问题描述
请告诉我如何在 C++ 中存储 50 多个数字。 你可能会说这个问题被问到并使用了字符串。但我希望对这些存储的数据执行“加”、“减”和“或”操作。
解决方法
标准库中没有 bigint 实现。 50 位小数将需要 166 位。最大的原始类型是 std::uint64_t
。即使你有一个 128 位的扩展,它也不会给你带来好处,因为你仍然有点短。
如果您需要精确到如此大的数字,您必须滚动自己的 bigint 类型或搜索支持它的库(boost 可能有一个)。
如果您不需要绝对精度并且可以按位或,您可以使用浮点类型之一,例如double
。
正如位掩码已经回答的那样,到目前为止,C++ 中的 std 中没有 bigint。但是我们可以自己实现一个Bigint结构,虽然会增加操作的复杂度。
/*
######################################################################
####################### THE BIG INT ##########################
*/
const int base = 1000000000;
const int base_digits = 9;
struct Int
{
vector<int> a;
int sign;
/*<arpa>*/
int size()
{
if (a.empty())
return 0;
int ans = (a.size() - 1) * base_digits;
int ca = a.back();
while (ca)
ans++,ca /= 10;
return ans;
}
Int operator^(const Int &v)
{
Int ans = 1,a = *this,b = v;
while (!b.isZero())
{
if (b % 2)
ans *= a;
a *= a,b /= 2;
}
return ans;
}
string to_string()
{
stringstream ss;
ss << *this;
string s;
ss >> s;
return s;
}
int sumof()
{
string s = to_string();
int ans = 0;
for (auto c : s)
ans += c - '0';
return ans;
}
/*</arpa>*/
Int() : sign(1)
{
}
Int(long long v)
{
*this = v;
}
Int(const string &s)
{
read(s);
}
void operator=(const Int &v)
{
sign = v.sign;
a = v.a;
}
void operator=(long long v)
{
sign = 1;
a.clear();
if (v < 0)
sign = -1,v = -v;
for (; v > 0; v = v / base)
a.push_back(v % base);
}
Int operator+(const Int &v) const
{
if (sign == v.sign)
{
Int res = v;
for (int i = 0,carry = 0; i < (int)max(a.size(),v.a.size()) || carry; ++i)
{
if (i == (int)res.a.size())
res.a.push_back(0);
res.a[i] += carry + (i < (int)a.size() ? a[i] : 0);
carry = res.a[i] >= base;
if (carry)
res.a[i] -= base;
}
return res;
}
return *this - (-v);
}
Int operator-(const Int &v) const
{
if (sign == v.sign)
{
if (abs() >= v.abs())
{
Int res = *this;
for (int i = 0,carry = 0; i < (int)v.a.size() || carry; ++i)
{
res.a[i] -= carry + (i < (int)v.a.size() ? v.a[i] : 0);
carry = res.a[i] < 0;
if (carry)
res.a[i] += base;
}
res.trim();
return res;
}
return -(v - *this);
}
return *this + (-v);
}
void operator*=(int v)
{
if (v < 0)
sign = -sign,v = -v;
for (int i = 0,carry = 0; i < (int)a.size() || carry; ++i)
{
if (i == (int)a.size())
a.push_back(0);
long long cur = a[i] * (long long)v + carry;
carry = (int)(cur / base);
a[i] = (int)(cur % base);
//asm("divl %%ecx" : "=a"(carry),"=d"(a[i]) : "A"(cur),"c"(base));
}
trim();
}
Int operator*(int v) const
{
Int res = *this;
res *= v;
return res;
}
void operator*=(long long v)
{
if (v < 0)
sign = -sign,"c"(base));
}
trim();
}
Int operator*(long long v) const
{
Int res = *this;
res *= v;
return res;
}
friend pair<Int,Int> divmod(const Int &a1,const Int &b1)
{
int norm = base / (b1.a.back() + 1);
Int a = a1.abs() * norm;
Int b = b1.abs() * norm;
Int q,r;
q.a.resize(a.a.size());
for (int i = a.a.size() - 1; i >= 0; i--)
{
r *= base;
r += a.a[i];
int s1 = r.a.size() <= b.a.size() ? 0 : r.a[b.a.size()];
int s2 = r.a.size() <= b.a.size() - 1 ? 0 : r.a[b.a.size() - 1];
int d = ((long long)base * s1 + s2) / b.a.back();
r -= b * d;
while (r < 0)
r += b,--d;
q.a[i] = d;
}
q.sign = a1.sign * b1.sign;
r.sign = a1.sign;
q.trim();
r.trim();
return make_pair(q,r / norm);
}
Int operator/(const Int &v) const
{
return divmod(*this,v).first;
}
Int operator%(const Int &v) const
{
return divmod(*this,v).second;
}
void operator/=(int v)
{
if (v < 0)
sign = -sign,v = -v;
for (int i = (int)a.size() - 1,rem = 0; i >= 0; --i)
{
long long cur = a[i] + rem * (long long)base;
a[i] = (int)(cur / v);
rem = (int)(cur % v);
}
trim();
}
Int operator/(int v) const
{
Int res = *this;
res /= v;
return res;
}
int operator%(int v) const
{
if (v < 0)
v = -v;
int m = 0;
for (int i = a.size() - 1; i >= 0; --i)
m = (a[i] + m * (long long)base) % v;
return m * sign;
}
void operator+=(const Int &v)
{
*this = *this + v;
}
void operator-=(const Int &v)
{
*this = *this - v;
}
void operator*=(const Int &v)
{
*this = *this * v;
}
void operator/=(const Int &v)
{
*this = *this / v;
}
Int operator++()
{
