有理数クラス

struct frac {
	long long nume, deno;
	frac(long long n = 0, long long d = 1) {
		if (d < 0) nume = -n, deno = -d;
		else nume = n, deno = d;
	}
	void reduce() {
		if (deno < 0) {
			deno *= -1;
			nume *= -1;
		}
		long long g = gcd(nume, deno);
		nume /= g;
		deno /= g;
	}
	frac& operator+=(const frac& other) {
		long long nnume = nume * other.deno + deno * other.nume;
		long long ndeno = deno * other.deno;
		(*this).nume = nnume;
		(*this).deno = ndeno;
		(*this).reduce();
		return *this;
	}
	frac& operator-=(const frac& other) {
		long long nnume = nume * other.deno - deno * other.nume;
		long long ndeno = deno * other.deno;
		(*this).nume = nnume;
		(*this).deno = ndeno;
		(*this).reduce();
		return *this;
	}
	frac& operator*=(const frac& other) {
		long long nnume = nume * other.nume;
		long long ndeno = deno * other.deno;
		(*this).nume = nnume;
		(*this).deno = ndeno;
		(*this).reduce();
		return *this;
	}
	frac& operator/=(const frac& other) {
		long long nnume = nume * other.deno;
		long long ndeno = deno * other.nume;
		(*this).nume = nnume;
		(*this).deno = ndeno;
		(*this).reduce();
		return *this;
	}
	frac& operator=(const frac& other) {
		(*this).nume = other.nume;
		(*this).deno = other.deno;
		(*this).reduce();
		return *this;
	}
	frac operator+(const frac& other) const { return frac(*this) += other; }
	frac operator-(const frac& other) const { return frac(*this) -= other; }
	frac operator*(const frac& other) const { return frac(*this) *= other; }
	frac operator/(const frac& other) const { return frac(*this) /= other; }
	bool operator==(frac other) { return nume * other.deno == other.nume*deno; }
	bool operator!=(frac other) { return nume * other.deno != other.nume*deno; }
	bool operator<(frac other) { return nume * other.deno < other.nume*deno; }
	bool operator>(frac other) { return nume * other.deno > other.nume*deno; }
	friend bool operator==(const frac&x, const frac&y) { return (frac)x == y; }
	friend bool operator!=(const frac&x, const frac&y) { return (frac)x != y; }
	friend bool operator<(const frac&x, const frac&y) { return (frac)x < y; }
	friend bool operator>(const frac&x, const frac&y) { return (frac)x > y; }
	double getDoulbeValue() { return (double)nume / deno; }
	void output() const {
		if (1 == deno)cout << nume << endl;
		else cout << nume << "/" << deno << endl;
	}
};

拡張double

struct ext_double {
	double value;
	const double EPS = 1e-10;
	ext_double(double value) : value(value) {}
	ext_double& operator+=(const ext_double& other) {
		(*this).value += other.value;
		return *this;
	}
	ext_double& operator-=(const ext_double& other) {
		(*this).value -= other.value;
		return *this;
	}
	ext_double& operator*=(const ext_double& other) {
		(*this).value *= other.value;
		return *this;
	}
	ext_double& operator/=(const ext_double& other) {
		(*this).value /= other.value;
		return *this;
	}
	ext_double& operator=(const ext_double& other) {
		(*this).value = other.value;
		return *this;
	}
	ext_double operator+(const ext_double& other) const { return ext_double(*this) += other; }
	ext_double operator-(const ext_double& other) const { return ext_double(*this) -= other; }
	ext_double operator*(const ext_double& other) const { return ext_double(*this) *= other; }
	ext_double operator/(const ext_double& other) const { return ext_double(*this) /= other; }
	bool operator==(ext_double other) { return abs(value - other.value) < EPS; }
	bool operator!=(ext_double other) { return abs(value - other.value) >= EPS; }
	bool operator<(ext_double other) { return value - EPS <= other.value; }
	bool operator<=(ext_double other) { return ((*this) < other) || ((*this) == other); }
	bool operator>(ext_double other) { return other.value - EPS <= value; }
	bool operator>=(ext_double other) { return ((*this) > other) || ((*this) == other); }
	friend bool operator==(const ext_double&x, const ext_double&y) { return (ext_double)x == y; }
	friend bool operator!=(const ext_double&x, const ext_double&y) { return (ext_double)x != y; }
	friend bool operator<(const ext_double&x, const ext_double&y) { return (ext_double)x < y; }
	friend bool operator<=(const ext_double&x, const ext_double&y) { return (ext_double)x <= y; }
	friend bool operator>(const ext_double&x, const ext_double&y) { return (ext_double)x > y; }
	friend bool operator>=(const ext_double&x, const ext_double&y) { return (ext_double)x >= y; }
};