結果

問題 No.2483 Yet Another Increasing XOR Problem
ユーザー 👑 hos.lyrichos.lyric
提出日時 2023-09-22 21:42:28
言語 D
(dmd 2.106.1)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 4,854 bytes
コンパイル時間 1,554 ms
コンパイル使用メモリ 155,204 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-07-08 12:27:12
合計ジャッジ時間 2,057 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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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
6,944 KB
testcase_02 AC 1 ms
6,940 KB
testcase_03 AC 1 ms
6,944 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 1 ms
6,944 KB
testcase_08 AC 1 ms
6,944 KB
testcase_09 AC 1 ms
6,940 KB
testcase_10 AC 1 ms
6,940 KB
testcase_11 AC 1 ms
6,940 KB
testcase_12 AC 1 ms
6,944 KB
testcase_13 AC 1 ms
6,944 KB
testcase_14 AC 1 ms
6,940 KB
testcase_15 AC 1 ms
6,940 KB
testcase_16 AC 1 ms
6,940 KB
testcase_17 AC 1 ms
6,944 KB
testcase_18 AC 1 ms
6,944 KB
testcase_19 AC 2 ms
6,944 KB
testcase_20 AC 1 ms
6,940 KB
testcase_21 AC 1 ms
6,940 KB
testcase_22 AC 1 ms
6,940 KB
testcase_23 AC 1 ms
6,940 KB
testcase_24 AC 2 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; }

string COLOR(string s = "") { return "\x1b[" ~ s ~ "m"; }

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 = cast(uint)(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 M = readLong;
      
      Mint ans;
      if (M == 1) {
        ans = 1;
      } else if (M == 2) {
        ans = 3;
      } else {
        const E = bsr(M - 1);
        debug {
          writeln("M = ", M, ", E = ", E);
        }
        
        ans += Mint(2)^^(1L<<E) - 1;
        ans += Mint(2)^^((1L<<E) - 1) * (1 - Mint(2)^^(-(M - (1L<<E)))) / (1 - Mint(2)^^-1);
        
        auto ps = new Mint[E + 1];
        auto qs = new Mint[E + 1];
        ps[0] = 2;
        qs[0] = Mint(2).inv;
        foreach (e; 0 .. E) {
          ps[e + 1] = ps[e] * ps[e];
          qs[e + 1] = qs[e] * qs[e];
        }
        auto dp = new Mint[2][E + 1];
        dp[E][0] = 1;
        foreach_reverse (e; 0 .. E) {
          const m = M >> e & 1;
          foreach (s; 0 .. 2) {
            const f = dp[e + 1][s];
            foreach (a; 0 .. 2) foreach (b; 0 .. 2) {
              if (s || (a ^ b) <= m) {
                Mint ff = f;
                if (a) ff *= ps[e];
                if (b) ff *= qs[e];
                dp[e][(s || (a ^ b) < m) ? 1 : 0] += ff;
              }
            }
          }
        }
        ans += Mint(2)^^((1L<<E) - 1) * dp[0][1];
        
        debug {
          Mint brt;
          brt += Mint(2)^^(1L<<E) - 1;
          foreach (b; 0 .. 1L<<E) {
            if (b < M - (1L<<E)) {
              brt += Mint(2)^^((1L<<E) - 1 - b);
            }
          }
          foreach (a; 0 .. 1L<<E) foreach (b; 0 .. 1L<<E) {
            if ((a ^ b) < M - (1L<<E)) {
              brt += Mint(2)^^(a + ((1L<<E) - 1 - b));
            }
          }
          writeln("brt = ", brt);
        }
      }
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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