#448857 (D) No.502 階乗を計算するだけ

• 問題: No.502 階乗を計算するだけ
• ユーザー: Ark
• 提出日時: 2020-03-25 02:42:51
• 言語: D (dmd 2.109.1)
• 結果: RE
• 実行時間: -
• コード長: 8,448 bytes
• コンパイル時間: 1,870 ms
• コンパイル使用メモリ: 174,004 KB
• 実行使用メモリ: 19,868 KB
• 最終ジャッジ日時: 2024-06-22 05:47:54
• 合計ジャッジ時間: 3,654 ms
• ジャッジサーバーID （参考情報）: judge5 / judge2

ファイルパターン	結果
other	AC * 42 RE * 10

ソースコード

import std.stdio;
import std.string;
import std.format;
import std.conv;
import std.typecons;
import std.algorithm;
import std.functional;
import std.bigint;
import std.numeric;
import std.array;
import std.math;
import std.range;
import std.container;
import std.concurrency;
import std.traits;
import std.uni;
import std.regex;
import core.bitop : popcnt;
alias Generator = std.concurrency.Generator;

enum long INF = long.max/5;

void main() {
  long n;
  scanln(n);
  ModNum.fact(n).writeln;
}

enum long MOD = 10L^^9+7;
alias ModNum = ModNumber!(long, MOD);

struct ModNumber(T, T mod) if (__traits(isIntegral, T)) {
  private enum FACT_MAX = 2000010;

  T value;
  this(T value) {
    this.value = value;
    this.value %= mod;
    this.value += mod;
    this.value %= mod;
  }

  ModNumber opAssign(T value) {
    return this = ModNumber(value);
  }

  ModNumber opBinary(string op)(ModNumber that) if (op=="+" || op=="-" || op=="*") {
    return ModNumber(mixin("this.value "~op~" that.value"));
  }
  ModNumber opBinary(string op)(T that) if (op=="+" || op=="-" || op=="*") {
    return ModNumber(mixin("this.value "~op~" that"));
  }
  ModNumber opBinaryRight(string op)(T that) if (op=="+" || op=="-" || op=="*") {
    return ModNumber(mixin("that "~op~" this.value"));
  }

  ModNumber opBinary(string op)(ModNumber that) if (op == "/") {
    return this*getReciprocal(that);
  }
  ModNumber opBinary(string op)(T that) if (op == "/") {
    return this*getReciprocal(ModNumber(that));
  }
  ModNumber opBinaryRight(string op)(T that) if (op == "/") {
    return ModNumber(that)*getReciprocal(this);
  }

  ModNumber opBinary(string op)(ModNumber that) if (op == "^^") {
    return ModNumber(modPow(this.value, that.value));
  }
  ModNumber opBinary(string op)(T that) if (op == "^^") {
    return ModNumber(modPow(this.value, that));
  }
  ModNumber opBinaryRight(string op)(T that) if (op == "^^") {
    return ModNumber(modPow(that, this.value));
  }

  void opOpAssign(string op)(ModNumber that) if (op=="+" || op=="-" || op=="*" || op=="/") {
    this = mixin("this" ~op~ "that");
  }
  void opOpAssign(string op)(T that) if (op=="+" || op=="-" || op=="*" || op=="/") {
    this = mixin("this" ~op~ "that");
  }

  ModNumber getReciprocal(ModNumber x) in {
    debug assert(isPrime(mod));
  } body {
    return ModNumber(modPow(x.value, mod-2));
  }
  T modPow(T base, T power)  {
    T result = 1;
    for (; power > 0; power >>= 1) {
      if (power & 1) {
        result = (result * base) % mod;
      }
      base = base*base % mod;
    }
    return result;
  }

  static bool isPrime(T n) {
    if (n<2) {
      return false;
    } else if (n==2) {
      return true;
    } else if (n%2==0) {
      return false;
    } else {
      for(T i=3; i*i<=n; i+=2) {
        if (n%i==0) return false;
      }
      return true;
    }
  }

  // n! : 階乗
  static ModNumber fact(T n) {
    if (n >= mod) {
      return ModNumber(0);
    }

    assert(0<=n && n<=FACT_MAX);
    static ModNumber[] memo;
    if (memo.length == 0) {
      memo = new ModNumber[FACT_MAX+1];
      memo[0] = ModNumber(1);
      assert(memo[0] != ModNumber.init);
    }
    foreach_reverse(i; 0..n+1) {
      if (memo[i] != ModNumber.init) {
        foreach(j; i+1..n+1) {
          memo[j] = memo[j-1] * j;
        }
        return memo[n];
      }
    }
    assert(false);
  }

  // 1/(n!) : 階乗の逆元 (逆元テーブルを用いる)
  static ModNumber invFact(T n) {
    assert(0<=n && n<=FACT_MAX);
    static ModNumber inverse(T n) {
      assert(1<=n && n<=FACT_MAX);
      static ModNumber[] memo;
      if (memo.length == 0) {
        memo = new ModNumber[FACT_MAX+1];
      }
      if (memo[n] != ModNumber.init) {
        return memo[n];
      } else {
        return memo[n] = n==1 ? ModNumber(1) : ModNumber(-mod/n)*inverse(mod%n);
      }
    }
    static ModNumber[] memo;
    if (memo.length == 0) {
      memo = new ModNumber[FACT_MAX+1];
      memo[0] = 1;
      assert(memo[0] != ModNumber.init);
    }
    foreach_reverse(i; 0..n+1) {
      if (memo[i] != ModNumber.init) {
        foreach(j; i+1..n+1) {
          memo[j] = memo[j-1] * inverse(j);
        }
        return memo[n];
      }
    }
    assert(false);
  }

