結果

問題 No.1750 ラムドスウイルスの感染拡大-hard
ユーザー yudedako
提出日時 2022-01-26 23:20:14
言語 Scala(Beta)
(3.6.2)
結果
AC  
実行時間 1,637 ms / 2,000 ms
コード長 4,244 bytes
コンパイル時間 18,965 ms
コンパイル使用メモリ 277,732 KB
実行使用メモリ 65,908 KB
最終ジャッジ日時 2024-12-23 19:34:14
合計ジャッジ時間 62,962 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 30
権限があれば一括ダウンロードができます

ソースコード

diff # 

import Matrix.{inPlaceTimes, tabulate}

import scala.annotation.tailrec
import scala.io.StdIn.*
import scala.math.*
import scala.util.chaining.*

object ModInt:
  opaque type ModInt = Long
  val zero: ModInt = 0
  val one: ModInt = 1
  extension (value: Long)
    inline def asModInt(using inline mod: Int): ModInt =  value % mod
  extension (value: Int)
    inline def asModInt(using inline mod: Int): ModInt = value % mod
  trait Converter[T]:
    inline def convert(value: T)(using inline mod: Int): ModInt
  inline given Converter[Int] with
    override inline def convert(value: Int)(using inline mod: Int) = value.asModInt
  inline given Converter[Long] with
    override inline def convert(value: Long)(using inline mod: Int) = value.asModInt
  inline given Converter[ModInt] with
    override inline def convert(value: ModInt)(using inline mod: Int) = value
  extension (modInt: ModInt)
    inline def asLong(using inline mod: Int): Long = (modInt + mod) % mod
    inline def inverse(using inline mod: Int): ModInt = modInt.powMod(mod - 2)
    inline def powMod(exp: Long)(using inline mod: Int): ModInt =
      var result = 1L
      var base = modInt
      var e = exp
      while e > 0 do
        if (e & 1) == 1 then
          result = result * base % mod
        base = base * base % mod
        e >>= 1
      result
    inline def powMod(exp: Int)(using inline mod: Int): ModInt = powMod(exp.toLong)
  extension [L: Converter, R: Converter] (left: L)
    inline def +(right: R)(using inline mod: Int): ModInt = (summon[Converter[L]].convert(left) + summon[Converter[R]].convert(right)).asModInt
    inline def -(right: R)(using inline mod: Int): ModInt = (summon[Converter[L]].convert(left) - summon[Converter[R]].convert(right)).asModInt
    inline def *(right: R)(using inline mod: Int): ModInt = (summon[Converter[L]].convert(left) * summon[Converter[R]].convert(right)).asModInt
    inline def /(right: R)(using inline mod: Int): ModInt = (summon[Converter[L]].convert(left) * summon[Converter[R]].convert(right).inverse).asModInt

import ModInt.*
inline given mod: Int = 998244353
class Matrix private(val row: Int, val column: Int, private val matrix: Array[Array[ModInt]]):
  def this(row: Int, column: Int) =
    this(row, column, Array.fill(row){Array.fill(column){ModInt.zero}})
  def apply(i: Int, j: Int): ModInt =
    matrix(i)(j)
  def update(i: Int, j: Int, value: ModInt) =
    matrix(i)(j) = value
  def *(right: Matrix): Matrix =
    val newRow = row
    val newColumn = right.column
    val mid = column
    Matrix.tabulate(newRow, newColumn){(i, j) =>
      (0 until mid).foldLeft(ModInt.zero){(acc, k) => acc + matrix(i)(k) * right.matrix(k)(j) }
    }
  def pow(exp: Long): Matrix =
    require(row == column)
    var temp = Matrix(row, row)
    var result = Matrix.e(row, row)
    var base = this
    var e = exp
    while e > 0 do
      if (e & 1) == 1 then
        inPlaceTimes(result, base, temp)
        val t = temp
        temp = result
        result = t
      inPlaceTimes(base, base, temp)
      val t = temp
      temp = base
      base = t
      e >>= 1
    result
object Matrix:
  def tabulate(row: Int, column: Int)(generator: (Int, Int) => ModInt): Matrix =
    Matrix(row, column, Array.tabulate(row){i => Array.tabulate(column){j => generator(i, j)}})
  def e(row: Int, column: Int): Matrix =
    Matrix.tabulate(row, column){(i, j) =>
      if i == j then ModInt.one else ModInt.zero
    }
  private def inPlaceTimes(left: Matrix, right: Matrix, dest: Matrix) =
    val newRow = left.row
    val newColumn = right.column
    val mid = left.column
    for
      i <- 0 until newRow
      j <- 0 until newColumn
    do
      var sum = ModInt.zero
      for k <- 0 until mid do
        sum += left(i, k) * right(k, j)
      dest(i, j) = sum


@main def main =
  val (n, m, t) = readLine().split(' ').pipe{case Array(n, m, t) => (n.toInt, m.toInt, t.toLong)}
  val roads = Array.fill(m){
    val Array(u, v) = readLine().split(' ').map(_.toInt)
    (u, v)
  }
  val matrix = Matrix(n, n)
  for (u, v) <- roads do
    matrix(u, v) = ModInt.one
    matrix(v, u) = ModInt.one
  val initial = Matrix(n, 1).tap(m => m(0, 0) = ModInt.one)
  val result = matrix.pow(t) * initial
  println(result(0, 0))
0