結果

問題 No.875 Range Mindex Query
ユーザー 草苺奶昔草苺奶昔
提出日時 2023-06-14 23:43:55
言語 TypeScript
(5.4.3)
結果
AC  
実行時間 1,754 ms / 2,000 ms
コード長 9,162 bytes
コンパイル時間 7,430 ms
コンパイル使用メモリ 262,232 KB
実行使用メモリ 102,960 KB
最終ジャッジ日時 2023-09-05 08:51:47
合計ジャッジ時間 21,756 ms
ジャッジサーバーID
（参考情報） 		judge14 / judge15
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 78 ms
42,588 KB
testcase_01 AC 131 ms
49,068 KB
testcase_02 AC 141 ms
49,380 KB
testcase_03 AC 93 ms
43,368 KB
testcase_04 AC 107 ms
48,192 KB
testcase_05 AC 100 ms
47,928 KB
testcase_06 AC 132 ms
49,372 KB
testcase_07 AC 129 ms
48,640 KB
testcase_08 AC 112 ms
48,192 KB
testcase_09 AC 105 ms
47,832 KB
testcase_10 AC 140 ms
49,244 KB
testcase_11 AC 1,542 ms
101,160 KB
testcase_12 AC 1,354 ms
99,216 KB
testcase_13 AC 1,269 ms
102,960 KB
testcase_14 AC 1,248 ms
102,460 KB
testcase_15 AC 1,524 ms
100,804 KB
testcase_16 AC 1,651 ms
98,028 KB
testcase_17 AC 1,754 ms
98,800 KB
testcase_18 AC 1,698 ms
98,800 KB
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ソースコード

diff # 

import * as fs from 'fs'
import { resolve } from 'path'
type SegNode<E> = {
  left: SegNode<E> | undefined
  right: SegNode<E> | undefined
  index: number
  data: E
  sum: E
}

class SegmentTreeDynamic<E = number> {
  private static _isPrimitive(
    o: unknown
  ): o is number | string | boolean | symbol | bigint | null | undefined {
    return o === null || (typeof o !== 'object' && typeof o !== 'function')
  }

  private readonly _lower: number
  private readonly _upper: number
  private readonly _e: () => E
  private readonly _op: (a: E, b: E) => E
  private readonly _persistent: boolean
  private _root: SegNode<E>

  /**
   * 单点修改区间查询的动态开点懒标记线段树.线段树维护的值域为`[start, end)`.
   * @param start 值域下界.start>=0.
   * @param end 值域上界.
   * @param e 幺元.
   * @param op 结合律的二元操作.
   * @param persistent 是否持久化.持久化后,每次修改都会新建一个结点,否则会复用原来的结点.
   */
  constructor(start: number, end: number, e: () => E, op: (a: E, b: E) => E, persistent = false) {
    if (persistent && !SegmentTreeDynamic._isPrimitive(e())) {
      throw new Error('persistent is only supported when e() return primitive values')
    }
    this._lower = start
    this._upper = end + 5
    this._e = e
    this._op = op
    this._persistent = persistent
    this._root = this.newRoot()
  }

  newRoot(): SegNode<E> {
    return undefined as any // nil
  }

  get(index: number, root: SegNode<E> = this._root): E {
    if (index < this._lower || index >= this._upper) return this._e()
    return this._get(root, index)
  }

  set(index: number, value: E, root: SegNode<E> = this._root): SegNode<E> {
    if (index < this._lower || index >= this._upper) return root
    const newRoot = this._set(root, this._lower, this._upper, index, value)
    this._root = newRoot
    return newRoot
  }

  update(index: number, value: E, root: SegNode<E> = this._root): SegNode<E> {
    if (index < this._lower || index >= this._upper) return root
    const newRoot = this._update(root, this._lower, this._upper, index, value)
    this._root = newRoot
    return newRoot
  }

  /**
   * 查询区间`[start,end)`的聚合值.
   * {@link _lower} <= start <= end <= {@link _upper}.
   */
  query(start: number, end: number, root: SegNode<E> = this._root): E {
    if (start < this._lower) start = this._lower
    if (end > this._upper) end = this._upper
    if (start >= end) return this._e()

    let res = this._e()
    const _query = (node: SegNode<E> | undefined, l: number, r: number, ql: number, qr: number) => {
      if (!node) return
      ql = l > ql ? l : ql
      qr = r < qr ? r : qr
      if (ql >= qr) return
      if (l === ql && r === qr) {
        res = this._op(res, node.sum)
        return
      }
      const m = Math.floor(l + (r - l) / 2)
      _query(node.left, l, m, ql, qr)
      if (ql <= node.index && node.index < qr) {
        res = this._op(res, node.data)
      }
      _query(node.right, m, r, ql, qr)
    }

    _query(root, this._lower, this._upper, start, end)
    return res
  }

  queryAll(root: SegNode<E> = this._root): E {
    return root.sum
  }

  /**
   * 二分查询最大的`end`使得切片`[start:end)`内的聚合值满足`check`.
   * {@link _lower} <= start <= {@link _upper}.
   * @alias findFirst
   */
  maxRight(start: number, check: (e: E) => boolean, root: SegNode<E> = this._root): number {
    if (start < this._lower) start = this._lower
    if (start >= this._upper) return this._upper

    let x = this._e()
    const _maxRight = (node: SegNode<E> | undefined, l: number, r: number, ql: number): number => {
      if (!node || r <= ql) return this._upper
      const tmp = this._op(x, node.sum)
      if (check(tmp)) {
        x = tmp
        return this._upper
      }
      const m = Math.floor(l + (r - l) / 2)
      const k = _maxRight(node.left, l, m, ql)
      if (k !== this._upper) return k
      if (ql <= node.index) {
        x = this._op(x, node.data)
        if (!check(x)) {
          return node.index
        }
      }
      return _maxRight(node.right, m, r, ql)
    }

