经确保 left 和 right 一定存在了
+      if (start <= node.left!.end) this.modifyNode(node.left!, start, end, tracked)
+      if (end >= node.right!.start) this.modifyNode(node.right!, start, end, tracked)
+      this.pushup(node)
+    }
+  }
+
+  pushdown (node: Node) {
+    const mid = node.start + node.end >> 1
+    node.left ??= new Node(node.start, mid)
+    node.right ??= new Node(mid + 1, node.end)
+    if (node.lazy) {
+      node.left.lazy = node.lazy
+      node.left.val = (node.lazy === Tracked.TRUE) ? (node.left.end - node.left.start + 1) : 0
+
+      node.right.lazy = node.lazy
+      node.right.val = (node.lazy === Tracked.TRUE) ? (node.right.end - node.right.start + 1) : 0
+
+      node.lazy = null
+    }
+  }
+
+  pushup (node: Node) {
+    node.val = node.left!.val + node.right!.val
+  }
+
+  query (start: number, end: number) {
+    return this.queryNode(this.root, start, end)
+  }
+
+  queryNode (node: Node, start: number, end: number) {
+    if (start <= node.start && end >= node.end) return node.val
+
+    this.pushdown(node)
+    let sum = 0
+    if (start <= node.left!.end) sum += this.queryNode(node.left!, start, end)
+    if (end >= node.right!.start) sum += this.queryNode(node.right!, start, end)
+    return sum
+  }
+}

leetcode/残酷刷题/README.md

@@ -37,6 +37,7 @@
         - [括号匹配](#括号匹配)
         - [分治 (Divide and Conquer)](#分治-divide-and-conquer)
         - [扫描线 (Sweep Line)](#扫描线-sweep-line)
+    - [线段树](#线段树)
     - [Links](#links)
 
 ## Problems
@@ -277,6 +278,10 @@
 - 56. Merge Intervals
 - 218. The Skyline Problem
 
+## 线段树
+
+- 715. Range Module
+
 ## Links
 
 - https://wisdompeak.github.io/lc-score-board/

template-typescript.md

@@ -3,17 +3,18 @@
 > 为了训练自己的 JavaScript/TypeScript 编程能力，能用 TS 写的地方尽量用，不行再换 C++
 
 - [算法模板（JS/TS 版本）](#算法模板jsts-版本)
-    - [输入](#输入)
-        - [`readline` 输入](#readline-输入)
-        - [`process.stdin.on` 输入](#processstdinon-输入)
-        - [fs 输入](#fs-输入)
-    - [常用函数缩写](#常用函数缩写)
-    - [快速幂](#快速幂)
-    - [邻接表](#邻接表)
-    - [快速幂](#快速幂-1)
-    - [并查集](#并查集)
-    - [拓扑排序](#拓扑排序)
-    - [字符串哈希](#字符串哈希)
+  - [输入](#输入)
+    - [`readline` 输入](#readline-输入)
+    - [`process.stdin.on` 输入](#processstdinon-输入)
+    - [fs 输入](#fs-输入)
+  - [常用函数缩写](#常用函数缩写)
+  - [快速幂](#快速幂)
+  - [邻接表](#邻接表)
+  - [快速幂](#快速幂-1)
+  - [并查集](#并查集)
+  - [拓扑排序](#拓扑排序)
+  - [字符串哈希](#字符串哈希)
+  - [线段树](#线段树)
 
 ## 输入
 
@@ -261,3 +262,84 @@ const hash = (i, j) => {
   return (f[j] - f[i - 1] * p[j - i + 1] % Q + Q) % Q
 }
 ```
+
+## 线段树
+
+```ts
+enum Tracked {
+  TRUE = 'TRUE',
+  FALSE = 'FALSE'
+}
+
+class Node {
+  start: number
+  end: number
+  val: number = 0
+  lazy: Tracked | null = null
+  left: null | Node = null
+  right: null | Node = null
+  constructor (start: number, end: number) {
+    this.start = start
+    this.end = end
+  }
+}
+
+// https://www.acwing.com/activity/content/code/content/167900/
+class SegmentTree {
+  root: Node
+  constructor (start: number, end: number) {
+    this.root = new Node(start, end)
+  }
+
+  modify (start: number, end: number, tracked: boolean) {
+    this.modifyNode(this.root, start, end, tracked)
+  }
+
+  modifyNode (node: Node, start: number, end: number, tracked: boolean) {
+    if (start <= node.start && end >= node.end) {
+      node.val = tracked ? (node.end - node.start + 1) : 0
+      node.lazy = tracked ? Tracked.TRUE : Tracked.FALSE
+    } else {
+      this.pushdown(node)
+      // pushdown 已经确保 left 和 right 一定存在了
+      if (start <= node.left!.end) this.modifyNode(node.left!, start, end, tracked)
+      if (end >= node.right!.start) this.modifyNode(node.right!, start, end, tracked)
+      this.pushup(node)
+    }
+  }
+
+  pushdown (node: Node) {
+    const mid = node.start + node.end >> 1
+    node.left ??= new Node(node.start, mid)
+    node.right ??= new Node(mid + 1, node.end)
+    if (node.lazy) {
+      node.left.lazy = node.lazy
+      node.left.val = (node.lazy === Tracked.TRUE) ? (node.left.end - node.left.start + 1) : 0
+
+      node.right.lazy = node.lazy
+      node.right.val = (node.lazy === Tracked.TRUE) ? (node.right.end - node.right.start + 1) : 0
+
+      node.lazy = null
+    }
+  }
+
+  pushup (node: Node) {
+    node.val = node.left!.val + node.right!.val
+  }
+
+  query (start: number, end: number) {
+    return this.queryNode(this.root, start, end)
+  }
+
+  queryNode (node: Node, start: number, end: number) {
+    if (start <= node.start && end >= node.end) return node.val
+
+    this.pushdown(node)
+    let sum = 0
+    if (start <= node.left!.end) sum += this.queryNode(node.left!, start, end)
+    if (end >= node.right!.start) sum += this.queryNode(node.right!, start, end)
+    return sum
+  }
+}
+
+```