高精度封装类（重载运算符版）

蛟龙_wangyanxi

2026-08-07 22:17:05

发布于：广东

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#include <bits/stdc++.h>
#define ll long long
#define ld long double
using namespace std;
const ll MAXN = 1e6 + 5;

struct Big {
	int a[MAXN];
	bool neg;
	Big() {
		memset(a, 0, sizeof(a));
		a[0] = 1;
		neg = false;
	}
	Big(const Big &o) {
		memcpy(a, o.a, sizeof(a));
		neg = o.neg;
	}
	Big(const string &s) {
		memset(a, 0, sizeof(a));
		a[0] = 1;
		neg = false;
		ll st = 0;
		if (s[0] == '-') {
			neg = true;
			st = 1;
		} else if (s[0] == '+') {
			st = 1;
		}
		a[0] = s.size() - st;
		if (a[0] == 0) {
			a[0] = 1;
			a[1] = 0;
			neg = false;
			return;
		}
		for (ll i = 0; i < a[0]; i++) {
			a[a[0] - i] = s[st + i] - '0';
		}
		while (a[0] > 1 && !a[a[0]]) {
			a[0]--;
		}
		if (a[0] == 1 && a[1] == 0) {
			neg = false;
		}
	}
	Big(ll num) {
		memset(a, 0, sizeof(a));
		neg = false;
		if (num < 0) {
			neg = true;
			num = -num;
		}
		if (num == 0) {
			a[0] = 1;
			a[1] = 0;
			return;
		}
		a[0] = 0;
		while (num) {
			a[++a[0]] = num % 10;
			num /= 10;
		}
	}
	inline Big& operator = (const Big &o) {
		if (this != &o) {
			memcpy(a, o.a, sizeof(a));
			neg = o.neg;
		}
		return *this;
	}
	static inline ll abscmp(const Big &x, const Big &y) {
		if (x.a[0] != y.a[0]) {
			return x.a[0] > y.a[0] ? 1 : -1;
		}
		for (ll i = x.a[0]; i >= 1; i--) {
			if (x.a[i] != y.a[i]) {
				return x.a[i] > y.a[i] ? 1 : -1;
			}
		}
		return 0;
	}
	inline Big abs() const {
		Big res = *this;
		res.neg = false;
		return res;
	}
	static inline Big abs_add(const Big &x, const Big &y) {
		Big res;
		res.a[0] = max(x.a[0], y.a[0]);
		ll c = 0;
		for (ll i = 1; i <= res.a[0]; i++) {
			ll sum = c + x.a[i] + y.a[i];
			c = sum / 10;
			res.a[i] = sum % 10;
		}
		while (c) {
			res.a[++res.a[0]] = c % 10;
			c /= 10;
		}
		return res;
	}
	static inline Big abs_sub(const Big &x, const Big &y) {
		Big res;
		if (abscmp(x, y) < 0) {
			res.a[0] = y.a[0];
			ll b = 0;
			for (ll i = 1; i <= res.a[0]; i++) {
				ll d = y.a[i] - b - x.a[i];
				if (d < 0) {
					d += 10;
					b = 1;
				} else {
					b = 0;
				}
				res.a[i] = d;
			}
		} else {
			res.a[0] = x.a[0];
			ll b = 0;
			for (ll i = 1; i <= res.a[0]; i++) {
				ll d = x.a[i] - b - y.a[i];
				if (d < 0) {
					d += 10;
					b = 1;
				} else {
					b = 0;
				}
				res.a[i] = d;
			}
		}
		while (res.a[0] > 1 && !res.a[res.a[0]]) {
			res.a[0]--;
		}
		if (res.a[0] == 1 && res.a[1] == 0) {
			res.neg = false;
		}
		return res;
	}
	inline Big operator + (const Big &o) const {
		if (neg == o.neg) {
			Big res = abs_add(*this, o);
			res.neg = neg;
			return res;
		} else {
			Big res = abs_sub(*this, o);
			if (abscmp(*this, o) < 0) {
				res.neg = o.neg;
			} else {
				res.neg = neg;
			}
			return res;
		}
	}
	inline Big& operator += (const Big &o) {
		*this = *this + o;
		return *this;
	}
	inline Big operator - (const Big &o) const {
		Big tmp = o;
		tmp.neg = !tmp.neg;
		return *this + tmp;
	}
	inline Big& operator -= (const Big &o) {
		*this = *this - o;
		return *this;
	}
	inline Big abs_mul(const Big &o) const {
		Big res;
		res.a[0] = a[0] + o.a[0] + 1;
		for (ll i = 1; i <= a[0]; i++) {
			for (ll j = 1; j <= o.a[0]; j++) {
				res.a[i + j - 1] += a[i] * o.a[j];
			}
		}
		for (ll i = 1; i < res.a[0]; i++) {
			if (res.a[i] >= 10) {
				res.a[i + 1] += res.a[i] / 10;
				res.a[i] %= 10;
			}
		}
		while (res.a[0] > 1 && !res.a[res.a[0]]) {
			res.a[0]--;
		}
		return res;
	}
	inline Big operator * (const Big &o) const {
		Big res = abs_mul(o);
		res.neg = (neg != o.neg);
		if (res.a[0] == 1 && res.a[1] == 0) {
			res.neg = false;
		}
		return res;
	}
	inline Big& operator *= (const Big &o) {
		*this = *this * o;
		return *this;
	}
	inline Big operator * (const ll &k) const {
		Big res;
		if (k == 0) {
			res.a[0] = 1;
			res.a[1] = 0;
			res.neg = false;
			return res;
		}
		ll kk = k;
		if (kk < 0) {
			kk = -kk;
			res.neg = !neg;
		} else {
			res.neg = neg;
		}
		res.a[0] = a[0];
		ll g = 0;
		for (ll i = 1; i <= a[0]; i++) {
			ll sum = g + a[i] * kk;
			res.a[i] = sum % 10;
			g = sum / 10;
		}
		while (g) {
			res.a[++res.a[0]] = g % 10;
			g /= 10;
		}
		if (res.a[0] == 1 && res.a[1] == 0) {
			res.neg = false;
		}
		return res;
	}
	inline Big& operator *= (const ll &k) {
		*this = *this * k;
		return *this;
	}
	inline Big operator / (const ll &k) const {
		if (k == 0) {
			throw "Division by zero";
		}
		Big res;
		ll kk = k;
		if (kk < 0) {
			kk = -kk;
			res.neg = !neg;
		} else {
			res.neg = neg;
		}
		res.a[0] = a[0];
		ll r = 0;
		for (ll i = a[0]; i >= 1; i--) {
			ll cur = r * 10 + a[i];
