結果

問題 No.2995 The Ruler Sequence Concatenation
ユーザー 👑 hos.lyrichos.lyric
提出日時 2024-12-20 04:17:15
言語 D
(dmd 2.106.1)
結果
AC  
実行時間 2 ms / 1,000 ms
コード長 5,278 bytes
コンパイル時間 3,375 ms
コンパイル使用メモリ 152,840 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-12-20 04:17:21
合計ジャッジ時間 2,352 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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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
6,816 KB
testcase_01 AC 1 ms
6,816 KB
testcase_02 AC 1 ms
6,816 KB
testcase_03 AC 2 ms
6,816 KB
testcase_04 AC 2 ms
6,816 KB
testcase_05 AC 1 ms
6,820 KB
testcase_06 AC 2 ms
6,820 KB
testcase_07 AC 1 ms
6,816 KB
testcase_08 AC 2 ms
6,820 KB
testcase_09 AC 1 ms
6,820 KB
testcase_10 AC 1 ms
6,816 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 N = readLong;
      
      Mint ten = 1, now = 0;
      for (int e = 1; ; ++e) {
        const l = 10L^^(e-1);
        const r = min(10L^^e, N + 1);
        if (l >= r) break;
        debug writeln([l, r]);
        
        /*
          \sum[0<i<2^n] (now 10L^^e + l + bsf(i)) a^i
          = \sum[0<=j<n] (now 10L^^e + l + j) a^(2^j)/(1-a^(2^(j+1)))
          
          a^(2^j) has short period ~ 23+119
        */
        const n = r - l;
        const a = ten * 10L^^e;
        const nowe = now * 10L^^e;
        Mint[] bs;
        long[uint] app;
        long j0, j1;
        {
          Mint b = a;
          for (long j = 0; ; ++j) {
            if (b.x in app) {
              j0 = app[b.x];
              j1 = j;
              break;
            }
            bs ~= b;
            app[b.x] = j;
            b = b * b;
          }
        }
        debug writeln("a = ", a, ": ", [j0, j1], " ", bs);
        
        Mint calc(Mint b) {
          return b / (1 - b*b);
        }
        Mint sum;
        foreach (j; 0 .. j0) if (j < n) {
          sum += (nowe + l + j) * calc(bs[j]);
        }
        if (j0 < n) {
          const quo = (n - j0) / (j1 - j0);
          const rem = (n - j0) % (j1 - j0);
          foreach (j; j0 .. j1) {
            const Mint q = quo + ((j - j0 < rem) ? 1 : 0);
            sum += ((nowe + l + j) * q + (j1 - j0) * (q*(q-1)/2)) * calc(bs[j]);
          }
        }
        
        const bb = bs[(n < j0) ? n : (j0 + (n - j0) % (j1 - j0))];
        // (1 - a^(2^n))
        sum *= (1 - bb);
        // fix
        sum /= 10L^^e;
        sum += now;
        
        ten = bb / 10L^^e;
        now = sum;
        debug writeln("ten = ", ten, ", now = ", now);
      }
      
      writeln(now);
      
      debug if (N <= 20) {
        Mint brt;
        void dfs(long n) {
          if (n) {
            dfs(n - 1);
            foreach (c; n.to!string) (brt *= 10) += (c - '0');
            dfs(n - 1);
          }
        }
        dfs(N);
        writeln("brt = ", brt);
        writeln;
        assert(brt == now);
      }
    }
  } catch (EOFException e) {
  }
}
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