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(-1);

struct complex
{
    double a, b;
    
    inline complex(
        double _a = 0,
        double _b = 0) 
    {
        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 == 1)return a;
    
    complex w_k(1, 0);
    complex w_n = alpha(pi*2/n);
    
    vec ar[2], yr[2], y(n);
    
    for (int i = 0; i < n; ++i)
        ar[i & 1].push_back(a[i]);
        
    for (int i = 0; i < 2; ++i)
        yr[i] = FFT(ar[i]);
        
    for (int i = 0; i < n/2; ++i, w_k *= w_n)
    {
        y[i] = yr[0][i] + w_k * yr[1][i];
        y[i + n/2] = yr[0][i] - w_k * yr[1][i];
    }
        
    return y;
}

vec IFFT(const vec &a)
{
    int n = a.size();
    
    if (n == 1)return a;
    
    complex w_k(1, 0);
    complex w_n = alpha(-pi*2/n);
    
    vec ar[2], yr[2], y(n);
    
    for (int i = 0; i < n; ++i)
        ar[i & 1].push_back(a[i]);
        
    for (int i = 0; i < 2; ++i)
        yr[i] = IFFT(ar[i]);
        
    for (int i = 0; i < n/2; ++i, w_k *= w_n)
    {
        y[i] = yr[0][i] + w_k * yr[1][i];
        y[i + n/2] = yr[0][i] - w_k * yr[1][i];
    }
        
    return y;
}

char s1[100005]; int len1;
char s2[100005]; 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 - 1; ~i; --i)v1.push_back(complex(s1[i] - '0', 0));
    for (int i = len2 - 1; ~i; --i)v2.push_back(complex(s2[i] - '0', 0));
    
    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 = 0; i < len; ++i)
        mul.push_back(p1[i] * p2[i]);
        
    ans = IFFT(mul);
    
    std::vector<int> ret;
    
    for (int i = 0; i < len; ++i)
        ret.push_back((int)round(ans[i].a / len));
        
    for (int i = 0; i < len; ++i)
        if (ret[i] >= 10)
        {
            ret[i + 1] += ret[i] / 10;
            ret[i] %= 10;
        }
        
    while (ret.size() != 1 && !ret[ret.size() - 1])
        ret.pop_back();
        
    for (int i = ret.size() - 1; i >= 0; --i)
        putchar('0' + ret[i]);
    putchar('
');
}

@Author: YouSiki