507 lines
14 KiB
C++
507 lines
14 KiB
C++
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#include <vector>
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#include <cstdlib>
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#include <iostream>
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#include <iomanip>
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#include <string>
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#include <complex>
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#include <ctime>
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#include <cstdio>
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using namespace std;
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// base and base_digits must be consistent
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const int base = 1000000000;
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const int base_digits = 9;
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struct bigint {
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vector<int> a;
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int sign;
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bigint() :
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sign(1) {
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}
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bigint(long long v) {
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*this = v;
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}
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bigint(const string &s) {
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read(s);
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}
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void operator=(const bigint &v) {
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sign = v.sign;
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a = v.a;
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}
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void operator=(long long v) {
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sign = 1;
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if (v < 0)
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sign = -1, v = -v;
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a.clear();
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for (; v > 0; v = v / base)
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a.push_back(v % base);
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}
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bigint operator+(const bigint &v) const {
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if (sign == v.sign) {
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bigint res = v;
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for (int i = 0, carry = 0; i < (int) max(a.size(), v.a.size()) || carry; ++i) {
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if (i == (int) res.a.size())
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res.a.push_back(0);
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res.a[i] += carry + (i < (int) a.size() ? a[i] : 0);
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carry = res.a[i] >= base;
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if (carry)
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res.a[i] -= base;
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}
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return res;
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}
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return *this - (-v);
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}
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bigint operator-(const bigint &v) const {
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if (sign == v.sign) {
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if (abs() >= v.abs()) {
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bigint res = *this;
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for (int i = 0, carry = 0; i < (int) v.a.size() || carry; ++i) {
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res.a[i] -= carry + (i < (int) v.a.size() ? v.a[i] : 0);
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carry = res.a[i] < 0;
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if (carry)
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res.a[i] += base;
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}
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res.trim();
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return res;
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}
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return -(v - *this);
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}
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return *this + (-v);
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}
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void operator*=(int v) {
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if (v < 0)
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sign = -sign, v = -v;
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for (int i = 0, carry = 0; i < (int) a.size() || carry; ++i) {
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if (i == (int) a.size())
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a.push_back(0);
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long long cur = a[i] * (long long) v + carry;
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carry = (int) (cur / base);
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a[i] = (int) (cur % base);
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//asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur), "c"(base));
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/*
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int val;
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__asm {
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lea esi, cur
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mov eax, [esi]
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mov edx, [esi+4]
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mov ecx, base
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div ecx
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mov carry, eax
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mov val, edx;
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}
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a[i] = val;
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*/
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}
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trim();
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}
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bigint operator*(int v) const {
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bigint res = *this;
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res *= v;
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return res;
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}
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friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) {
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int norm = base / (b1.a.back() + 1);
