結果

問題 No.2149 Vanitas Vanitatum
ユーザー 👑 hos.lyrichos.lyric
提出日時 2022-12-06 00:40:50
言語 D
(dmd 2.107.1)
結果
AC  
実行時間 128 ms / 2,000 ms
コード長 6,325 bytes
コンパイル時間 1,958 ms
コンパイル使用メモリ 162,484 KB
実行使用メモリ 54,456 KB
最終ジャッジ日時 2023-09-04 19:16:38
合計ジャッジ時間 5,707 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge11
このコードへのチャレンジ（β）

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 128 ms
53,720 KB
testcase_01 AC 111 ms
53,092 KB
testcase_02 AC 116 ms
52,988 KB
testcase_03 AC 112 ms
53,208 KB
testcase_04 AC 113 ms
52,104 KB
testcase_05 AC 115 ms
53,380 KB
testcase_06 AC 115 ms
53,548 KB
testcase_07 AC 117 ms
54,028 KB
testcase_08 AC 114 ms
54,360 KB
testcase_09 AC 113 ms
54,388 KB
testcase_10 AC 119 ms
52,536 KB
testcase_11 AC 114 ms
52,124 KB
testcase_12 AC 115 ms
52,680 KB
testcase_13 AC 115 ms
52,892 KB
testcase_14 AC 114 ms
53,692 KB
testcase_15 AC 127 ms
53,284 KB
testcase_16 AC 113 ms
51,864 KB
testcase_17 AC 116 ms
54,456 KB
testcase_18 AC 114 ms
52,180 KB
testcase_19 AC 115 ms
53,044 KB
testcase_20 AC 117 ms
54,060 KB
testcase_21 AC 119 ms
52,464 KB
testcase_22 AC 118 ms
52,220 KB
testcase_23 AC 114 ms
52,796 KB
testcase_24 AC 118 ms
53,168 KB
testcase_25 AC 113 ms
53,392 KB
testcase_26 AC 117 ms
53,476 KB
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 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 = 4 * 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);
    }
  }
}

/*
  http://www.math.aoyama.ac.jp/~kyo/sotsuken/2008/konishi.pdf
  Th. 2.2.1
*/

alias Result = Tuple!(int, "area", Mint, "way");
Result solve(int[] seq) {
  const m = cast(int)(seq.count(0));
  const n = cast(int)(seq.count(1));
  auto as = new int[m];
  auto bs = new int[n];
  {
    int x = 0, y = n;
    foreach (s; seq) {
      if (s == 0) {
        as[x++] = y;
      } else {
        bs[--y] = x;
      }
    }
    assert(x == m);
    assert(y == 0);
  }
  debug {
    if (m <= 10 && n <= 10) {
      writeln("seq = ", seq);
      writeln("as = ", as);
      writeln("bs = ", bs);
    }
  }
  int area;
  Mint way = 1;
  foreach (x; 0 .. m) {
    foreach (y; 0 .. as[x]) {
      ++area;
      way *= inv[(as[x] - y) + (bs[y] - x) - 1];
    }
  }
  return Result(area, way);
}

void main() {
  prepare;
  
  try {
    for (; ; ) {
      const M = readInt;
      auto A = new int[M];
      foreach (x; 0 .. M) {
        A[x] = readInt;
      }
      A.sort.reverse;
      A ~= 0;
      
      bool special;
      
      if (A.sum % 2 != 0) {
        writeln(0);
      } else {
        int[] seq;
        foreach (x; 0 .. M) {
          seq ~= 0;
          foreach_reverse (y; A[x + 1] .. A[x]) {
            seq ~= 1;
          }
        }
        debug {
          if (M <= 10 && A[0] <= 10) {
            writeln("A = ", A);
            writeln("seq = ", seq);
          }
        }
        
        bool check() {
          int[] stack;
          foreach (s; seq) {
            if (!stack.empty && stack.back == s) {
              stack.popBack;
            } else {
              stack ~= s;
            }
          }
          foreach (i; 0 .. cast(int)(stack.length) - 1) {
            if (stack[i] == 0 && stack[i + 1] == 1) {
              return false;
            }
          }
          return true;
        }
        if (!check) {
          writeln(0);
        } else {
          int[][2] seqs;
          foreach (i; 0 .. cast(int)(seq.length)) {
            seqs[i & 1] ~= seq[i];
          }
          const res0 = solve(seqs[0]);
          const res1 = solve(seqs[1]);
          debug {
            writeln("res0 = ", res0);
            writeln("res1 = ", res1);
          }
          Mint ans = fac[res0.area + res1.area];
          ans *= res0.way;
          ans *= res1.way;
          writeln(ans);
        }
      }
    }
  } catch (EOFException e) {
  }
}
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