結果

問題 No.1080 Strange Squared Score Sum
ユーザー 👑 hos.lyrichos.lyric
提出日時 2020-06-12 22:31:24
言語 D
(dmd 2.105.2)
結果
AC  
実行時間 4,869 ms / 5,000 ms
コード長 14,266 bytes
コンパイル時間 2,807 ms
コンパイル使用メモリ 154,120 KB
実行使用メモリ 55,328 KB
最終ジャッジ日時 2023-09-04 08:06:59
合計ジャッジ時間 55,265 ms
ジャッジサーバーID
(参考情報)
judge15 / judge13
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 13 ms
11,336 KB
testcase_01 AC 13 ms
11,564 KB
testcase_02 AC 2,305 ms
38,868 KB
testcase_03 AC 4,863 ms
55,328 KB
testcase_04 AC 1,080 ms
24,996 KB
testcase_05 AC 1,087 ms
25,256 KB
testcase_06 AC 244 ms
14,708 KB
testcase_07 AC 510 ms
23,872 KB
testcase_08 AC 2,288 ms
38,600 KB
testcase_09 AC 2,292 ms
38,644 KB
testcase_10 AC 243 ms
14,776 KB
testcase_11 AC 4,852 ms
55,316 KB
testcase_12 AC 2,284 ms
38,636 KB
testcase_13 AC 4,856 ms
55,260 KB
testcase_14 AC 2,287 ms
38,604 KB
testcase_15 AC 13 ms
11,276 KB
testcase_16 AC 4,869 ms
54,272 KB
testcase_17 AC 2,306 ms
38,904 KB
testcase_18 AC 2,306 ms
38,856 KB
testcase_19 AC 2,300 ms
38,868 KB
testcase_20 AC 4,850 ms
55,328 KB
testcase_21 AC 4,849 ms
55,284 KB
権限があれば一括ダウンロードができます
コンパイルメッセージ
Main.d(319): Deprecation: returning `this` escapes a reference to parameter `this`
Main.d(317):        perhaps annotate the function with `return`
Main.d(324): Deprecation: returning `this` escapes a reference to parameter `this`
Main.d(321):        perhaps annotate the function with `return`

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(int M_) {
  import std.conv : to;
  alias M = M_;
  int x;
  this(ModInt a) { x = a.x; }
  this(long a) { x = cast(int)(a % M); if (x < 0) x += M; }
  ref ModInt opAssign(long a) { return (this = ModInt(a)); }
  ref ModInt opOpAssign(string op)(ModInt a) {
    static if (op == "+") { x += a.x; if (x >= M) x -= M; }
    else static if (op == "-") { x -= a.x; if (x < 0) x += M; }
    else static if (op == "*") { x = cast(int)((cast(long)(x) * a.x) % M); }
    else static if (op == "/") { this *= a.inv(); }
    else static assert(false);
    return this;
  }
  ref ModInt opOpAssign(string op)(long a) {
    static if (op == "^^") {
      if (a < 0) return (this = inv()^^(-a));
      ModInt t2 = this, te = ModInt(1);
      for (long e = a; e > 0; e >>= 1) {
        if (e & 1) te *= t2;
        t2 *= t2;
      }
      x = cast(int)(te.x);
      return this;
    } else return mixin("this " ~ op ~ "= ModInt(a)");
  }
  ModInt inv() const {
    int a = x, b = M, y = 1, z = 0, t;
    for (; ; ) {
      t = a / b; a -= t * b;
      if (a == 0) {
        assert(b == 1 || b == -1);
        return ModInt(b * z);
      }
      y -= t * z;
      t = b / a; b -= t * a;
      if (b == 0) {
        assert(a == 1 || a == -1);
        return ModInt(a * y);
      }
      z -= t * y;
    }
  }
  ModInt opUnary(string op: "-")() const { return ModInt(-x); }
  ModInt opBinary(string op, T)(T a) const {
    return mixin("ModInt(this) " ~ op ~ "= a");
  }
  ModInt opBinaryRight(string op)(long a) const {
    return mixin("ModInt(a) " ~ op ~ "= this");
  }
  bool opCast(T: bool)() const { return (x != 0); }
  string toString() const { return x.to!string; }
}

enum MO = 10^^9 + 9;
alias Mint = ModInt!MO;

enum Mint I = 569522298;