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bigint a = a1.abs() * norm;
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bigint b = b1.abs() * norm;
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bigint q, r;
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q.a.resize(a.a.size());
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for (int i = a.a.size() - 1; i >= 0; i--) {
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r *= base;
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r += a.a[i];
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int s1 = r.a.size() <= b.a.size() ? 0 : r.a[b.a.size()];
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int s2 = r.a.size() <= b.a.size() - 1 ? 0 : r.a[b.a.size() - 1];
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int d = ((long long) base * s1 + s2) / b.a.back();
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r -= b * d;
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while (r < 0)
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r += b, --d;
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q.a[i] = d;
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}
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q.sign = a1.sign * b1.sign;
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r.sign = a1.sign;
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q.trim();
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r.trim();
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return make_pair(q, r / norm);
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}
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bigint operator/(const bigint &v) const {
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return divmod(*this, v).first;
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}
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bigint operator%(const bigint &v) const {
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return divmod(*this, v).second;
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}
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void operator/=(int v) {
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if (v < 0)
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sign = -sign, v = -v;
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for (int i = (int) a.size() - 1, rem = 0; i >= 0; --i) {
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long long cur = a[i] + rem * (long long) base;
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a[i] = (int) (cur / v);
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rem = (int) (cur % v);
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}
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trim();
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}
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bigint operator/(int v) const {
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bigint res = *this;
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res /= v;
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return res;
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}
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int operator%(int v) const {
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if (v < 0)
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v = -v;
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int m = 0;
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for (int i = a.size() - 1; i >= 0; --i)
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m = (a[i] + m * (long long) base) % v;
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return m * sign;
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}
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void operator+=(const bigint &v) {
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*this = *this + v;
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}
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void operator-=(const bigint &v) {
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*this = *this - v;
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}
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void operator*=(const bigint &v) {
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*this = *this * v;
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}
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void operator/=(const bigint &v) {
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*this = *this / v;
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}
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bool operator<(const bigint &v) const {
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if (sign != v.sign)
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return sign < v.sign;
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if (a.size() != v.a.size())
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return a.size() * sign < v.a.size() * v.sign;
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for (int i = a.size() - 1; i >= 0; i--)
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if (a[i] != v.a[i])
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return a[i] * sign < v.a[i] * sign;
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return false;
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}
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bool operator>(const bigint &v) const {
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return v < *this;
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}
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bool operator<=(const bigint &v) const {
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return !(v < *this);
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}
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bool operator>=(const bigint &v) const {
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return !(*this < v);
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}
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bool operator==(const bigint &v) const {
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return !(*this < v) && !(v < *this);
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}
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bool operator!=(const bigint &v) const {
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return *this < v || v < *this;
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}
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void trim() {
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while (!a.empty() && a.back() == 0)
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a.pop_back();
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if (a.empty())
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sign = 1;
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}
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bool isZero() const {
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return a.empty() || (a.size() == 1 && !a[0]);
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}
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bigint operator-() const {
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bigint res = *this;
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res.sign = -sign;
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return res;
