結果

問題 No.1510 Simple Integral
ユーザー 👑 hos.lyrichos.lyric
提出日時 2021-05-14 23:10:22
言語 D
(dmd 2.106.1)
結果
AC  
実行時間 7 ms / 2,000 ms
コード長 5,075 bytes
コンパイル時間 1,479 ms
コンパイル使用メモリ 157,772 KB
実行使用メモリ 4,384 KB
最終ジャッジ日時 2023-09-04 12:39:45
合計ジャッジ時間 4,062 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge13
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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
4,380 KB
testcase_01 AC 2 ms
4,380 KB
testcase_02 AC 2 ms
4,384 KB
testcase_03 AC 2 ms
4,380 KB
testcase_04 AC 2 ms
4,376 KB
testcase_05 AC 2 ms
4,376 KB
testcase_06 AC 6 ms
4,376 KB
testcase_07 AC 6 ms
4,376 KB
testcase_08 AC 6 ms
4,376 KB
testcase_09 AC 7 ms
4,380 KB
testcase_10 AC 6 ms
4,380 KB
testcase_11 AC 6 ms
4,376 KB
testcase_12 AC 6 ms
4,376 KB
testcase_13 AC 6 ms
4,380 KB
testcase_14 AC 6 ms
4,376 KB
testcase_15 AC 7 ms
4,380 KB
testcase_16 AC 6 ms
4,376 KB
testcase_17 AC 6 ms
4,380 KB
testcase_18 AC 7 ms
4,376 KB
testcase_19 AC 6 ms
4,380 KB
testcase_20 AC 7 ms
4,376 KB
testcase_21 AC 6 ms
4,380 KB
testcase_22 AC 6 ms
4,380 KB
testcase_23 AC 6 ms
4,380 KB
testcase_24 AC 6 ms
4,380 KB
testcase_25 AC 6 ms
4,376 KB
testcase_26 AC 7 ms
4,380 KB
testcase_27 AC 6 ms
4,380 KB
testcase_28 AC 6 ms
4,376 KB
testcase_29 AC 6 ms
4,380 KB
testcase_30 AC 6 ms
4,376 KB
testcase_31 AC 7 ms
4,380 KB
testcase_32 AC 7 ms
4,380 KB
testcase_33 AC 7 ms
4,376 KB
testcase_34 AC 6 ms
4,380 KB
testcase_35 AC 6 ms
4,376 KB
testcase_36 AC 6 ms
4,380 KB
testcase_37 AC 6 ms
4,380 KB
testcase_38 AC 6 ms
4,376 KB
testcase_39 AC 6 ms
4,376 KB
testcase_40 AC 7 ms
4,380 KB
testcase_41 AC 7 ms
4,376 KB
testcase_42 AC 6 ms
4,376 KB
testcase_43 AC 1 ms
4,380 KB
testcase_44 AC 1 ms
4,380 KB
testcase_45 AC 2 ms
4,376 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";
      
      auto fs = [Mint(1)];
      foreach (i; 0 .. N) {
        auto gs = new Mint[i + 2];
        foreach (j; 0 .. i + 1) {
          gs[j] += fs[j] * A[i]^^2;
          gs[j + 1] += fs[j];
        }
        fs = gs;
      }
      debug {
        writeln("fs = ", fs);
      }
      
      auto b = new Mint[][](N, N + 1);
      b[0][N] = 1;
      for (int i, j; i < N; i = j) {
        auto gs = fs.dup;
        for (j = i; j < N && A[i] == A[j]; ++j) {}
        foreach (k; i .. j) {
          foreach_reverse (l; 1 .. gs.length) {
            gs[l - 1] -= A[i]^^2 * gs[l];
          }
          assert(!gs[0]);
          gs = gs[1 .. $];
          debug {
            writeln(k, ": ", gs);
          }
          foreach (l; 0 .. gs.length) {
            b[l][k] = gs[l];
          }
        }
      }
      
      foreach (h; 0 .. N) {
        foreach (i; h .. N) {
          if (b[i][h]) {
            swap(b[h], b[i]);
            break;
          }
        }
        assert(b[h][h]);
        const r = b[h][h].inv;
        foreach (j; h .. N + 1) {
          b[h][j] *= r;
        }
        foreach (i; h + 1 .. N) {
          const s = b[i][h];
          foreach (j; h .. N + 1) {
            b[i][j] -= s * b[h][j];
          }
        }
      }
      auto cs = new Mint[N];
      foreach_reverse (i; 0 .. N) {
        cs[i] = b[i][N];
        foreach (j; i + 1 .. N) {
          cs[i] -= b[i][j] * cs[j];
        }
      }
      debug {
        writeln("cs = ", cs);
      }
      
      auto coef = new Mint[N + 1];
      coef[1] = 1;
      foreach (l; 1 .. N) {
        coef[l + 1] = coef[l] * (2 * l - 1) / (2 * l);
      }
      debug {
        writeln("coef = ", coef);
      }
      Mint ans;
      for (int i, j; i < N; i = j) {
        for (j = i; j < N && A[i] == A[j]; ++j) {}
        foreach (k; i .. j) {
          const d = k - i + 1;
          ans += cs[k] * coef[d] * A[i]^^(-(2 * d - 1));
        }
      }
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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