結果

問題 No.2149 Vanitas Vanitatum
コンテスト
ユーザー 箱星
提出日時 2022-07-31 01:45:48
言語 Kotlin
(2.1.0)
結果
AC  
実行時間 533 ms / 2,000 ms
コード長 5,262 bytes
コンパイル時間 17,159 ms
コンパイル使用メモリ 471,800 KB
実行使用メモリ 136,152 KB
最終ジャッジ日時 2024-10-09 21:38:15
合計ジャッジ時間 29,887 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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 * 3
other AC * 24
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 java.io.PrintWriter
import java.util.*
import kotlin.math.*

fun youngToMaya(a: Array<Int>): String {
    val n = a.size
    val sb = java.lang.StringBuilder()
    sb.append("1".repeat(a[0]))
    sb.append("0")
    for (i in 1 until n) {
        sb.append("1".repeat(a[i] - a[i - 1]))
        sb.append("0")
    }
    return sb.toString()
}

fun mayaToYoung(s: String): Array<Int> {
    var now = 0
    val a = mutableListOf<Int>()
    for (c in s) {
        if (c == '1') {
            now++
        } else {
            if (now != 0) {
                a.add(now)
            }
        }
    }
    return a.toTypedArray()
}

fun hookProd(a: Array<Int>): ModInt {
    val n = a.size
    if (n == 0) return ModInt(1)
    val m = a.last()
    val down = Array(m + 1) { 0 }
    var ret = ModInt(1)
    for (i in 0 until n) {
        for (j in a[i] downTo 1) {
            val l = down[j] + (a[i] - j + 1)
            down[j]++
            ret *= ModInt(l)
        }
    }
    return ret
}

fun PrintWriter.solve() {
    val n = nextInt()
    val a = Array(n) { nextInt() }
    val s = youngToMaya(a)
    val s1 = s.indices.filter { it % 2 == 0 }.map { s[it] }.joinToString("")
    val s2 = s.indices.filter { it % 2 == 1 }.map { s[it] }.joinToString("")
    val b1 = mayaToYoung(s1)
    val b2 = mayaToYoung(s2)
    val sum1 = b1.sum()
    val sum2 = b2.sum()
    if ((sum1 + sum2) * 2 != a.sum()) {
        println(0)
        return
    }
    val cc = CombinationCalculator()
    println(cc.binom(sum1 + sum2.toLong(), sum1.toLong()) * cc.fac(sum1) * cc.fac(sum2) / (hookProd(b1) * hookProd(b2)))
}

// region ModInt
class ModInt(x: Long) {
    companion object {
        const val MOD = 998244353L
        //const val MOD = 1000000007L
    }

    constructor(y: Int) : this(y.toLong())

    val x = (x % MOD + MOD) % MOD

    operator fun plus(other: ModInt): ModInt {
        return ModInt(x + other.x)
    }

    operator fun minus(other: ModInt): ModInt {
        return ModInt(x - other.x)
    }

    operator fun times(other: ModInt): ModInt {
        return ModInt(x * other.x)
    }

    operator fun div(other: ModInt): ModInt {
        return this * other.inv()
    }

    fun pow(exp: Long): ModInt {
        if (exp == 0L) return ModInt(1L)
        var a = pow(exp shr 1)
        a *= a
        if (exp and 1L == 0L) return a
        return this * a
    }

    fun inv(): ModInt {
        return this.pow(MOD - 2)
    }

    override fun equals(other: Any?): Boolean {
        if (this === other) return true
        if (javaClass != other?.javaClass) return false

        other as ModInt

        if (x != other.x) return false

        return true
    }

    override fun hashCode(): Int {
        return x.hashCode()
    }

    override fun toString(): String {
        return "$x"
    }
}

class ModIntArray(n: Int) {
    private val a = LongArray(n) { 0L }

    constructor(n: Int, init: (Int) -> ModInt) : this(n) {
        for (i in 0 until n) {
            a[i] = init(i).x
        }
    }

    operator fun set(i: Int, x: ModInt) {
        a[i] = x.x
    }

    operator fun get(i: Int): ModInt {
        return ModInt(a[i])
    }

    fun joinToString(s: String = ", "): String {
        return a.joinToString(s)
    }
}

fun Long.toModInt(): ModInt {
    return ModInt(this)
}

fun Int.toModInt(): ModInt {
    return ModInt(this)
}

fun binomSimple(n: Long, k: Long): ModInt {
    var numer = ModInt(1)
    var denom = ModInt(1)
    for (i in 0 until k) {
        numer *= ModInt(n - i)
        denom *= ModInt(k - i)
    }
    return numer / denom
}
// endregion

class CombinationCalculator {
    companion object {
        private const val fac_size = 600000
    }

    private val arrFac = Array(fac_size) { ModInt(1) }
    private val arrInvfac = Array(fac_size) { ModInt(1) }

    init {
        for (i in 1 until fac_size) {
            arrFac[i] = arrFac[i - 1] * ModInt(i)
        }
        arrInvfac[fac_size - 1] = arrFac[fac_size - 1].inv()
        for (i in fac_size - 2 downTo 1) {
            arrInvfac[i] = arrInvfac[i + 1] * ModInt(i + 1)
        }
    }

    fun fac(n: Int): ModInt {
        return arrFac[n]
    }

    fun fac(n: Long): ModInt {
        return fac(n.toInt())
    }

    fun invfac(n: Int): ModInt {
        return arrInvfac[n]
    }

    fun invfac(n: Long): ModInt {
        return invfac(n.toInt())
    }

    fun binom(n: Long, k: Long): ModInt {
        return if (k in 0..n) {
            arrFac[n.toInt()] * arrInvfac[k.toInt()] * arrInvfac[(n - k).toInt()]
        } else {
            ModInt(0)
        }
    }
}

fun main() {
    Thread(null, {
        val writer = PrintWriter(System.out, false)
        writer.solve()
        writer.flush()
    }, "solve", abs(1L.shl(26)))
        .apply { setUncaughtExceptionHandler { _, e -> e.printStackTrace(); kotlin.system.exitProcess(1) } }
        .apply { start() }.join()
}

// region Scanner
private var st = StringTokenizer("")
private val br = System.`in`.bufferedReader()

fun next(): String {
    while (!st.hasMoreTokens()) st = StringTokenizer(br.readLine())
    return st.nextToken()
}

fun nextInt() = next().toInt()
fun nextLong() = next().toLong()
fun nextLine() = br.readLine()
fun nextDouble() = next().toDouble()
// endregion
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