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}
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bigint abs() const {
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bigint res = *this;
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res.sign *= res.sign;
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return res;
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}
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long long longValue() const {
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long long res = 0;
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for (int i = a.size() - 1; i >= 0; i--)
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res = res * base + a[i];
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return res * sign;
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}
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friend bigint gcd(const bigint &a, const bigint &b) {
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return b.isZero() ? a : gcd(b, a % b);
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}
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friend bigint lcm(const bigint &a, const bigint &b) {
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return a / gcd(a, b) * b;
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}
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void read(const string &s) {
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sign = 1;
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a.clear();
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int pos = 0;
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while (pos < (int) s.size() && (s[pos] == '-' || s[pos] == '+')) {
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if (s[pos] == '-')
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sign = -sign;
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++pos;
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}
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for (int i = s.size() - 1; i >= pos; i -= base_digits) {
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int x = 0;
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for (int j = max(pos, i - base_digits + 1); j <= i; j++)
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x = x * 10 + s[j] - '0';
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a.push_back(x);
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}
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trim();
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}
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friend istream& operator>>(istream &stream, bigint &v) {
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string s;
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stream >> s;
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v.read(s);
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return stream;
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}
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friend ostream& operator<<(ostream &stream, const bigint &v) {
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if (v.sign == -1)
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stream << '-';
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stream << (v.a.empty() ? 0 : v.a.back());
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for (int i = (int) v.a.size() - 2; i >= 0; --i)
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stream << setw(base_digits) << setfill('0') << v.a[i];
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return stream;
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}
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static vector<int> convert_base(const vector<int> &a, int old_digits, int new_digits) {
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vector<long long> p(max(old_digits, new_digits) + 1);
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p[0] = 1;
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for (int i = 1; i < (int) p.size(); i++)
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p[i] = p[i - 1] * 10;
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vector<int> res;
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long long cur = 0;
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int cur_digits = 0;
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for (int i = 0; i < (int) a.size(); i++) {
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cur += a[i] * p[cur_digits];
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cur_digits += old_digits;
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while (cur_digits >= new_digits) {
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res.push_back(int(cur % p[new_digits]));
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cur /= p[new_digits];
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cur_digits -= new_digits;
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}
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}
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res.push_back((int) cur);
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while (!res.empty() && res.back() == 0)
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res.pop_back();
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return res;
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}
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void fft(vector<complex<double> > & a, bool invert) const {
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int n = (int) a.size();
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for (int i = 1, j = 0; i < n; ++i) {
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int bit = n >> 1;
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for (; j >= bit; bit >>= 1)
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j -= bit;
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j += bit;
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if (i < j)
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swap(a[i], a[j]);
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}
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for (int len = 2; len <= n; len <<= 1) {
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double ang = 2 * 3.14159265358979323846 / len * (invert ? -1 : 1);
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complex<double> wlen(cos(ang), sin(ang));
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for (int i = 0; i < n; i += len) {
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complex<double> w(1);
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for (int j = 0; j < len / 2; ++j) {
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complex<double> u = a[i + j];
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complex<double> v = a[i + j + len / 2] * w;
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a[i + j] = u + v;
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a[i + j + len / 2] = u - v;
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w *= wlen;
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}
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}
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}
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if (invert)
