結果

問題 No.1758 Lazy Segment Tree...?
ユーザー 👑 hos.lyrichos.lyric
提出日時 2021-11-20 16:09:50
言語 D
(dmd 2.107.1)
結果
AC  
実行時間 549 ms / 8,000 ms
コード長 5,718 bytes
コンパイル時間 2,023 ms
コンパイル使用メモリ 154,764 KB
実行使用メモリ 4,380 KB
最終ジャッジ日時 2023-09-04 15:04:45
合計ジャッジ時間 11,152 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge12
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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
4,376 KB
testcase_01 AC 2 ms
4,380 KB
testcase_02 AC 4 ms
4,376 KB
testcase_03 AC 1 ms
4,380 KB
testcase_04 AC 2 ms
4,380 KB
testcase_05 AC 1 ms
4,380 KB
testcase_06 AC 1 ms
4,376 KB
testcase_07 AC 3 ms
4,380 KB
testcase_08 AC 3 ms
4,376 KB
testcase_09 AC 6 ms
4,380 KB
testcase_10 AC 4 ms
4,380 KB
testcase_11 AC 5 ms
4,376 KB
testcase_12 AC 4 ms
4,376 KB
testcase_13 AC 5 ms
4,380 KB
testcase_14 AC 3 ms
4,380 KB
testcase_15 AC 4 ms
4,376 KB
testcase_16 AC 4 ms
4,380 KB
testcase_17 AC 6 ms
4,376 KB
testcase_18 AC 4 ms
4,380 KB
testcase_19 AC 5 ms
4,380 KB
testcase_20 AC 4 ms
4,380 KB
testcase_21 AC 348 ms
4,376 KB
testcase_22 AC 337 ms
4,376 KB
testcase_23 AC 412 ms
4,380 KB
testcase_24 AC 364 ms
4,376 KB
testcase_25 AC 295 ms
4,380 KB
testcase_26 AC 401 ms
4,380 KB
testcase_27 AC 286 ms
4,380 KB
testcase_28 AC 490 ms
4,376 KB
testcase_29 AC 394 ms
4,376 KB
testcase_30 AC 524 ms
4,376 KB
testcase_31 AC 308 ms
4,376 KB
testcase_32 AC 421 ms
4,376 KB
testcase_33 AC 406 ms
4,380 KB
testcase_34 AC 392 ms
4,376 KB
testcase_35 AC 196 ms
4,376 KB
testcase_36 AC 549 ms
4,376 KB
testcase_37 AC 526 ms
4,376 KB
testcase_38 AC 476 ms
4,380 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(uint M_) {
  import std.conv : to;
  alias M = M_;
  uint x;
  this(ModInt a) { x = a.x; }
  this(uint x_) { x = x_ % M; }
  this(ulong x_) { x = x_ % M; }
  this(int x_) { x = ((x_ %= cast(int)(M)) < 0) ? (x_ + cast(int)(M)) : x_; }
  this(long x_) { x = cast(uint)(((x_ %= cast(long)(M)) < 0) ? (x_ + cast(long)(M)) : x_); }
  ref ModInt opAssign(T)(inout(T) a) if (is(T == uint) || is(T == ulong) || is(T == int) || is(T == long)) { return this = ModInt(a); }
  ref ModInt opOpAssign(string op, T)(T a) {
    static if (is(T == ModInt)) {
      static if (op == "+") { x = ((x += a.x) >= M) ? (x - M) : x; }
      else static if (op == "-") { x = ((x -= a.x) >= M) ? (x + M) : x; }
      else static if (op == "*") { x = cast(uint)((cast(ulong)(x) * a.x) % M); }
      else static if (op == "/") { this *= a.inv(); }
      else static assert(false);
      return this;
    } else static if (op == "^^") {
      if (a < 0) return this = inv()^^(-a);
      ModInt b = this, c = 1U;
      for (long e = a; e; e >>= 1) { if (e & 1) c *= b; b *= b; }
      return this = c;
    } else {
      return mixin("this " ~ op ~ "= ModInt(a)");
    }
  }
  ModInt inv() const {
    uint a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const q = a / b; const c = a - q * b; a = b; b = c; const w = y - cast(int)(q) * z; y = z; z = w; }
    assert(a == 1); return ModInt(y);
  }
  ModInt opUnary(string op)() const {
    static if (op == "+") { return this; }
    else static if (op == "-") { ModInt a; a.x = x ? (M - x) : 0U; return a; }
    else static assert(false);
  }
  ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); }
  ModInt opBinaryRight(string op, T)(T a) const { return mixin("ModInt(a) " ~ op ~ "= this"); }
  bool opCast(T: bool)() const { return (x != 0U); }
  string toString() const { return x.to!string; }
}

enum MO = 998244353;
alias Mint = ModInt!MO;


void main() {
  try {
    for (; ; ) {
      const N = readInt();
      const Q = readInt();
      