  // {}_n C_r: 組合せ
  static ModNumber comb(T n, T r) {
    import std.functional : memoize;
    if (r<0 || r>n) return ModNumber(0);
    if (r*2 > n) return comb(n, n-r);

    if (n<=FACT_MAX) {
      return fact(n) * invFact(r) * invFact(n-r); // 逆元テーブルを使用する
      // return fact(n) / fact(r) / fact(n-r); // 逆元テーブルを使用しない
    }

    // n!/r!
    static ModNumber reverseFact(T n, T r) {
      T t = n - r;
      assert(0<=t && t<=FACT_MAX);
      static ModNumber[][T] memo;
      if (n !in memo) {
        memo[n] = new ModNumber[FACT_MAX];
        memo[n][0] = 1;
        assert(memo[n][0] != ModNumber.init);
      }
      auto xs = memo[n];
      foreach_reverse(i; 0..t+1) {
        if (xs[i] != ModNumber.init) {
          foreach(j; i+1..t+1) {
            xs[j] = xs[j-1] * (n - j + 1);
          }
          return xs[t];
        }
      }
      assert(false);
    }

    return reverseFact(n, n-r) / fact(r);
  }

  // {}_n H_r: 重複組合せ (Homogeneous Combination)
  static ModNumber hComb(T n, T r) {
    return comb(n+r-1, r);
  }

  string toString() const {
    import std.conv : to;
    return this.value.to!string;
  }

  invariant {
    assert(this.value>=0);
    assert(this.value<mod);
  }
}

@safe pure unittest {
  enum p = 10L^^9 + 7;
  alias ModNum = ModNumber!(long, p);

  ModNum x;
  assert(x.value == 0);
  x = 10;
  assert(x.value == 10);
  x = -10;
  assert(x.value == -10 + p);
  x = 10L^^9 + 7 + 10;
  assert(x.value == 10);
}

@safe pure unittest {
  enum p = 10L^^9 + 7;
  alias ModNum = ModNumber!(long, p);

  ModNum x = 10;
  ModNum y = p - 5;
  assert(x + y == ModNum(5));
  assert(x - y == ModNum(15));
  assert(x * y == ModNum(10*p - 50));

  ModNum z = x / y;
  assert(z * y == x);
}


// ----------------------------------------------


void times(alias fun)(long n) {
  // n.iota.each!(i => fun());
  foreach(i; 0..n) fun();
}
auto rep(alias fun, T = typeof(fun()))(long n) {
  // return n.iota.map!(i => fun()).array;
  T[] res = new T[n];
  foreach(ref e; res) e = fun();
  return res;
}

T ceil(T)(T x, T y) if (isIntegral!T || is(T == BigInt)) {
  // `(x+y-1)/y` will only work for positive numbers ...
  T t = x / y;
  if (y > 0 && t * y < x) t++;
  if (y < 0 && t * y > x) t++;
  return t;
}

T floor(T)(T x, T y) if (isIntegral!T || is(T == BigInt)) {
  T t = x / y;
  if (y > 0 && t * y > x) t--;
  if (y < 0 && t * y < x) t--;
  return t;
}

ref T ch(alias fun, T, S...)(ref T lhs, S rhs) {
  return lhs = fun(lhs, rhs);
}
unittest {
  long x = 1000;
  x.ch!min(2000);
  assert(x == 1000);
  x.ch!min(3, 2, 1);
  assert(x == 1);
  x.ch!max(100).ch!min(1000); // clamp
  assert(x == 100);
  x.ch!max(0).ch!min(10); // clamp
  assert(x == 10);
}

mixin template Constructor() {
  import std.traits : FieldNameTuple;
  this(Args...)(Args args) {
    // static foreach(i, v; args) {
    foreach(i, v; args) {
      mixin("this." ~ FieldNameTuple!(typeof(this))[i]) = v;
    }
  }
}

void scanln(Args...)(auto ref Args args) {
  enum sep = " ";
  enum n = Args.length;
  enum fmt = n.rep!(()=>"%s").join(sep);

  string line = readln.chomp;
  static if (__VERSION__ >= 2074) {
    line.formattedRead!fmt(args);
  } else {
    enum argsTemp = n.iota.map!(
      i => "&args[%d]".format(i)
    ).join(", ");
    mixin(
      "line.formattedRead(fmt, " ~ argsTemp ~ ");"
    );
  }
}

// fold was added in D 2.071.0
static if (__VERSION__ < 2071) {
  template fold(fun...) if (fun.length >= 1) {
    auto fold(R, S...)(R r, S seed) {
      static if (S.length < 2) {
        return reduce!fun(seed, r);
      } else {
        return reduce!fun(tuple(seed), r);
      }
    }
  }
}

// popcnt with ulongs was added in D 2.071.0
static if (__VERSION__ < 2071) {
  ulong popcnt(ulong x) {
    x = (x & 0x5555555555555555L) + (x>> 1 & 0x5555555555555555L);
    x = (x & 0x3333333333333333L) + (x>> 2 & 0x3333333333333333L);
    x = (x & 0x0f0f0f0f0f0f0f0fL) + (x>> 4 & 0x0f0f0f0f0f0f0f0fL);
    x = (x & 0x00ff00ff00ff00ffL) + (x>> 8 & 0x00ff00ff00ff00ffL);
    x = (x & 0x0000ffff0000ffffL) + (x>>16 & 0x0000ffff0000ffffL);
    x = (x & 0x00000000ffffffffL) + (x>>32 & 0x00000000ffffffffL);
    return x;
  }
}