結果

問題 No.1193 Penguin Sequence
コンテスト
ユーザー hos.lyric
提出日時 2020-08-22 13:40:35
言語 D
(dmd 2.109.1)
結果
AC  
実行時間 149 ms / 2,000 ms
コード長 5,547 bytes
コンパイル時間 1,675 ms
コンパイル使用メモリ 162,568 KB
実行使用メモリ 17,976 KB
最終ジャッジ日時 2024-06-22 08:13:04
合計ジャッジ時間 8,554 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 38
権限があれば一括ダウンロードができます

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;


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 (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);
  }
}


void bAdd(T)(T[] bit, int pos, T val)
in {
  assert(0 <= pos && pos < bit.length, "bAdd: 0 <= pos < |bit| must hold");
}
do {
  for (int x = pos; x < bit.length; x |= x + 1) {
    bit[x] += val;
  }
}

// sum of [0, pos)
T bSum(T)(T[] bit, int pos)
in {
  assert(0 <= pos && pos <= bit.length, "bSum: 0 <= pos <= |bit| must hold");
}
do {
  T ret = 0;
  for (int x = pos - 1; x >= 0; x = (x & (x + 1)) - 1) {
    ret += bit[x];
  }
  return ret;
}


void main() {
  prepare;
  
  try {
    for (; ; ) {
      const N = readInt();
      auto A = new int[N];
      foreach (i; 0 .. N) {
        A[i] = readInt();
      }
      
      auto as = A.dup;
      as = as.sort.uniq.array;
      const asLen = cast(int)(as.length);
      auto bit = new int[asLen];
      long num0, num1;
      foreach (i; 0 .. N) {
        const pos = as.lowerBound(A[i]);
        num0 += bit.bSum(pos);
        num1 += i - bit.bSum(pos + 1);
        bit.bAdd(pos, 1);
      }
      debug {
        writeln("num0 = ", num0);
        writeln("num1 = ", num1);
      }
      
      Mint ans;
      
      Mint prod = 1;
      foreach (i; 1 .. N + 1) {
        prod *= binom(N, i);
      }
      
      // i
      Mint sum1;
      foreach (i; 2 .. N + 1) {
        sum1 += Mint(i) * Mint(i - 1) * inv[N] * inv[N - 1];
      }
      sum1 *= prod;
      ans += num1 * sum1;
      
      // i < j
      Mint sum2;
      foreach (i; 1 .. N + 1) {
        sum2 += Mint(i) * inv[N];
      }
      sum2 = sum2^^2;
      foreach (i; 1 .. N + 1) {
        sum2 -= (Mint(i) * inv[N])^^2;
      }
      sum2 /= 2;
      sum2 *= prod;
      ans += (num0 + num1) * sum2;
      debug {
        Mint brt;
        foreach (i; 1 .. N + 1) foreach (j; i + 1 .. N + 1) {
          Mint tmp = binom(N - 1, i - 1) * binom(N - 1, j - 1);
          foreach (k; 1 .. N + 1) {
            if (k != i && k != j) {
              tmp *= binom(N, k);
            }
          }
          brt += tmp;
        }
        writeln("brt = ", brt, ", sum2 = ", sum2);
      }
      
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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