結果

問題 No.2149 Vanitas Vanitatum
ユーザー 👑 hos.lyrichos.lyric
提出日時 2022-12-07 01:36:42
言語 D
(dmd 2.106.1)
結果
RE  
実行時間 -
コード長 5,467 bytes
コンパイル時間 1,783 ms
コンパイル使用メモリ 156,852 KB
実行使用メモリ 30,148 KB
最終ジャッジ日時 2024-06-22 17:00:22
合計ジャッジ時間 5,564 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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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 60 ms
28,380 KB
testcase_01 AC 61 ms
29,116 KB
testcase_02 AC 61 ms
27,912 KB
testcase_03 AC 59 ms
28,396 KB
testcase_04 RE -
testcase_05 RE -
testcase_06 AC 60 ms
28,992 KB
testcase_07 AC 57 ms
29,096 KB
testcase_08 AC 60 ms
28,096 KB
testcase_09 AC 61 ms
28,908 KB
testcase_10 AC 59 ms
28,336 KB
testcase_11 AC 59 ms
28,656 KB
testcase_12 AC 59 ms
30,148 KB
testcase_13 AC 63 ms
29,624 KB
testcase_14 AC 61 ms
29,536 KB
testcase_15 AC 60 ms
29,976 KB
testcase_16 AC 62 ms
29,628 KB
testcase_17 AC 60 ms
29,464 KB
testcase_18 AC 66 ms
28,572 KB
testcase_19 AC 61 ms
28,764 KB
testcase_20 AC 63 ms
28,812 KB
testcase_21 AC 61 ms
29,456 KB
testcase_22 AC 62 ms
29,112 KB
testcase_23 AC 59 ms
29,552 KB
testcase_24 AC 60 ms
28,440 KB
testcase_25 AC 61 ms
29,860 KB
testcase_26 AC 62 ms
29,224 KB
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ソースコード

diff # 

import std.conv, std.functional, std.range, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons;
import core.bitop;

class EOFException : Throwable { this() { super("EOF"); } }
string[] tokens;
string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; }
int readInt() { return readToken.to!int; }
long readLong() { return readToken.to!long; }
real readReal() { return readToken.to!real; }

bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }
bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }

int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }
int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }
int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }

struct ModInt(uint M_) {
  import std.conv : to;
  alias M = M_;
  uint x;
  this(ModInt a) { x = a.x; }
  this(uint x_) { x = x_ % M; }
  this(ulong x_) { x = cast(uint)(x_ % M); }
  this(int x_) { x = ((x_ %= cast(int)(M)) < 0) ? (x_ + cast(int)(M)) : x_; }
  this(long x_) { x = cast(uint)(((x_ %= cast(long)(M)) < 0) ? (x_ + cast(long)(M)) : x_); }
  ref ModInt opAssign(T)(inout(T) a) if (is(T == uint) || is(T == ulong) || is(T == int) || is(T == long)) { return this = ModInt(a); }
  ref ModInt opOpAssign(string op, T)(T a) {
    static if (is(T == ModInt)) {
      static if (op == "+") { x = ((x += a.x) >= M) ? (x - M) : x; }
      else static if (op == "-") { x = ((x -= a.x) >= M) ? (x + M) : x; }
      else static if (op == "*") { x = cast(uint)((cast(ulong)(x) * a.x) % M); }
      else static if (op == "/") { this *= a.inv(); }
      else static assert(false);
      return this;
    } else static if (op == "^^") {
      if (a < 0) return this = inv()^^(-a);
      ModInt b = this, c = 1U;
      for (long e = a; e; e >>= 1) { if (e & 1) c *= b; b *= b; }
      return this = c;
    } else {
      return mixin("this " ~ op ~ "= ModInt(a)");
    }
  }
  ModInt inv() const {
    uint a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const q = a / b; const c = a - q * b; a = b; b = c; const w = y - cast(int)(q) * z; y = z; z = w; }
    assert(a == 1); return ModInt(y);
  }
  ModInt opUnary(string op)() const {
    static if (op == "+") { return this; }
    else static if (op == "-") { ModInt a; a.x = x ? (M - x) : 0U; return a; }
    else static assert(false);
  }
  ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); }
  ModInt opBinaryRight(string op, T)(T a) const { return mixin("ModInt(a) " ~ op ~ "= this"); }
  bool opCast(T: bool)() const { return (x != 0U); }
  string toString() const { return x.to!string; }
}

