結果

問題 No.2083 OR Subset
ユーザー 👑 hos.lyrichos.lyric
提出日時 2022-09-25 21:33:37
言語 D
(dmd 2.106.1)
結果
AC  
実行時間 831 ms / 3,000 ms
コード長 5,483 bytes
コンパイル時間 1,439 ms
コンパイル使用メモリ 155,940 KB
実行使用メモリ 104,736 KB
最終ジャッジ日時 2024-06-22 16:17:38
合計ジャッジ時間 11,581 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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 176 ms
104,488 KB
testcase_01 AC 176 ms
104,084 KB
testcase_02 AC 178 ms
104,296 KB
testcase_03 AC 482 ms
104,736 KB
testcase_04 AC 364 ms
104,392 KB
testcase_05 AC 752 ms
104,240 KB
testcase_06 AC 316 ms
104,608 KB
testcase_07 AC 185 ms
104,020 KB
testcase_08 AC 193 ms
104,092 KB
testcase_09 AC 479 ms
104,528 KB
testcase_10 AC 371 ms
104,252 KB
testcase_11 AC 271 ms
103,916 KB
testcase_12 AC 243 ms
104,388 KB
testcase_13 AC 770 ms
103,488 KB
testcase_14 AC 757 ms
103,960 KB
testcase_15 AC 762 ms
103,632 KB
testcase_16 AC 831 ms
103,832 KB
testcase_17 AC 819 ms
103,848 KB
testcase_18 AC 177 ms
103,956 KB
testcase_19 AC 827 ms
104,096 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 = 5010;
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);
    }
  }
}


void main() {
  prepare;
  auto S2 = new Mint[][](LIM_INV, LIM_INV);
  foreach (n; 0 .. LIM_INV) {
    S2[n][0] = 0;
    S2[n][n] = 1;
    foreach (k; 1 .. n) {
      S2[n][k] = S2[n - 1][k - 1] + k * S2[n - 1][k];
    }
  }
  
  debug {
    foreach (n; 0 .. 4 + 1) {
      auto freq = new int[1 << n];
      foreach (p; 0 .. 1 << (1 << n)) if (popcnt(p) <= 4) {
        int[] xs;
        foreach (x; 0 .. 1 << n) if (p >> x & 1) {
          xs ~= x;
        }
        const xsLen = cast(int)(xs.length);
        auto xsOr = new int[1 << xsLen];
        foreach (i; 0 .. xsLen) foreach (q; 0 .. 1 << i) {
          xsOr[q | 1 << i] = xsOr[q] | xs[i];
        }
        xsOr.sort;
        bool ok = true;
        foreach (q; 1 .. 1 << xsLen) {
          ok = ok && (xsOr[q - 1] != xsOr[q]);
        }
        if (ok) {
          ++freq[xs.length];
          if (n == 3) {
            writeln("  ", xs);
          }
        }
      }
      writeln(n, ": ", freq);
    }
  }
  
  try {
    for (; ; ) {
      const N = readInt;
      
      Mint ans;
      foreach (m; 0 .. N + 1) {
        Mint sum;
        const two = Mint(2)^^m;
        Mint pw = 1;
        foreach_reverse (l; m .. N + 1) {
          Mint num = 1;
          num *= S2[l][m];
          num *= binom(N, l);
          num *= pw;
          pw *= (two - m);
          sum += num;
        }
        debug {
          if (N <= 10) {
            writeln(N, " ", m, ": ", sum);
          }
        }
        ans += sum;
      }
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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