feat: 2271. Maximum White Tiles Covered by a Carpet : 线段树

Author: upupming

leetcode/残酷刷题/2271. Maximum White Tiles Covered by a Carpet.ts

@@ -0,0 +1,116 @@
+function maximumWhiteTiles (tiles: number[][], carpetLen: number): number {
+  const tree = new SegmentTree(0, 1e9)
+  for (const [l, r] of tiles) {
+    tree.modifyRange(l, r, 1)
+  }
+  let ans = 0
+  for (const [l, r] of tiles) {
+    const { sum } = tree.query(l, Math.min(l + carpetLen - 1, 1e9))
+    ans = Math.max(ans, sum)
+  }
+  return ans
+};
+
+export declare const a: 1
+
+class Node {
+  start: number
+  end: number
+  max: number = 0
+  sum: number = 0
+  lazy: number | 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 (pos: number, val: number) {
+    this.modifyNode(this.root, pos, val)
+  }
+
+  modifyNode (node: Node, pos: number, val: number) {
+    if (node.start === pos && node.end === pos) {
+      node.max = node.sum = val
+    } else {
+      this.pushdown(node)
+      if (pos <= node.left!.end) this.modifyNode(node.left!, pos, val)
+      if (pos >= node.right!.start) this.modifyNode(node.right!, pos, val)
+      this.pushup(node)
+    }
+  }
+
+  // 使用 modify 和 modifyRange 是等价的，modifyRange 更加通用
+  modifyRange (start: number, end: number, val: number) {
+    this.modifyNodeRange(this.root, start, end, val)
+  }
+
+  modifyNodeRange (node: Node, start: number, end: number, val: number) {
+    if (start <= node.start && end >= node.end) {
+      node.sum = val * (node.end - node.start + 1)
+      node.max = val
+      node.lazy = val
+    } else {
+      this.pushdown(node)
+      if (start <= node.left!.end) this.modifyNodeRange(node.left!, start, end, val)
+      if (end >= node.right!.start) this.modifyNodeRange(node.right!, start, end, val)
+      this.pushup(node)
+    }
+  }
+
+  // 这里 pushdown 同时保证了 left, right 一定存在
+  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 != null) {
+      node.left.lazy = node.lazy
+      node.left.max = node.lazy
+      node.left.sum = node.lazy * (node.left.end - node.left.start + 1)
+
+      node.right.lazy = node.lazy
+      node.right.max = node.lazy
+      node.right.sum = node.lazy * (node.right.end - node.right.start + 1)
+
+      node.lazy = null
+    }
+  }
+
+  pushup (node: Node) {
+    node.max = Math.max(node.left!.max, node.right!.max)
+    node.sum = node.left!.sum + node.right!.sum
+  }
+
+  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 { max: node.max, sum: node.sum }
+    }
+
+    this.pushdown(node)
+    let max = 0; let sum = 0
+    if (start <= node.left!.end) {
+      const { max: _m, sum: _s } = this.queryNode(node.left!, start, end)
+      max = Math.max(max, _m)
+      sum += _s
+    }
+    if (end >= node.right!.start) {
+      const { max: _m, sum: _s } = this.queryNode(node.right!, start, end)
+      max = Math.max(max, _m)
+      sum += _s
+    }
+    return { max, sum }
+  }
+}

leetcode/残酷刷题/README.md

@@ -283,6 +283,7 @@
 - 715. Range Module
 - 2213. Longest Substring of One Repeating Character
 - 2286. Booking Concert Tickets in Groups
+- 2271. Maximum White Tiles Covered by a Carpet
 
 ## Links
 

template-typescript.md

@@ -570,7 +570,7 @@ class SegmentTree {
 
   modifyNodeRange (node: Node, start: number, end: number, val: number) {
     if (start <= node.start && end >= node.end) {
-      node.sum = val * (end - start + 1)
+      node.sum = val * (node.end - node.start + 1)
       node.max = val
       node.lazy = val
     } else {
@@ -609,21 +609,23 @@ class SegmentTree {
   }
 
   queryNode (node: Node, start: number, end: number) {
-    if (start <= node.start && end >= node.end) return [node.max, node.sum]
+    if (start <= node.start && end >= node.end) {
+      return { max: node.max, sum: node.sum }
+    }
 
     this.pushdown(node)
     let max = 0; let sum = 0
     if (start <= node.left!.end) {
-      const [_m, _s] = this.queryNode(node.left!, start, end)
+      const { max: _m, sum: _s } = this.queryNode(node.left!, start, end)
       max = Math.max(max, _m)
       sum += _s
     }
     if (end >= node.right!.start) {
-      const [_m, _s] = this.queryNode(node.right!, start, end)
+      const { max: _m, sum: _s } = this.queryNode(node.right!, start, end)
       max = Math.max(max, _m)
       sum += _s
     }
-    return [max, sum]
+    return { max, sum }
   }
 }