結果

問題 No.1510 Simple Integral
ユーザー 👑 hos.lyrichos.lyric
提出日時 2021-05-15 02:20:52
言語 D
(dmd 2.106.1)
結果
AC  
実行時間 6 ms / 2,000 ms
コード長 4,407 bytes
コンパイル時間 1,784 ms
コンパイル使用メモリ 158,448 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-06-22 11:18:17
合計ジャッジ時間 3,117 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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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 1 ms
6,812 KB
testcase_01 AC 1 ms
6,940 KB
testcase_02 AC 1 ms
6,944 KB
testcase_03 AC 1 ms
6,940 KB
testcase_04 AC 1 ms
6,940 KB
testcase_05 AC 1 ms
6,944 KB
testcase_06 AC 1 ms
6,940 KB
testcase_07 AC 2 ms
6,940 KB
testcase_08 AC 1 ms
6,940 KB
testcase_09 AC 1 ms
6,940 KB
testcase_10 AC 1 ms
6,940 KB
testcase_11 AC 2 ms
6,940 KB
testcase_12 AC 2 ms
6,940 KB
testcase_13 AC 3 ms
6,944 KB
testcase_14 AC 3 ms
6,944 KB
testcase_15 AC 3 ms
6,940 KB
testcase_16 AC 4 ms
6,940 KB
testcase_17 AC 3 ms
6,944 KB
testcase_18 AC 3 ms
6,944 KB
testcase_19 AC 3 ms
6,944 KB
testcase_20 AC 3 ms
6,944 KB
testcase_21 AC 4 ms
6,940 KB
testcase_22 AC 3 ms
6,944 KB
testcase_23 AC 5 ms
6,944 KB
testcase_24 AC 5 ms
6,940 KB
testcase_25 AC 5 ms
6,940 KB
testcase_26 AC 5 ms
6,940 KB
testcase_27 AC 6 ms
6,944 KB
testcase_28 AC 5 ms
6,940 KB
testcase_29 AC 5 ms
6,944 KB
testcase_30 AC 5 ms
6,944 KB
testcase_31 AC 6 ms
6,940 KB
testcase_32 AC 5 ms
6,940 KB
testcase_33 AC 4 ms
6,940 KB
testcase_34 AC 4 ms
6,940 KB
testcase_35 AC 4 ms
6,940 KB
testcase_36 AC 4 ms
6,940 KB
testcase_37 AC 4 ms
6,944 KB
testcase_38 AC 4 ms
6,944 KB
testcase_39 AC 4 ms
6,940 KB
testcase_40 AC 4 ms
6,940 KB
testcase_41 AC 4 ms
6,940 KB
testcase_42 AC 4 ms
6,940 KB
testcase_43 AC 1 ms
6,944 KB
testcase_44 AC 2 ms
6,944 KB
testcase_45 AC 1 ms
6,940 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(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 = 998244353;
alias Mint = ModInt!MO;


void main() {
  try {
    for (; ; ) {
      const N = readInt();
      auto A = new Mint[N];
      foreach (i; 0 .. N) {
        A[i] = readInt();
      }
      A.sort!"a.x < b.x";
      
      Mint ans;
      for (int i, j; i < N; i = j) {
        for (j = i; j < N && A[i] == A[j]; ++j) {}
        const d = j - i;
        /*
          (residue at sqrt(-1) A[i])
          = [(x - sqrt(-1) A[i])^-1] f(x)
          = [y^(d-1)] y^d f(y + sqrt(-1) A[i])
          = (y + sqrt(-1) (2 A[i]))^-1 \prod_{k!=i} (y + sqrt(-1) (A[i] - A[k]))^-1 (y + sqrt(-1) (A[i] + A[k]))^-1
        */
        auto fs = new Mint[d];
        fs[0] = 1;
        /*
          (y - b)^-1
          = -b^-1 y^0 - b^-2 y^1 - b^-3 y^2 - ...
        */
        void mul(Mint b) {
          const invB = b.inv;
          fs[0] = -fs[0] * invB;
          foreach (h; 1 .. d) {
            fs[h] = (fs[h - 1] - fs[h]) * invB;
          }
        }
        foreach (k; 0 .. N) {
          // x - sqrt(-1) A[k]
          if (A[i] != A[k]) {
            mul(A[i] - A[k]);
          }
          // x + sqrt(-1) A[k]
          mul(A[i] + A[k]);
        }
        /*
          [y^(d-1)] \prod (y + sqrt(-1) b)^-1
          = sqrt(-1)^(2N-d) [y^(d-1)] \prod (sqrt(-1) y - b)^-1
          = sqrt(-1)^(2N-1) [y^(d-1)] \prod (y - b)^-1
          
          multiply by (2 pi sqrt(-1))
          (-1)^N [y^(d-1)] \prod (y - b)^-1
        */
        ans += 2 * (-1)^^(N & 1) * fs[d - 1];
      }
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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