// a^-1 (mod m)
long modInv(long a, long m)
in {
  assert(m > 0, "modInv: m > 0 must hold");
}
do {
  long b = m, x = 1, y = 0, t;
  for (; ; ) {
    t = a / b; a -= t * b;
    if (a == 0) {
      assert(b == 1 || b == -1, "modInv: gcd(a, m) != 1");
      if (b == -1) y = -y;
      return (y < 0) ? (y + m) : y;
    }
    x -= t * y;
    t = b / a; b -= t * a;
    if (b == 0) {
      assert(a == 1 || a == -1, "modInv: gcd(a, m) != 1");
      if (a == -1) x = -x;
      return (x < 0) ? (x + m) : x;
    }
    y -= t * x;
  }
}


// M: prime, G: primitive root
class Fft(int M_, int G, int K) {
  import std.algorithm : reverse;
  import std.traits : isIntegral;
  alias M = M_;
  // 1, 1/4, 1/8, 3/8, 1/16, 5/16, 3/16, 7/16, ...
  int[] gs;
  this() {
    static assert(2 <= K && K <= 30, "Fft: 2 <= K <= 30 must hold");
    static assert(!((M - 1) & ((1 << K) - 1)), "Fft: 2^K | M - 1 must hold");
    gs = new int[1 << (K - 1)];
    gs[0] = 1;
    long g2 = G, gg = 1;
    for (int e = (M - 1) >> K; e; e >>= 1) {
      if (e & 1) gg = (gg * g2) % M;
      g2 = (g2 * g2) % M;
    }
    gs[1 << (K - 2)] = cast(int)(gg);
    for (int l = 1 << (K - 2); l >= 2; l >>= 1) {
      gs[l >> 1] = cast(int)((cast(long)(gs[l]) * gs[l]) % M);
    }
    assert((cast(long)(gs[1]) * gs[1]) % M == M - 1,
           "Fft: g^(2^(K-1)) == -1 (mod M) must hold");
    for (int l = 2; l <= 1 << (K - 2); l <<= 1) {
      foreach (i; 1 .. l) {
        gs[l + i] = cast(int)((cast(long)(gs[l]) * gs[i]) % M);
      }
    }
  }
  void fft(int[] xs) const {
    const n = cast(int)(xs.length);
    assert(!(n & (n - 1)), "Fft.fft: |xs| must be a power of two");
    assert(n <= 1 << K, "Fft.fft: |xs| <= 2^K must hold");
    for (int l = n; l >>= 1; ) {
      foreach (i; 0 .. (n >> 1) / l) {
        const(long) g = gs[i];
        foreach (j; (i << 1) * l .. (i << 1 | 1) * l) {
          const t = cast(int)((g * xs[j + l]) % M);
          if ((xs[j + l] = xs[j] - t) < 0) xs[j + l] += M;
          if ((xs[j] += t) >= M) xs[j] -= M;
        }
      }
    }
  }
  void invFft(int[] xs) const {
    const n = cast(int)(xs.length);
    assert(!(n & (n - 1)), "Fft.invFft: |xs| must be a power of two");
    assert(n <= 1 << K, "Fft.invFft: |xs| <= 2^K must hold");
    for (int l = 1; l < n; l <<= 1) reverse(xs[l .. l << 1]);
    for (int l = 1; l < n; l <<= 1) {
      foreach (i; 0 .. (n >> 1) / l) {
        const(long) g = gs[i];
        foreach (j; (i << 1) * l .. (i << 1 | 1) * l) {
          int t = cast(int)((g * (xs[j] - xs[j + l])) % M);
          if (t < 0) t += M;
