#741823 (D) No.1856 Mex Sum 2

提出ソース

結果

問題	No.1856 Mex Sum 2
ユーザー	👑 hos.lyric
提出日時	2022-02-25 21:38:07
言語	D (dmd 2.106.1)
結果	AC
実行時間	117 ms / 3,000 ms
コード長	4,813 bytes
コンパイル時間	1,370 ms
コンパイル使用メモリ	154,676 KB
実行使用メモリ	20,776 KB
最終ジャッジ日時	2024-06-22 14:24:20
合計ジャッジ時間	7,041 ms
ジャッジサーバーID （参考情報）	judge4 / judge3

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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	35 ms 19,144 KB
testcase_01	AC	34 ms 19,868 KB
testcase_02	AC	33 ms 19,328 KB
testcase_03	AC	35 ms 20,576 KB
testcase_04	AC	34 ms 19,216 KB
testcase_05	AC	33 ms 19,324 KB
testcase_06	AC	34 ms 19,368 KB
testcase_07	AC	34 ms 19,624 KB
testcase_08	AC	34 ms 19,880 KB
testcase_09	AC	34 ms 19,664 KB
testcase_10	AC	35 ms 20,660 KB
testcase_11	AC	34 ms 20,000 KB
testcase_12	AC	34 ms 19,084 KB
testcase_13	AC	34 ms 19,540 KB
testcase_14	AC	34 ms 20,776 KB
testcase_15	AC	33 ms 19,992 KB
testcase_16	AC	35 ms 19,200 KB
testcase_17	AC	35 ms 19,100 KB
testcase_18	AC	33 ms 19,912 KB
testcase_19	AC	34 ms 20,684 KB
testcase_20	AC	34 ms 19,060 KB
testcase_21	AC	33 ms 19,572 KB
testcase_22	AC	33 ms 19,444 KB
testcase_23	AC	33 ms 19,188 KB
testcase_24	AC	32 ms 19,416 KB
testcase_25	AC	34 ms 19,596 KB
testcase_26	AC	32 ms 19,588 KB
testcase_27	AC	34 ms 19,984 KB
testcase_28	AC	35 ms 20,644 KB
testcase_29	AC	63 ms 19,608 KB
testcase_30	AC	62 ms 19,072 KB
testcase_31	AC	64 ms 19,864 KB
testcase_32	AC	72 ms 19,432 KB
testcase_33	AC	82 ms 20,128 KB
testcase_34	AC	68 ms 20,276 KB
testcase_35	AC	54 ms 19,688 KB
testcase_36	AC	54 ms 20,696 KB
testcase_37	AC	65 ms 19,456 KB
testcase_38	AC	58 ms 19,332 KB
testcase_39	AC	58 ms 19,372 KB
testcase_40	AC	59 ms 19,240 KB
testcase_41	AC	58 ms 20,468 KB
testcase_42	AC	99 ms 19,804 KB
testcase_43	AC	86 ms 20,096 KB
testcase_44	AC	94 ms 19,188 KB
testcase_45	AC	97 ms 19,228 KB
testcase_46	AC	87 ms 19,748 KB
testcase_47	AC	98 ms 19,272 KB
testcase_48	AC	105 ms 19,424 KB
testcase_49	AC	101 ms 19,488 KB
testcase_50	AC	76 ms 19,556 KB
testcase_51	AC	102 ms 19,704 KB
testcase_52	AC	100 ms 19,260 KB
testcase_53	AC	103 ms 20,252 KB
testcase_54	AC	106 ms 19,764 KB
testcase_55	AC	103 ms 19,144 KB
testcase_56	AC	103 ms 19,996 KB
testcase_57	AC	102 ms 19,936 KB
testcase_58	AC	103 ms 19,788 KB
testcase_59	AC	102 ms 19,380 KB
testcase_60	AC	102 ms 19,668 KB
testcase_61	AC	102 ms 19,828 KB
testcase_62	AC	104 ms 20,592 KB
testcase_63	AC	104 ms 19,776 KB
testcase_64	AC	117 ms 20,220 KB
testcase_65	AC	103 ms 19,664 KB
testcase_66	AC	102 ms 19,272 KB

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ソースコード

raw source code

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 = 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 = 2010;
Mint[] inv, fac, invFac;
void prepare() {
  inv = new Mint[LIM];
  fac = new Mint[LIM];
  invFac = new Mint[LIM];
  inv[1] = 1;
  foreach (i; 2 .. LIM) {
    inv[i] = -((Mint.M / i) * inv[cast(size_t)(Mint.M % i)]);
  }
  fac[0] = invFac[0] = 1;
  foreach (i; 1 .. LIM) {
    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);
      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, LIM);
  foreach (n; 0 .. LIM) {
    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];
    }
  }
  
  try {
    for (; ; ) {
      const N = readInt;
      const M = readLong;
      
      // k kinds
      auto fs = new Mint[N + 1];
      foreach (n; 1 .. N + 1) {
        const num = binom(N, n) * Mint(M + 1)^^(N - n);
        foreach (k; 1 .. n + 1) {
          fs[k] += num * S2[n][k];
        }
      }
      
      Mint ans;
      // mex >= a
      // 0,...,a-1 appears
      foreach (a; 1 .. N + 1) if (a - 1 <= M) {
        // binom(M + 1 - a, k - a)
        Mint bn = 1;
        foreach (k; a .. N + 1) {
          ans += fac[k] * bn * fs[k];
          bn *= (M + 1 - a - (k - a));
          bn *= inv[k - a + 1];
        }
      }
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}

yukicoder

結果

テストケース

ソースコード