			res.a[i] = cur / kk;
			r = cur % kk;
		}
		while (res.a[0] > 1 && !res.a[res.a[0]]) {
			res.a[0]--;
		}
		if (res.a[0] == 1 && res.a[1] == 0) {
			res.neg = false;
		}
		return res;
	}
	inline Big& operator /= (const ll &k) {
		*this = *this / k;
		return *this;
	}
	inline ll operator % (const ll &k) const {
		if (k == 0) {
			throw "Modulo by zero";
		}
		ll kk = k < 0 ? -k : k;
		ll r = 0;
		for (ll i = a[0]; i >= 1; i--) {
			r = (r * 10 + a[i]) % kk;
		}
		return neg ? -r : r;
	}
	inline Big operator / (const Big &o) const {
		if (o.a[0] == 1 && o.a[1] == 0) {
			throw "Division by zero";
		}
		if (abscmp(*this, o) < 0) {
			return Big();
		}
		Big res;
		res.neg = (neg != o.neg);
		Big rem;
		for (ll i = a[0]; i >= 1; i--) {
			for (ll j = rem.a[0]; j >= 1; j--) {
				rem.a[j + 1] = rem.a[j];
			}
			rem.a[1] = a[i];
			if (rem.a[rem.a[0] + 1]) {
				rem.a[0]++;
			}
			ll l = 0, r = 9, mid, ans = 0;
			while (l <= r) {
				mid = (l + r) >> 1;
				Big tmp = o.abs() * mid;
				if (abscmp(tmp, rem.abs()) <= 0) {
					ans = mid;
					l = mid + 1;
				} else {
					r = mid - 1;
				}
			}
			res.a[i] = ans;
			Big tmp = o.abs() * ans;
			rem = rem.abs() - tmp;
		}
		while (res.a[0] > 1 && !res.a[res.a[0]]) {
			res.a[0]--;
		}
		if (res.a[0] == 1 && res.a[1] == 0) {
			res.neg = false;
		}
		return res;
	}
	inline Big& operator /= (const Big &o) {
		*this = *this / o;
		return *this;
	}
	inline Big operator % (const Big &o) const {
		if (o.a[0] == 1 && o.a[1] == 0) {
			throw "Modulo by zero";
		}
		if (abscmp(*this, o) < 0) {
			return *this;
		}
		Big rem;
		for (ll i = a[0]; i >= 1; i--) {
			for (ll j = rem.a[0]; j >= 1; j--) {
				rem.a[j + 1] = rem.a[j];
			}
			rem.a[1] = a[i];
			if (rem.a[rem.a[0] + 1]) {
				rem.a[0]++;
			}
			ll l = 0, r = 9, mid, ans = 0;
			while (l <= r) {
				mid = (l + r) >> 1;
				Big tmp = o.abs() * mid;
				if (abscmp(tmp, rem.abs()) <= 0) {
					ans = mid;
					l = mid + 1;
				} else {
					r = mid - 1;
				}
			}
			Big tmp = o.abs() * ans;
			rem = rem.abs() - tmp;
		}
		rem.neg = neg;
		if (rem.a[0] == 1 && rem.a[1] == 0) {
			rem.neg = false;
		}
		return rem;
	}
	inline Big& operator %= (const Big &o) {
		*this = *this % o;
		return *this;
	}
	inline Big pow(ll n) const {
		if (n == 0) {
			return Big("1");
		}
		if (n < 0) {
			throw "Negative exponent not supported";
		}
		Big base = this->abs();
		Big res("1");
		while (n) {
			if (n & 1) {
				res = res * base;
			}
			base = base * base;
			n >>= 1;
		}
		if (neg && (n & 1)) {
			res.neg = true;
		}
		return res;
	}
	inline Big sqrt(ll n = 2) const {
		if (n < 1) {
			throw "Root index must be positive";
		}
		if (neg) {
			throw "Cannot take root of negative number";
		}
		if (n == 1) {
			return *this;
		}
		Big l("1"), r = *this, mid, pow_mid;
		while (abscmp(l, r) <= 0) {
			mid = (l + r) / 2;
			pow_mid = mid.pow(n);
			if (abscmp(pow_mid, *this) == 0) {
				return mid;
			} else if (abscmp(pow_mid, *this) < 0) {
				l = mid + 1;
			} else {
				r = mid - 1;
			}
		}
		return r;
	}
	inline Big shl(ll k) const {
		if (k < 0) return shr(-k);
		if (a[0] == 1 && a[1] == 0) return *this;
		Big res = *this;
		for (ll i = res.a[0]; i >= 1; i--) {
			res.a[i + k] = res.a[i];
		}
		for (ll i = 1; i <= k; i++) {
			res.a[i] = 0;
		}
		res.a[0] += k;
		return res;
	}
	inline Big shr(ll k) const {
		if (k < 0) return shl(-k);
		if (k >= a[0]) return Big("0");
		Big res = *this;
		for (ll i = 1; i <= res.a[0] - k; i++) {
			res.a[i] = res.a[i + k];
		}
		res.a[0] -= k;
		while (res.a[0] > 1 && !res.a[res.a[0]]) {
			res.a[0]--;
		}
		return res;
	}
	inline bool operator == (const Big &o) const {
		if (neg != o.neg) return false;
		if (a[0] != o.a[0]) return false;
		for (ll i = 1; i <= a[0]; i++) {
			if (a[i] != o.a[i]) return false;
		}
		return true;
	}
	inline bool operator != (const Big &o) const {
		return !(*this == o);
	}
	inline bool operator < (const Big &o) const {
		if (neg != o.neg) return neg && !o.neg;
		if (neg && o.neg) return abscmp(*this, o) > 0;
		return abscmp(*this, o) < 0;
	}
	inline bool operator > (const Big &o) const {
		return o < *this;
	}
	inline bool operator <= (const Big &o) const {
		return !(*this > o);
	}
	inline bool operator >= (const Big &o) const {
		return !(*this < o);
	}
	inline void print() const {
		if (neg && !(a[0] == 1 && a[1] == 0)) {
			cout << "-";
		}
		for (ll i = a[0]; i >= 1; i--) {
			cout << a[i];
		}
		cout << endl;
	}
	inline string to_string() const {
		string res;
		if (neg && !(a[0] == 1 && a[1] == 0)) {
			res += '-';
		}
		for (ll i = a[0]; i >= 1; i--) {
			res += char('0' + a[i]);
		}
		return res;
	}
};