          if ((xs[j] += xs[j + l]) >= M) xs[j] -= M;
          xs[j + l] = t;
        }
      }
    }
  }
  T[] convolute(T)(inout(T)[] as, inout(T)[] bs) const if (isIntegral!T) {
    const na = cast(int)(as.length), nb = cast(int)(bs.length);
    int n, invN = 1;
    for (n = 1; n < na + nb - 1; n <<= 1) {
      invN = ((invN & 1) ? (invN + M) : invN) >> 1;
    }
    auto xs = new int[n], ys = new int[n];
    foreach (i; 0 .. na) if ((xs[i] = cast(int)(as[i] % M)) < 0) xs[i] += M;
    foreach (i; 0 .. nb) if ((ys[i] = cast(int)(bs[i] % M)) < 0) ys[i] += M;
    fft(xs);
    fft(ys);
    foreach (i; 0 .. n) {
      xs[i] = cast(int)((((cast(long)(xs[i]) * ys[i]) % M) * invN) % M);
    }
    invFft(xs);
    auto cs = new T[na + nb - 1];
    foreach (i; 0 .. na + nb - 1) cs[i] = cast(T)(xs[i]);
    return cs;
  }
  ModInt!M[] convolute(inout(ModInt!M)[] as, inout(ModInt!M)[] bs) const {
    const na = cast(int)(as.length), nb = cast(int)(bs.length);
    int n, invN = 1;
    for (n = 1; n < na + nb - 1; n <<= 1) {
      invN = ((invN & 1) ? (invN + M) : invN) >> 1;
    }
    auto xs = new int[n], ys = new int[n];
    foreach (i; 0 .. na) xs[i] = as[i].x;
    foreach (i; 0 .. nb) ys[i] = bs[i].x;
    fft(xs);
    fft(ys);
    foreach (i; 0 .. n) {
      xs[i] = cast(int)((((cast(long)(xs[i]) * ys[i]) % M) * invN) % M);
    }
    invFft(xs);
    auto cs = new ModInt!M[na + nb - 1];
    foreach (i; 0 .. na + nb - 1) cs[i].x = xs[i];
    return cs;
  }
  int[] convolute(int M1)(inout(ModInt!M1)[] as, inout(ModInt!M1)[] bs) const
      if (M != M1) {
    const na = cast(int)(as.length), nb = cast(int)(bs.length);
    int n, invN = 1;
    for (n = 1; n < na + nb - 1; n <<= 1) {
      invN = ((invN & 1) ? (invN + M) : invN) >> 1;
    }
    auto xs = new int[n], ys = new int[n];
    foreach (i; 0 .. na) xs[i] = as[i].x;
    foreach (i; 0 .. nb) ys[i] = bs[i].x;
    fft(xs);
    fft(ys);
    foreach (i; 0 .. n) {
      xs[i] = cast(int)((((cast(long)(xs[i]) * ys[i]) % M) * invN) % M);
    }
    invFft(xs);
    return xs[0 .. na + nb - 1];
  }
  int[] square(int M1)(inout(ModInt!M1)[] as) const
      if (M != M1) {
    const na = cast(int)(as.length);
    int n, invN = 1;
    for (n = 1; n < na + na - 1; n <<= 1) {
      invN = ((invN & 1) ? (invN + M) : invN) >> 1;
    }
    auto xs = new int[n];
    foreach (i; 0 .. na) xs[i] = as[i].x;
    fft(xs);
    foreach (i; 0 .. n) {
      xs[i] = cast(int)((((cast(long)(xs[i]) * xs[i]) % M) * invN) % M);
    }
    invFft(xs);
    return xs[0 .. na + na - 1];
  }
}


