結果

問題 No.28 末尾最適化
ユーザー te-shte-sh
提出日時 2020-01-23 10:24:26
言語 D
(dmd 2.095.1)
結果
AC  
実行時間 392 ms / 5,000 ms
コード長 4,816 Byte
コンパイル時間 3,345 ms
使用メモリ 7,184 KB
最終ジャッジ日時 2021-04-30 18:18:26
合計ジャッジ時間 4,693 ms
ジャッジサーバーID
(参考情報)
judge10 / judge6
このコードへのチャレンジ(β)

テストケース

テストケース表示
入力 結果 実行時間
使用メモリ
testcase_00 AC 2 ms
3,128 KB
testcase_01 AC 392 ms
7,056 KB
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 #

// URL: https://yukicoder.me/problems/no/28

import std.algorithm, std.array, std.container, std.math, std.range, std.typecons, std.string;

version(unittest) {} else
void main()
{
  int Q; io.getV(Q);

  auto primes = Prime(6);
  alias Factor = primes.Factor;

  auto expo(int x, int p)
  {
    auto e = 0;
    for (; x%p == 0; x /= p) ++e;
    return e;
  }
  
  auto calc()
  {
    int seed, N, K, B; io.getV(seed, N, K, B);

    auto bd = primes.div(B);

    auto xl = new long[](N+1); xl[0] = seed;
    foreach (i; 1..N+1)
      xl[i] = 1 + (xl[i-1]^^2 + xl[i-1]*12345)%100000009;
    auto X = xl.map!"cast(int)a".array;

    auto k = 10^^9;
    foreach (i; 0..bd.length) {
      auto xd = new int[](N+1), s = 0;
      foreach (j; 0..N+1) {
	auto e = expo(X[j], bd[i].prime);
	xd[j] = e;
	s += e;
      }
      xd.sort!"a>b";
      k = min(k, (s-xd[0..N+1-K].sum)/bd[i].exp);
    }

    io.put(k);
  }

  foreach (_; 0..Q) calc();
}

pure T isqrt(T)(T n)
{
  static if (is(T == int)) auto max = 46341;
  else static if (is(T == long)) auto max = 3037000500L;
  auto bs = iota(T(0), max).map!(x => tuple(x, x^^2)).assumeSorted!"a[1]<=b[1]";
  return bs.lowerBound(tuple(0, n)).back[0];
}

pure T icbrt(T)(T n)
{
  static if (is(T == int)) auto max = 1291;
  else static if (is(T == long)) auto max = 2097152L;
  auto bs = iota(T(0), max).map!(x => tuple(x, x^^3)).assumeSorted!"a[1]<=b[1]";
  return bs.lowerBound(tuple(0, n)).back[0];
}

pure T powr(alias pred = "a*b", T, U)(T a, U n, T one)
{
  import std.functional;
  alias predFun = binaryFun!pred;
  if (n == 0) return one;
  auto r = one;
  for (; n > 0; n >>= 1) { if (n&1) r = predFun(r, a); a = predFun(a, a); }
  return r;
}
pure T powr(alias pred = "a*b", T, U)(T a, U n) { return powr!(pred, T, U)(a, n, T(1)); }

pure T extGcd(T)(T a, T b, out T x, out T y)
{
  auto g = a; x = 1; y = 0;
  if (b) { g = extGcd(b, a%b, y, x); y -= a/b*x; }
  return g;
}

struct Prime
{
  import std.bitmanip;
  struct Factor { int prime, exp; }

  const int n;
  @property array() { return primes; }
  alias array this;

  this(int n)
  {
    this.n = n;

    auto sieve = BitArray();
    sieve.length((n+1)/2);
    sieve = ~sieve;

    foreach (p; 1..(n.isqrt-1)/2+1)
      if (sieve[p])
        for (auto q = p*3+1; q < (n+1)/2; q += p*2+1)
          sieve[q] = false;

    primes = sieve.bitsSet.map!(p => cast(int)p*2+1).array;
    primes[0] = 2;
  }

  pure Factor[] div(int x) in { assert(x > 0 && x.isqrt <= n); } do
  {
    Factor[] factors;
    auto t = isqrt(x);
    foreach (p; primes) {
      if (p > t) break;
      auto c = 0;
      for (; x%p == 0; x /= p) ++c;
      if (c > 0) factors ~= Factor(p, c);
      if (x == 1) break;
    }
    if (x > 1) factors ~= [Factor(x, 1)];
    return factors;
  }

  pure int[] divisors(int x) in { assert(x > 0 && x.isqrt <= n); } do
  {
    auto factors = div(x);
    auto r = divisorsProc(factors, 0, 1);
    r.sort();
    return r;
  }

  private
  {
    int[] primes;

    pure int[] divisorsProc(Factor[] factors, int i, int c)
    {
      if (i == factors.length) return [c];
      int[] r;
      foreach (j; 0..factors[i].exp+1)
        r ~= divisorsProc(factors, i+1, c*factors[i].prime^^j);
      return r;
    }
  }
}

auto io = IO!()();
import std.stdio;
struct IO(string floatFormat = "%.10f", string delimiter = " ", alias IN = stdin, alias OUT = stdout)
{
  import std.conv, std.format, std.meta, std.traits;
  alias assignable = hasAssignableElements;

  auto getV(T...)(ref T v) { foreach (ref w; v) get(w); }
  auto getA(T)(size_t n, ref T v) if (assignable!T) { v = new T(n); foreach (ref w; v) get(w); }
  auto getC(T...)(size_t n, ref T v) if (allSatisfy!(assignable, T))
  {
    foreach (ref w; v) w = new typeof(w)(n);
    foreach (i; 0..n) foreach (ref w; v) get(w[i]);
  }
  auto getM(T)(size_t r, size_t c, ref T v) if (assignable!T && assignable!(ElementType!T))
  {
    v = new T(r); foreach (ref w; v) getA(c, w);
  }

  auto put(bool flush = false, T...)(T v)
  {
    foreach (i, w; v) { putA(w); if (i < v.length-1) OUT.write(delimiter); }
    OUT.writeln;
    static if (flush) OUT.flush();
  }
  auto putB(S, T)(bool c, S t, T f) { if (c) put(t); else put(f); }
  auto putRaw(T...)(T v) { OUT.write(v); OUT.writeln; }

  private
  {
    dchar[] buf;
    auto sp = (new dchar[](0)).splitter;
    void nextLine() { IN.readln(buf); sp = buf.splitter; }
    auto get(T)(ref T v) { if (sp.empty) nextLine(); v = sp.front.to!T; sp.popFront(); }

    auto putR(T)(T v)
    {
      auto w = v;
      while (!w.empty) { putA(w.front); w.popFront(); if (!w.empty) OUT.write(delimiter); }
    }
    auto putA(T)(T v)
    {
      static if (isInputRange!T && !isSomeString!T) putR(v);
      else if (isFloatingPoint!T) OUT.write(format(floatFormat, v));
      else OUT.write(v);
    }
  }
}
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