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for (int i = 0; i < n; ++i)
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a[i] /= n;
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}
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void multiply_fft(const vector<int> &a, const vector<int> &b, vector<int> &res) const {
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vector<complex<double> > fa(a.begin(), a.end());
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vector<complex<double> > fb(b.begin(), b.end());
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int n = 1;
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while (n < (int) max(a.size(), b.size()))
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n <<= 1;
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n <<= 1;
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fa.resize(n);
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fb.resize(n);
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fft(fa, false);
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fft(fb, false);
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for (int i = 0; i < n; ++i)
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fa[i] *= fb[i];
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fft(fa, true);
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res.resize(n);
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for (int i = 0, carry = 0; i < n; ++i) {
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res[i] = int(fa[i].real() + 0.5) + carry;
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carry = res[i] / 1000;
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res[i] %= 1000;
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}
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}
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bigint operator*(const bigint &v) const {
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bigint res;
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res.sign = sign * v.sign;
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multiply_fft(convert_base(a, base_digits, 3), convert_base(v.a, base_digits, 3), res.a);
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res.a = convert_base(res.a, 3, base_digits);
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res.trim();
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return res;
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}
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bigint mul_simple(const bigint &v) const {
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bigint res;
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res.sign = sign * v.sign;
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res.a.resize(a.size() + v.a.size());
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for (int i = 0; i < (int) a.size(); ++i)
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if (a[i])
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for (int j = 0, carry = 0; j < (int) v.a.size() || carry; ++j) {
|
||
|
|
long long cur = res.a[i + j] + (long long) a[i] * (j < (int) v.a.size() ? v.a[j] : 0) + carry;
|
||
|
|
carry = (int) (cur / base);
|
||
|
|
res.a[i + j] = (int) (cur % base);
|
||
|
|
}
|
||
|
|
res.trim();
|
||
|
|
return res;
|
||
|
|
}
|
||
|
|
|
||
|
|
typedef vector<long long> vll;
|
||
|
|
|
||
|
|
static vll karatsubaMultiply(const vll &a, const vll &b) {
|
||
|
|
int n = a.size();
|
||
|
|
vll res(n + n);
|
||
|
|
if (n <= 32) {
|
||
|
|
for (int i = 0; i < n; i++)
|
||
|
|
for (int j = 0; j < n; j++)
|
||
|
|
res[i + j] += a[i] * b[j];
|
||
|
|
return res;
|
||
|
|
}
|
||
|
|
|
||
|
|
int k = n >> 1;
|
||
|
|
vll a1(a.begin(), a.begin() + k);
|
||
|
|
vll a2(a.begin() + k, a.end());
|
||
|
|
vll b1(b.begin(), b.begin() + k);
|
||
|
|
vll b2(b.begin() + k, b.end());
|
||
|
|
|
||
|
|
vll a1b1 = karatsubaMultiply(a1, b1);
|
||
|
|
vll a2b2 = karatsubaMultiply(a2, b2);
|
||
|
|
|
||
|
|
for (int i = 0; i < k; i++)
|
||
|
|
a2[i] += a1[i];
|
||
|
|
for (int i = 0; i < k; i++)
|
||
|
|
b2[i] += b1[i];
|
||
|
|
|
||
|
|
vll r = karatsubaMultiply(a2, b2);
|
||
|
|
for (int i = 0; i < (int) a1b1.size(); i++)
|
||
|
|
r[i] -= a1b1[i];
|
||
|
|
for (int i = 0; i < (int) a2b2.size(); i++)
|
||
|
|
r[i] -= a2b2[i];
|
||
|
|
|
||
|
|
for (int i = 0; i < (int) r.size(); i++)
|
||
|
|
res[i + k] += r[i];
|
||
|
|
for (int i = 0; i < (int) a1b1.size(); i++)
|
||
|
|
res[i] += a1b1[i];
|
||
|
|
for (int i = 0; i < (int) a2b2.size(); i++)
|
||
|
|
res[i + n] += a2b2[i];
|
||
|
|
return res;
|
||
|
|
}
|
||
|
|
|
||
|
|
bigint mul_karatsuba(const bigint &v) const {
|
||
|
|
vector<int> a6 = convert_base(this->a, base_digits, 6);
|
||
|
|
vector<int> b6 = convert_base(v.a, base_digits, 6);
|
||
|
|
vll a(a6.begin(), a6.end());
|
||
|
|
vll b(b6.begin(), b6.end());
|
||
|
|
while (a.size() < b.size())
|
||
|
|
a.push_back(0);
|
||
|
|
while (b.size() < a.size())
|
||
|
|
b.push_back(0);
|
||
|
|
while (a.size() & (a.size() - 1))
|
||
|
|
a.push_back(0), b.push_back(0);
|
||
|
|
vll c = karatsubaMultiply(a, b);
|
||
|
|
bigint res;
|
||
|
|
res.sign = sign * v.sign;
|
||
|
|
for (int i = 0, carry = 0; i < (int) c.size(); i++) {
|
||
|
|
long long cur = c[i] + carry;
|
||
|
|
res.a.push_back((int) (cur % 1000000));
|
||
|
|
carry = (int) (cur / 1000000);
|
||
|
|
}
|
||
|
|
res.a = convert_base(res.a, 6, base_digits);
|
||
|
|
res.trim();
|
||
|
|
return res;
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
bigint getRandomBigint(int len) {
|
||
|
|
string s;
|
||
|
|
for (int i = 0; i < len; i++)
|
||
|
|
s += rand() % 10 + '0';
|
||
|
|
return bigint(s);
|
||
|
|
}
|
||
|
|
|
||
|
|
int main() {
|
||
|
|
srand(1);
|
||
|
|
bigint a("99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999");
|
||
|
|
bigint b("19999999999999999999999999999999999999999999999999999999999999999999999999999999999999998");
|
||
|
|
cout << a * b << endl;
|
||
|
|
cout << a.mul_karatsuba(b) << endl;
|
||
|
|
cout << a / b << endl;
|
||
|
|
|
||
|
|
for (int step = 0; step < 100; step++) {
|
||
|
|
bigint a = getRandomBigint(1000);
|
||
|
|
bigint b = getRandomBigint(1000);
|
||
|
|
|
||
|
|
bigint x = a * b;
|
||
|
|
bigint y = a.mul_simple(b);
|
||
|
|
bigint z = a.mul_karatsuba(b);
|
||
|
|
|
||
|
|
if (x != y || x != z) {
|
||
|
|
cout << a << " " << b << " " << x << " " << y << " " << z << endl;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
int steps = 1;
|
||
|
|
vector<bigint> x(steps), y(steps);
|
||
|
|
for (int i = 0; i < steps; i++) {
|
||
|
|
x[i] = getRandomBigint(60000);
|
||
|
|
y[i] = getRandomBigint(60000);
|
||
|
|
}
|
||
|
|
|
||
|
|
clock_t start = clock();
|
||
|
|
for (int i = 0; i < steps; i++)
|
||
|
|
bigint z = x[i] * y[i];
|
||
|
|
fprintf(stderr, "time=%.3lfsec\n", 0.001 * (clock() - start));
|
||
|
|
|
||
|
|
start = clock();
|
||
|
|
for (int i = 0; i < steps; i++)
|
||
|
|
bigint z = x[i].mul_karatsuba(y[i]);
|
||
|
|
fprintf(stderr, "time=%.3lfsec\n", 0.001 * (clock() - start));
|
||
|
|
|
||
|
|
a = getRandomBigint(10000);
|
||
|
|
b = getRandomBigint(2000);
|
||
|
|
start = clock();
|
||
|
|
bigint c = a / b;
|
||
|
|
fprintf(stderr, "time=%.3lfsec\n", 0.001 * (clock() - start));
|
||
|
|
|
||
|
|
bigint z = 5;
|
||
|
|
z = 6;
|
||
|
|
cout << z << endl;
|
||
|
|
}
|