      Mint[4] anss;
      
      // 0: 1
      anss[0] = Q;
      anss[0] *= Mint(-1 + N) * Mint(2 + N) / 24;
      
      // 1: (2 i + 2 i^2 - n - 2 i n + n^2)
      foreach (i; 0 .. N) {
        Mint q = 2 * i + 2 * Mint(i)^^2 - N - 2 * Mint(i) * Mint(N) + Mint(N)^^2;
        q /= Mint(N) * Mint(N + 1);
        Mint tmp = (q.x == 1) ? Mint(Q) : ((1 - q^^Q) / (1 - q));
        tmp *= Mint(1 + i) * Mint(i - N) * Mint(1 + i - N) / (2 * Mint(N) * Mint(1 + N));
        anss[1] += tmp;
      }
      
      // 2: (2 j + 2 j^2 - n - 2 j n + n^2)
      foreach (j; 0 .. N) {
        Mint q = 2 * j + 2 * Mint(j)^^2 - N - 2 * Mint(j) * Mint(N) + Mint(N)^^2;
        q /= Mint(N) * Mint(N + 1);
        Mint tmp = (q.x == 1) ? Mint(Q) : ((1 - q^^Q) / (1 - q));
        tmp *= -Mint(j) * Mint(1 + j) * Mint(j - N) / (2 * Mint(N) * Mint(1 + N));
        anss[2] += tmp;
      }
      
      // 3: (2 (j - i)^2 + (1 + n) (2 i - 2 j + n))
      foreach (d; 1 .. N) {
        Mint q = 2 * Mint(d)^^2 + Mint(1 + N) * Mint(-2 * d + N);
        q /= Mint(N) * Mint(N + 1);
        Mint tmp = (q.x == 1) ? Mint(Q) : ((1 - q^^Q) / (1 - q));
        tmp *= Mint(-d + N) * Mint(1 - d + N) * Mint(2 - d + N) / (6 * Mint(N) * Mint(1 + N));
        anss[3] += tmp;
      }
      
      foreach (s; 0 .. 4) {
        anss[s] /= 4;
      }
      
      Mint ans = (anss[0] + anss[1] - anss[2] - anss[3]);
      ans *= (Mint(N) * Mint(N + 1))^^Q;
      debug {
        writeln("anss = ", anss);
      }
      writeln(ans);
      
      debug {
        if (N <= 10) {
          Mint[4] brts;
          foreach (i; 0 .. N) foreach (j; i + 1 .. N) {
            Mint[4] ps, qs;
            ps[1] = Mint(i + 1) * Mint(j - i);
            ps[3] = Mint(i + 1) * Mint(N - j);
            ps[2] = Mint(j - i) * Mint(N - j);
            ps[0] = Mint(N) * Mint(N + 1) - ps[1] - ps[2] - ps[3];
            foreach (s; 0 .. 4) {
              ps[s] /= Mint(N) * Mint(N + 1);
            }
            foreach (s; 0 .. 4) foreach (t; 0 .. 4) {
              qs[s] += (-1)^^popcnt(s & t) * ps[t];
            }
            foreach (s; 0 .. 4) {
              qs[s] = (qs[s].x == 1) ? Mint(Q) : ((1 - qs[s]^^Q) / (1 - qs[s]));
            }
            foreach (s; 0 .. 4) {
              brts[s] += ps[3] * qs[s] / 4;
            }
          }
          Mint brt = (brts[0] + brts[1] - brts[2] - brts[3]);
          brt *= (Mint(N) * Mint(N + 1))^^Q;
          writeln("brts = ", brts, ", brt = ", brt);
        }
      }
    }
  } catch (EOFException e) {
  }
}
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