結果

問題 No.931 Multiplicative Convolution
コンテスト
ユーザー hos.lyric
提出日時 2019-11-22 21:46:32
言語 D
(dmd 2.109.1)
結果
AC  
実行時間 212 ms / 2,000 ms
コード長 6,448 bytes
コンパイル時間 670 ms
コンパイル使用メモリ 122,672 KB
実行使用メモリ 20,276 KB
最終ジャッジ日時 2024-06-22 03:03:10
合計ジャッジ時間 4,079 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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ファイルパターン 結果
sample AC * 3
other AC * 14
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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.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)); }

// a^-1 (mod 2^64)
long modInv(long a)
in {
  assert(a & 1, "modInv: a must be odd");
}
do {
  long b = ((a << 1) + a) ^ 2;
  b *= 2 - a * b;
  b *= 2 - a * b;
  b *= 2 - a * b;
  b *= 2 - a * b;
  return b;
}

// 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;
  }
}

// 2^-31 a (mod M)
long montgomery(long M)(long a) if (1 <= M && M <= 0x7fffffff && (M & 1))
in {
  assert(0 <= a && a < (M << 31), "montgomery: 0 <= a < 2^31 M must hold");
}
do {
  enum negInvM = -modInv(M) & 0x7fffffff;
  const b = (a + ((a * negInvM) & 0x7fffffff) * M) >> 31;
  return (b >= M) ? (b - M) : b;
}

// FFT on Z / M Z with Montgomery multiplication (x -> 2^31 x)
//   G: primitive 2^K-th root of unity
class FFT(long M, int K, long G)
    if (is(typeof(montgomery!(M)(0))) && K >= 0 && 0 < G && G < M) {
  import std.algorithm : swap;
  import core.bitop : bsf;

  int n, invN;
  long[] g;

  this(int n)
  in {
    assert(!(n & (n - 1)), "FFT.this: n must be a power of 2");
    assert(4 <= n && n <= 1 << K, "FFT.this: 4 <= n <= 2^K must hold");
  }
  do {
    this.n = n;
    this.invN = ((1L << 31) / n) % M;
    g.length = n + 1;
    g[0] = (1L << 31) % M;
    g[1] = (G << 31) % M;
    foreach (_; 0 .. K - bsf(n)) {
      g[1] = montgomery!(M)(g[1] * g[1]);
    }
    foreach (i; 2 .. n + 1) {
      g[i] = montgomery!(M)(g[i - 1] * g[1]);
    }
    assert(g[0] != g[n >> 1] && g[0] == g[n],
           "FFT.this: G must be a primitive 2^K-th root of unity");
    for (int i = 0, j = 0; i < n >> 1; ++i) {
      if (i < j) {
        swap(g[i], g[j]);
        swap(g[n - i], g[n - j]);
      }
      for (int m = n >> 1; (m >>= 1) && !((j ^= m) & m); ) {}
    }
  }

  void fftMontgomery(long[] x, bool inv)
  in {
    assert(x.length == n, "FFT.fftMontgomery: |x| = n must hold");
  }
  do {
    foreach_reverse (h; 0 .. bsf(n)) {
      const l = 1 << h;
      foreach (i; 0 .. n >> 1 >> h) {
        const gI = g[inv ? (n - i) : i];
        foreach (j; i << 1 << h .. ((i << 1) + 1) << h) {
          const t = montgomery!(M)(gI * x[j + l]);
          if ((x[j + l] = x[j] - t) < 0) {
            x[j + l] += M;
          }
          if ((x[j] += t) >= M) {
            x[j] -= M;
          }
        }
      }
    }
    for (int i = 0, j = 0; i < n; ++i) {
      if (i < j) {
        swap(x[i], x[j]);
      }
      for (int m = n; (m >>= 1) && !((j ^= m) & m); ) {}
    }
    if (inv) {
      foreach (i; 0 .. n) {
        x[i] = montgomery!(M)(invN * x[i]);
      }
    }
  }

  long[] convolution(long[] a, long[] b)
  in {
    assert(a.length <= n, "FFT.convolution: |a| <= n must hold");
    assert(b.length <= n, "FFT.convolution: |b| <= n must hold");
  }
  do {
    auto x = new long[n], y = new long[n];
    foreach (i; 0 .. a.length) {
      const t = a[i] % M;
      x[i] = (((t < 0) ? (t + M) : t) << 31) % M;
    }
    foreach (i; 0 .. b.length) {
      const t = b[i] % M;
      y[i] = (((t < 0) ? (t + M) : t) << 31) % M;
    }
    fftMontgomery(x, false);
    fftMontgomery(y, false);
    foreach (i; 0 .. n) {
      x[i] = montgomery!(M)(x[i] * y[i]);
    }
    fftMontgomery(x, true);
    foreach (i; 0 .. n) {
      x[i] = montgomery!(M)(x[i]);
    }
    return x;
  }
}


enum MO = 998244353;
alias FFT0 = FFT!(MO, 23, 31L);

void main() {
  try {
    for (; ; ) {
      const P = readInt;
      auto A = new long[P];
      foreach (i; 1 .. P) {
        A[i] = readLong();
      }
      auto B = new long[P];
      foreach (i; 1 .. P) {
        B[i] = readLong();
      }
      
      long[] divs;
      foreach (d; 1 .. P - 1) {
        if ((P - 1) % d == 0) {
          divs ~= d;
        }
      }
      long g;
      for (g = 2; ; ++g) {
        bool ok = true;
        foreach (d; divs) {
          long gg = g, gd = 1;
          for (long e = d; e; e >>= 1) {
            if (e & 1) gd = (gd * gg) % P;
            gg = (gg * gg) % P;
          }
          ok = ok && (gd != 1);
        }
        if (ok) {
          break;
        }
      }
      
      auto gs = new long[P - 1];
      gs[0] = 1;
      foreach (i; 1 .. P - 1) {
        gs[i] = (gs[i - 1] * g) % P;
      }
      debug {
        writeln("gs = ", gs);
      }
      
      int fftN;
      for (fftN = 4; fftN < 2 * P; fftN <<= 1) {}
      auto fft = new FFT0(fftN);
      auto a = new long[2 * P];
      auto b = new long[2 * P];
      foreach (i; 0 .. P - 1) {
        a[i] = A[cast(int)(gs[i])];
        b[i] = B[cast(int)(gs[i])];
      }
      const c = fft.convolution(a, b);
      auto ans = new long[P];
      foreach (i; 0 .. 2 * (P - 1)) {
        ans[cast(int)(gs[i % (P - 1)])] += c[i];
      }
      foreach (i; 0 .. P) {
        ans[i] = (ans[i] % MO + MO) % MO;
      }
      foreach (i; 1 .. P) {
        if (i > 1) write(" ");
        write(ans[i]);
      }
      writeln();
    }
  } catch (EOFException e) {
  }
}
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