enum MO = 998244353;
alias Mint = ModInt!MO;

enum LIM_INV = 2 * 10^^6 + 10;
Mint[] inv, fac, invFac;
void prepare() {
  inv = new Mint[LIM_INV];
  fac = new Mint[LIM_INV];
  invFac = new Mint[LIM_INV];
  inv[1] = 1;
  foreach (i; 2 .. LIM_INV) {
    inv[i] = -((Mint.M / i) * inv[cast(size_t)(Mint.M % i)]);
  }
  fac[0] = invFac[0] = 1;
  foreach (i; 1 .. LIM_INV) {
    fac[i] = fac[i - 1] * i;
    invFac[i] = invFac[i - 1] * inv[i];
  }
}
Mint binom(long n, long k) {
  if (n < 0) {
    if (k >= 0) {
      return (-1)^^(k & 1) * binom(-n + k - 1, k);
    } else if (n - k >= 0) {
      return (-1)^^((n - k) & 1) * binom(-k - 1, n - k);
    } else {
      return Mint(0);
    }
  } else {
    if (0 <= k && k <= n) {
      assert(n < LIM_INV);
      return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] * invFac[cast(size_t)(n - k)];
    } else {
      return Mint(0);
    }
  }
}


/*
  EC section 7.17
  
  (# of border-strip tableaux of shape A and type (2,...,2))
  = (-1)^* \chi^A(2,...,2)
  = (-1)^* [x^(A+\delta)] p[2]^* a[A+\delta]
  
  p[2] = x[0]^2 + ... + x[M-1]^2
  split (A+\delta) into even and odd
  
  (-1)^* binom(*,*) ([x^(even/2)] p[1]^* a[\delta]) ([x^((odd-1)/2)] p[1]^* a[\delta])
  = (-1)^* binom(*,*) (# of SYT) (# of SYT)
*/

Mint solve(int[] bs) {
  const bsLen = cast(int)(bs.length);
  auto cs = new int[(bsLen == 0) ? 0 : bs[0]];
  foreach (y; 0 .. bs[0]) {
    cs[y] = cast(int)(bs.count!(b => (b > y)));
  }
  Mint ret = 1;
  foreach (x; 0 .. bsLen) foreach (y; 0 .. bs[x]) {
    ret *= inv[(bs[x] - x) + (cs[y] - y) - 1];
  }
  return ret;
}

void main() {
  prepare;
  
  try {
    for (; ; ) {
      const M = readInt;
      auto A = new int[M];
      foreach (i; 0 .. M) {
        A[i] = readInt;
      }
      A.reverse;
      
      int[][2] bss;
      foreach (i; 0 .. M) {
        const ad = A[i] + (M - 1 - i);
        bss[ad & 1] ~= ad / 2;
      }
      foreach (h; 0 .. 2) {
        const bsLen = cast(int)(bss[h].length);
        foreach (i; 0 .. bsLen) {
          bss[h][i] -= (bsLen - 1 - i);
        }
      }
      debug {
        writeln("bss = ", bss);
      }
      
      Mint ans;
      if (bss[0].length == M - M / 2 && bss[1].length == M / 2 && bss[0].all!"a >= 0" && bss[1].all!"a >= 0") {
        ans = fac[A.sum / 2];
        ans *= solve(bss[0]);
        ans *= solve(bss[1]);
      }
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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