    return _maxRight(root, this._lower, this._upper, start)
  }

  /**
   * 二分查询最小的`start`使得切片`[start:end)`内的聚合值满足`check`.
   * {@link _lower} <= end <= {@link _upper}.
   * @alias findLast
   */
  minLeft(end: number, check: (e: E) => boolean, root: SegNode<E> = this._root): number {
    if (end > this._upper) end = this._upper
    if (end <= this._lower) return this._lower

    let x = this._e()
    const _minLeft = (node: SegNode<E> | undefined, l: number, r: number, qr: number): number => {
      if (!node || qr <= l) return this._lower
      const tmp = this._op(node.sum, x)
      if (check(tmp)) {
        x = tmp
        return this._lower
      }
      const m = Math.floor(l + (r - l) / 2)
      const k = _minLeft(node.right, m, r, qr)
      if (k !== this._lower) return k
      if (node.index < qr) {
        x = this._op(node.data, x)
        if (!check(x)) {
          return node.index + 1
        }
      }
      return _minLeft(node.left, l, m, qr)
    }

    return _minLeft(root, this._lower, this._upper, end)
  }

  getAll(root: SegNode<E> = this._root): [index: number, value: E][] {
    const res: [number, E][] = []
    const _getAll = (node: SegNode<E> | undefined) => {
      if (!node) return
      _getAll(node.left)
      res.push([node.index, node.data])
      _getAll(node.right)
    }
    _getAll(root)
    return res
  }

  private _copyNode(node: SegNode<E>): SegNode<E> {
    if (!node || !this._persistent) return node
    return { left: node.left, right: node.right, index: node.index, data: node.data, sum: node.sum }
  }

  private _get(root: SegNode<E> | undefined, index: number): E {
    if (!root) return this._e()
    if (index === root.index) return root.data
    if (index < root.index) return this._get(root.left, index)
    return this._get(root.right, index)
  }

  private _set(root: SegNode<E> | undefined, l: number, r: number, i: number, x: E): SegNode<E> {
    if (!root) return SegmentTreeDynamic._newNode(i, x)
    root = this._copyNode(root)
    if (root.index === i) {
      root.data = x
      this._pushUp(root)
      return root
    }
    const m = Math.floor(l + (r - l) / 2)
    if (i < m) {
      if (root.index < i) {
        const tmp1 = root.index
        root.index = i
        i = tmp1
        const tmp2 = root.data
        root.data = x
        x = tmp2
      }
      root.left = this._set(root.left, l, m, i, x)
    } else {
      if (i < root.index) {
        const tmp1 = root.index
        root.index = i
        i = tmp1
        const tmp2 = root.data
        root.data = x
        x = tmp2
      }
      root.right = this._set(root.right, m, r, i, x)
    }
    this._pushUp(root)
    return root
  }

  private _pushUp(root: SegNode<E>): void {
    root.sum = root.data
    if (root.left) root.sum = this._op(root.left.sum, root.sum)
    if (root.right) root.sum = this._op(root.sum, root.right.sum)
  }

  private _update(root: SegNode<E> | undefined, l: number, r: number, i: number, x: E): SegNode<E> {
    if (!root) return SegmentTreeDynamic._newNode(i, x)
    root = this._copyNode(root)
    if (root.index === i) {
      root.data = this._op(root.data, x)
      this._pushUp(root)
      return root
    }
    const m = Math.floor(l + (r - l) / 2)
    if (i < m) {
      if (root.index < i) {
        const tmp1 = root.index
        root.index = i
        i = tmp1
        const tmp2 = root.data
        root.data = x
        x = tmp2
      }
      root.left = this._update(root.left, l, m, i, x)
    } else {
      if (i < root.index) {
        const tmp1 = root.index
        root.index = i
        i = tmp1
        const tmp2 = root.data
        root.data = x
        x = tmp2
      }
      root.right = this._update(root.right, m, r, i, x)
    }
    this._pushUp(root)
    return root
  }

  private static _newNode<V>(index: number, value: V): SegNode<V> {
    return {
      index,
      left: undefined,
      right: undefined,
      data: value,
      sum: value
    }
  }
}

function useInput(path?: string) {
  let data: string
  if (path) {
    data = fs.readFileSync(resolve(__dirname, path), 'utf8')
  } else {
    data = fs.readFileSync(process.stdin.fd, 'utf8')
  }

  const lines = data.split(/\r\n|\r|\n/)
  let lineId = 0
  const input = (): string => lines[lineId++]

  return {
    input
  }
}

const { input } = useInput()

const [N, Q] = input().split(' ').map(Number)
const a = input().split(' ').map(Number)

const INF = 2e15
const seg = new SegmentTreeDynamic(0, a.length, () => INF, Math.min,true)
a.forEach((v, i) => seg.set(i, v))

for (let i = 0; i < Q; i++) {
  let [c, l, r] = input().split(' ').map(Number)
  if (c === 1) {
    l--
    r--
    const vl = seg.get(l)
    seg.set(l, seg.get(r))
    seg.set(r, vl)
  } else {
    l--

    const mn = seg.query(l, r)
    const a1 = seg.maxRight(l, n => n > mn)
    let a2 = seg.minLeft(r, n => n > mn)
    a2--
    if (a1 !== a2) {
      throw new Error('a1 !== a2')
    }
    console.log(a1 + 1)
  }
}
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