*this += 1;
return *this;
}
Int operator++(int)
{
Int temp = *this;
*this += 1;
return temp;
}
Int operator--()
{
*this -= 1;
return *this;
}
Int operator--(int)
{
Int temp = *this;
*this -= 1;
return temp;
}
bool operator<(const Int &v) const
{
if (sign != v.sign)
return sign < v.sign;
if (a.size() != v.a.size())
return a.size() * sign < v.a.size() * v.sign;
for (int i = a.size() - 1; i >= 0; i--)
if (a[i] != v.a[i])
return a[i] * sign < v.a[i] * sign;
return false;
}
bool operator>(const Int &v) const
{
return v < *this;
}
bool operator<=(const Int &v) const
{
return !(v < *this);
}
bool operator>=(const Int &v) const
{
return !(*this < v);
}
bool operator==(const Int &v) const
{
return !(*this < v) && !(v < *this);
}
bool operator!=(const Int &v) const
{
return *this < v || v < *this;
}
void trim()
{
while (!a.empty() && !a.back())
a.pop_back();
if (a.empty())
sign = 1;
}
bool isZero() const
{
return a.empty() || (a.size() == 1 && !a[0]);
}
Int operator-() const
{
Int res = *this;
res.sign = -sign;
return res;
}
Int abs() const
{
Int res = *this;
res.sign *= res.sign;
return res;
}
long long longValue() const
{
long long res = 0;
for (int i = a.size() - 1; i >= 0; i--)
res = res * base + a[i];
return res * sign;
}
friend Int gcd(const Int &a,const Int &b)
{
return b.isZero() ? a : gcd(b,a % b);
}
friend Int lcm(const Int &a,const Int &b)
{
return a / gcd(a,b) * b;
}
void read(const string &s)
{
sign = 1;
a.clear();
int pos = 0;
while (pos < (int)s.size() && (s[pos] == '-' || s[pos] == '+'))
{
if (s[pos] == '-')
sign = -sign;
++pos;
}
for (int i = s.size() - 1; i >= pos; i -= base_digits)
{
int x = 0;
for (int j = max(pos,i - base_digits + 1); j <= i; j++)
x = x * 10 + s[j] - '0';
a.push_back(x);
}
trim();
}
friend istream &operator>>(istream &stream,Int &v)
{
string s;
stream >> s;
v.read(s);
return stream;
}
friend ostream &operator<<(ostream &stream,const Int &v)
{
if (v.sign == -1)
stream << '-';
stream << (v.a.empty() ? 0 : v.a.back());
for (int i = (int)v.a.size() - 2; i >= 0; --i)
stream << setw(base_digits) << setfill('0') << v.a[i];
return stream;
}
static vector<int> convert_base(const vector<int> &a,int old_digits,int new_digits)
{
vector<long long> p(max(old_digits,new_digits) + 1);
p[0] = 1;
for (int i = 1; i < (int)p.size(); i++)
p[i] = p[i - 1] * 10;
vector<int> res;
long long cur = 0;
int cur_digits = 0;
for (int i = 0; i < (int)a.size(); i++)
{
cur += a[i] * p[cur_digits];
cur_digits += old_digits;
while (cur_digits >= new_digits)
{
res.push_back(int(cur % p[new_digits]));
cur /= p[new_digits];
cur_digits -= new_digits;
}
}
res.push_back((int)cur);
while (!res.empty() && !res.back())
res.pop_back();
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;
}
Int operator*(const Int &v) const
{
vector<int> a6 = convert_base(this->a,base_digits,6);
vector<int> b6 = convert_base(v.a,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);
Int 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;
}
//Added part.
friend Int max(const Int &a,const Int &b)
{
if (a < b)
{
return a;
}
return b;
}
friend Int max(const Int &a,const int32_t &B)
{
Int b = B;
return max(a,b);
}
friend Int max(const Int &a,const int64_t &B)
{
Int b = B;
return max(a,b);
}
friend Int min(const Int &a,const Int &b)
{
if (a > b)
{
return b;
}
return a;
}
friend Int min(const Int &a,const int32_t &B)
{
Int b = B;
return min(a,const int64_t &B)
{
Int b = B;
return min(a,b);
}
friend Int pow(const Int &a,const Int &b)
{
Int _c = 1;
Int _b = b;
Int _a = a;
while (_b != 0)
{
if (_b % 2)
{
_c *= _a;
}
_a *= _a;
_b /= 2;
}
return _c;
}
friend Int pow(const Int &a,const int32_t &B)
{
Int b = B;
return pow(a,const int64_t &B)
{
Int b = B;
return pow(a,b);
}
friend Int sqrt(Int a)
{
Int x0 = a,x1 = (a + 1) / 2;
while (x1 < x0)
{
x0 = x1;
x1 = (x1 + a / x1) / 2;
}
return x0;
}
};
/*
####################### THE BIG INT ##########################
######################################################################
*/