結果

問題 No.1970 ひよこ鑑定士
ユーザー 👑 hos.lyrichos.lyric
提出日時 2022-06-04 11:39:29
言語 D
(dmd 2.106.1)
結果
AC  
実行時間 39 ms / 2,000 ms
コード長 5,042 bytes
コンパイル時間 1,541 ms
コンパイル使用メモリ 155,444 KB
実行使用メモリ 8,256 KB
最終ジャッジ日時 2024-06-22 15:23:45
合計ジャッジ時間 2,576 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
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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 10 ms
8,256 KB
testcase_01 AC 10 ms
7,636 KB
testcase_02 AC 9 ms
7,316 KB
testcase_03 AC 9 ms
7,392 KB
testcase_04 AC 10 ms
7,380 KB
testcase_05 AC 10 ms
7,368 KB
testcase_06 AC 9 ms
7,684 KB
testcase_07 AC 11 ms
8,072 KB
testcase_08 AC 37 ms
7,884 KB
testcase_09 AC 20 ms
7,372 KB
testcase_10 AC 20 ms
8,080 KB
testcase_11 AC 12 ms
7,416 KB
testcase_12 AC 23 ms
7,316 KB
testcase_13 AC 26 ms
7,728 KB
testcase_14 AC 31 ms
7,496 KB
testcase_15 AC 11 ms
7,888 KB
testcase_16 AC 12 ms
7,688 KB
testcase_17 AC 16 ms
7,528 KB
testcase_18 AC 35 ms
7,884 KB
testcase_19 AC 31 ms
7,372 KB
testcase_20 AC 39 ms
7,404 KB
testcase_21 AC 31 ms
7,736 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 = 4 * 10^^5 + 10;
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);
    }
  }
}


// A <= min <= max <= B
// reflect wrt y - x = A - 1, B + 1
Mint pathBetween(int N, int A, int B) {
  Mint ret;
  if (A <= 0 && 0 <= B) {
    const w = (B + 1) - (A - 1);
    ret += binom(2 * N, N);
    for (int y1 = N + A - 1, y0 = N - w; ; y1 -= w, y0 -= w) {
      if (y1 < 0) break;
      ret -= binom(2 * N, y1);
      if (y0 < 0) break;
      ret += binom(2 * N, y0);
    }
    for (int y1 = N + B + 1, y0 = N + w; ; y1 += w, y0 += w) {
      if (y1 > 2 * N) break;
      ret -= binom(2 * N, y1);
      if (y0 > 2 * N) break;
      ret += binom(2 * N, y0);
    }
  }
  debug {
    writefln("pathBetween %s %s %s = %s", N, A, B, ret);
  }
  return ret;
}

// A = min <= max <= B
Mint solve(int N, int A, int B) {
  Mint ret;
  if (A <= 0 && 0 <= B) {
    ret += pathBetween(N, A, B);
    ret -= pathBetween(N, A + 1, B);
  }
  return ret;
}

void main() {
  prepare;
  try {
    for (; ; ) {
      const N = readInt;
      const K = readInt;
      
      Mint ans = binom(2 * N, N);
      foreach (i; 0 .. K) {
        ans -= solve(N, -i, -i + K - 1);
      }
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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