inline istream& operator >> (istream &in, Big &x) {
	string s;
	in >> s;
	x = Big(s);
	return in;
}

inline ostream& operator << (ostream &out, const Big &x) {
	if (x.neg && !(x.a[0] == 1 && x.a[1] == 0)) {
		out << '-';
	}
	for (ll i = x.a[0]; i >= 1; i--) {
		out << x.a[i];
	}
	return out;
}

inline Big operator << (const Big &x, const ll &k) {
	return x.shl(k);
}

inline Big& operator <<= (Big &x, const ll &k) {
	x = x.shl(k);
	return x;
}

inline Big operator >> (const Big &x, const ll &k) {
	return x.shr(k);
}

inline Big& operator >>= (Big &x, const ll &k) {
	x = x.shr(k);
	return x;
}

inline bool operator && (const Big &x, const Big &y) {
	return !(x.a[0] == 1 && x.a[1] == 0) && !(y.a[0] == 1 && y.a[1] == 0);
}

inline bool operator || (const Big &x, const Big &y) {
	return !(x.a[0] == 1 && x.a[1] == 0) || !(y.a[0] == 1 && y.a[1] == 0);
}

inline bool operator ! (const Big &x) {
	return x.a[0] == 1 && x.a[1] == 0;
}

inline Big operator + (const ll &k, const Big &o) {
	return o + k;
}

inline Big operator - (const ll &k, const Big &o) {
	return Big(k) - o;
}

inline Big operator * (const ll &k, const Big &o) {
	return o * k;
}

inline Big operator / (const ll &k, const Big &o) {
	return Big(k) / o;
}

int main() {
	// 函数： abs()    pow()     sqrt()      to_string()
	// 用法：a.abs() a.pow(10) a.sqrt(2)    a.to_string()
	// 说明：绝对值     幂       开n次方根    转为字符串
	
	// 实现了 = + += - -= * *= / /= % %= == != < > <= >= << <<= >> >>=（左移右移） && || ! >> <<（流输入输出）
	// 作者: wangyanxi 部！分！代码借助DeepSeek 原创内容超过80%
	// 求测试代码
	return 0;
}