Avoid silly overflow mistakes taking modulo in C++

Revision en2, by madhur4127, 2018-12-18 08:25:24

TL;DR This article features Modular class which can be conviniently used for modular arithmetic more "naturally".


Recent round featured an interesting problem 1081C - Colorful Bricks (if you plan to solve it, read this later). Combinatoric solution requires you to calculate:

Many contestants failed pretest because of missing modulo operation somewhere in code.


Many contestants use functions like add(ll a, ll b) or mul(ll a , ll b) which makes implementation somewhat clumsy.

I present you an alternate approach using Modular class.

template <int MOD=998'244'353>
struct Modular {
  int value;
  static const int MOD_value = MOD;

  Modular(long long v = 0) { value = v % MOD; if (value < 0) value += MOD;}
  Modular(long long a, long long b) : value(0){ *this += a; *this /= b;}

  Modular& operator+=(Modular const& b) {value += b.value; if (value >= MOD) value -= MOD; return *this;}
  Modular& operator-=(Modular const& b) {value -= b.value; if (value < 0) value += MOD;return *this;}
  Modular& operator*=(Modular const& b) {value = (long long)value * b.value % MOD;return *this;}

  friend Modular mexp(Modular a, long long e) {
    Modular res = 1; while (e) { if (e&1) res *= a; a *= a; e >>= 1; }
    return res;
  friend Modular inverse(Modular a) { return mexp(a, MOD - 2); }

  Modular& operator/=(Modular const& b) { return *this *= inverse(b); }
  friend Modular operator+(Modular a, Modular const b) { return a += b; }
  friend Modular operator-(Modular a, Modular const b) { return a -= b; }
  friend Modular operator-(Modular const a) { return 0 - a; }
  friend Modular operator*(Modular a, Modular const b) { return a *= b; }
  friend Modular operator/(Modular a, Modular const b) { return a /= b; }
  friend std::ostream& operator<<(std::ostream& os, Modular const& a) {return os << a.value;}
  friend bool operator==(Modular const& a, Modular const& b) {return a.value == b.value;}
  friend bool operator!=(Modular const& a, Modular const& b) {return a.value != b.value;}

Using this code can be written more naturally in modular field just like integers. This implementation simplifies usage, for example:

// Chained Multiplication or Successive Simple Multiplication
Modular<998244353> a=1, m=123456789;
a *= m * m * m; // a = 519994069
// Inverse
a=inverse(m) // a=25170271
// fractions
Modular<> frac=(1,2); // frac=1*2^(-1) % 998244353 = 499122177
// Modular exponentiation
Modular<> power(2);
power=mexp(power,500); // power = 616118644

Credits to Jakube and here's the link to original source. Link: Modular.h

Tags implementation, modular arithmetic, c++


  Rev. Lang. By When Δ Comment
en2 English madhur4127 2018-12-18 08:25:24 10 Tiny change: 'just like in **integer field**. This i' -> 'just like **integers**. This i'
en1 English madhur4127 2018-12-17 12:22:51 2938 Initial revision (published)