Code[VS] 3123 高精度练习之超大整数乘法

FFT 做 高精度乘法

 #include <bits/stdc++.h>

 const double pi = acos(-);

 struct complex
 {
     double a, b;

     inline complex(
         double _a = ,
         double _b = )
     {
         a = _a;
         b = _b;
     }

     inline friend complex operator +
     (const complex &a, const complex &b)
     {
         return complex(a.a + b.a, a.b + b.b);
     }

     inline friend complex operator -
     (const complex &a, const complex &b)
     {
         return complex(a.a - b.a, a.b - b.b);
     }

     inline friend complex operator *
     (const complex &a, const complex &b)
     {
         return complex(a.a*b.a - a.b*b.b, a.a*b.b + a.b*b.a);
     }

     inline friend complex & operator +=
     (complex &a, const complex &b)
     {
         return a = a+b;
     }

     inline friend complex & operator -=
     (complex &a, const complex &b)
     {
         return a = a-b;
     }

     inline friend complex & operator *=
     (complex &a, const complex &b)
     {
         return a = a*b;
     }
 };

 inline complex alpha(double a)
 {
     return complex(cos(a), sin(a));
 }

 typedef std::vector<complex> vec;

 vec FFT(const vec &a)
 {
     int n = a.size();

     if (n == )return a;

     complex w_k(, );
     complex w_n = alpha(pi*/n);

     vec ar[], yr[], y(n);

     for (int i = ; i < n; ++i)
         ar[i & ].push_back(a[i]);

     for (int i = ; i < ; ++i)
         yr[i] = FFT(ar[i]);

     for (int i = ; i < n/; ++i, w_k *= w_n)
     {
         y[i] = yr[][i] + w_k * yr[][i];
         y[i + n/] = yr[][i] - w_k * yr[][i];
     }

     return y;
 }

 vec IFFT(const vec &a)
 {
     int n = a.size();

     if (n == )return a;

     complex w_k(, );
     complex w_n = alpha(-pi*/n);

     vec ar[], yr[], y(n);

     for (int i = ; i < n; ++i)
         ar[i & ].push_back(a[i]);

     for (int i = ; i < ; ++i)
         yr[i] = IFFT(ar[i]);

     for (int i = ; i < n/; ++i, w_k *= w_n)
     {
         y[i] = yr[][i] + w_k * yr[][i];
         y[i + n/] = yr[][i] - w_k * yr[][i];
     }

     return y;
 }

 char s1[]; int len1;
 char s2[]; int len2;

 vec v1, v2, p1, p2, mul, ans;

 signed main(void)
 {
     scanf("%s", s1); len1 = strlen(s1);
     scanf("%s", s2); len2 = strlen(s2);

     int len = len1 + len2;

     while (len != (len&-len))++len;

     for (int i = len1 - ; ~i; --i)v1.push_back(complex(s1[i] - '', ));
     for (int i = len2 - ; ~i; --i)v2.push_back(complex(s2[i] - '', ));

     while ((int)v1.size() < len)v1.push_back(complex());
     while ((int)v2.size() < len)v2.push_back(complex());

     p1 = FFT(v1);
     p2 = FFT(v2);

     for (int i = ; i < len; ++i)
         mul.push_back(p1[i] * p2[i]);

     ans = IFFT(mul);

     std::vector<int> ret;

     for (int i = ; i < len; ++i)
         ret.push_back((int)round(ans[i].a / len));

     for (int i = ; i < len; ++i)
         if (ret[i] >= )
         {
             ret[i + ] += ret[i] / ;
             ret[i] %= ;
         }

     while (ret.size() !=  && !ret[ret.size() - ])
         ret.pop_back();

     for (int i = ret.size() - ; i >= ; --i)
         putchar('' + ret[i]);
     putchar('\n');
 }

@Author: YouSiki