enum FFT_K = 20;
alias Fft3_0 = Fft!(1045430273, 3, FFT_K);  // 2^20 997 + 1
alias Fft3_1 = Fft!(1051721729, 6, FFT_K);  // 2^20 1003 + 1
alias Fft3_2 = Fft!(1053818881, 7, FFT_K);  // 2^20 1005 + 1
enum long FFT_INV01 = modInv(Fft3_0.M, Fft3_1.M);
enum long FFT_INV012 = modInv(cast(long)(Fft3_0.M) * Fft3_1.M, Fft3_2.M);
Fft3_0 FFT3_0;
Fft3_1 FFT3_1;
Fft3_2 FFT3_2;
void initFft3() {
  FFT3_0 = new Fft3_0;
  FFT3_1 = new Fft3_1;
  FFT3_2 = new Fft3_2;
}
ModInt!M[] convolute(int M)(inout(ModInt!M)[] as, inout(ModInt!M)[] bs) {
  const cs0 = FFT3_0.convolute(as, bs);
  const cs1 = FFT3_1.convolute(as, bs);
  const cs2 = FFT3_2.convolute(as, bs);
  auto cs = new ModInt!M[cs0.length];
  foreach (i; 0 .. cs0.length) {
    long d0 = cs0[i] % Fft3_0.M;
    long d1 = (FFT_INV01 * (cs1[i] - d0)) % Fft3_1.M;
    if (d1 < 0) d1 += Fft3_1.M;
    long d2 =
        (FFT_INV012 * ((cs2[i] - d0 - Fft3_0.M * d1) % Fft3_2.M)) % Fft3_2.M;
    if (d2 < 0) d2 += Fft3_2.M;
    cs[i] =
        (d0 + Fft3_0.M * d1 + ((cast(long)(Fft3_0.M) * Fft3_1.M) % M) * d2) % M;
  }
  return cs;
}
ModInt!M[] Square(int M)(inout(ModInt!M)[] as) {
  const cs0 = FFT3_0.square(as);
  const cs1 = FFT3_1.square(as);
  const cs2 = FFT3_2.square(as);
  auto cs = new ModInt!M[cs0.length];
  foreach (i; 0 .. cs0.length) {
    long d0 = cs0[i] % Fft3_0.M;
    long d1 = (FFT_INV01 * (cs1[i] - d0)) % Fft3_1.M;
    if (d1 < 0) d1 += Fft3_1.M;
    long d2 =
        (FFT_INV012 * ((cs2[i] - d0 - Fft3_0.M * d1) % Fft3_2.M)) % Fft3_2.M;
    if (d2 < 0) d2 += Fft3_2.M;
    cs[i] =
        (d0 + Fft3_0.M * d1 + ((cast(long)(Fft3_0.M) * Fft3_1.M) % M) * d2) % M;
  }
  return cs;
}

struct Poly {
  Mint[] x;
  this(Poly f) {
    x = f.x.dup;
  }
  this(const(Poly) f) {
    x = f.x.dup;
  }
  this(int n) {
    x = new Mint[n];
  }
  this(const(Mint)[] x) {
    this.x = x.dup;
  }
  this(const(long)[] x) {
    this.x.length = x.length;
    foreach (i; 0 .. x.length) this.x[i] = Mint(x[i]);
  }
  int size() const {
    return cast(int)(x.length);
  }
  Poly take(int n) const {
    return Poly(x[0 .. min(max(n, 1), $)]);
  }

  ref Poly opAssign(const(Mint)[] x) {
    this.x = x.dup;
    return this;
  }
  ref Poly opAssign(const(long)[] x) {
    this.x.length = x.length;
    foreach (i; 0 .. x.length) this.x[i] = Mint(x[i]);
    return this;
  }
  Mint opIndex(int i) const {
    return x[i];
  }
  ref Mint opIndex(int i) {
    return x[i];
  }
  ref Poly opOpAssign(string op)(const(Poly) f) {
    static if (op == "+") {
      if (size() < f.size()) x.length = f.size();
      foreach (i; 0 .. f.size()) this[i] += f[i];
      return this;
    } else static if (op == "-") {
      if (size() < f.size()) x.length = f.size();
      foreach (i; 0 .. f.size()) this[i] -= f[i];
      return this;
    } else static if (op == "*") {
      // TODO: FFT
      /*
      Poly g = Poly(size() + f.size() - 1);
      foreach (i; 0 .. size()) foreach (j; 0 .. f.size()) {
        g[i + j] += this[i] * f[j];
      }
      this = g;
      return this;
      */
      return this = Poly(convolute!MO(x, f.x));
    } else {
      static assert(false);
    }
  }
  ref Poly opOpAssign(string op)(Mint a) if (op == "*") {
    foreach (i; 0 .. size()) this[i] *= a;
    return this;
  }
  Poly opBinary(string op, T)(T a) const {
    return mixin("Poly(this) " ~ op ~ "= a");
    // Poly f = Poly(this);
    // mixin("f " ~ op ~ "= a;");
    // return f;
  }
  Poly opBinaryRight(string op)(Mint a) const if (op == "*") {
    return this * a;
  }
  Poly opUnary(string op)() const if (op == "-") {
    return this * Mint(-1);
  }

  Poly square(int n) const {
    // TODO: FFT
    /*
    Poly f = Poly(n);
    foreach (i; 0 .. min(size(), (n + 1) / 2)) {
      f[i + i] += this[i] * this[i];
      foreach (j; i + 1 .. min(size(), n - i)) {
        f[i + j] += Mint(2) * this[i] * this[j];
      }
    }
    return f;
    */
    return Poly(Square!MO(x));
  }
  Poly inv(int n) const {
    // TODO: fft
    assert(this[0].x != 0);
    Poly f = Poly(n);
    f[0] = this[0].inv();
    foreach (i; 1 .. n) {
      foreach (j; 1 .. min(size(), i + 1)) {
        f[i] -= this[j] * f[i - j];
      }
      f[i] *= f[0];
    }
    return f;
  }
  Poly differential() const {
    Poly f = Poly(max(size() - 1, 1));
    foreach (i; 1 .. size()) f[i - 1] = Mint(i) * this[i];
    return f;
  }
  Poly integral() const {
    Poly f = Poly(size() + 1);
    foreach (i; 0 .. size()) f[i + 1] = Mint(i + 1).inv() * this[i];
    return f;
  }
  Poly exp(int n) const {
    assert(this[0].x == 0);
    const d = differential();
    Poly f = [1], g = [1];
    for (int m = 1; m < n; m <<= 1) {
      g = g + g - (f * g.square(m)).take(m);
      Poly h = d.take(m - 1);
      h += (g * (f.differential() - f * h)).take(2 * m - 1);
      f += (f * (take(2 * m) - h.integral())).take(2 * m);
    }
    return f.take(n);
  }
}
enum Poly1 = Poly([1]);
enum PolyQ = Poly([0, 1]);


void main() {
  initFft3;
  
  debug {
    // N = 3
    auto sums = new Mint[][](3 + 1, 9 + 1);
    sums[0][0] += 6 * 1^^2;
    foreach (a; 1 .. 3 + 1) {
      sums[1][a] += 6 * (a + 1)^^2;
    }
    // foreach (a; 1 .. 3 + 1) foreach (b; a .. 3 + 1) {
    foreach (a; 1 .. 3 + 1) foreach (b; 1 .. 3 + 1) {
      sums[2][a + b] += 3 * ((a + 1) * (b + 1))^^2;
    }
    // foreach (a; 1 .. 3 + 1) foreach (b; a .. 3 + 1) foreach (c; b .. 3 + 1) {
    foreach (a; 1 .. 3 + 1) foreach (b; 1 .. 3 + 1) foreach (c; 1 .. 3 + 1) {
      sums[3][a + b + c] += 1 * ((a + 1) * (b + 1) * (c + 1))^^2;
    }
    foreach (m; 0 .. 3 + 1) {
      writeln(sums[m]);
    }
    foreach (k; 0 .. 9 + 1) {
      writeln(sums[0][k] + sums[1][k] - sums[2][k] - sums[3][k]);
    }
  }
  
  try {
    for (; ; ) {
      const N = readInt();
      
      Mint fac = 1;
      foreach (i; 1 .. N + 1) {
        fac *= i;
      }
      
      auto f = Poly(N + 1);
      foreach (i; 1 .. N + 1) {
        f[i] = 1L * (i + 1) * (i + 1);
      }
      auto g0 = (f * I).exp(N + 1);
      auto g1 = (f * -I).exp(N + 1);
      auto re = (g0 + g1) * Mint(2).inv;
      auto im = (g0 - g1) * Mint(2 * I).inv;
      auto ans = (re + im) * fac;
      foreach (i; 1 .. N + 1) {
        writeln(ans[i]);
      }
    }
  } catch (EOFException e) {
  }
}
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