• FFT A*B模板


    从卿学姐那里偷了份FFT大数相乘的模板。。。果断交了一发HDU 1402

    还不孬

      1 //FFT 大整数乘法
      2 #include<cstdio>
      3 #include<cmath>
      4 #include<cstring>
      5 #include<algorithm>
      6 
      7 using namespace std;
      8 
      9 
     10 const int N = 500005;
     11 const double pi = acos(-1.0);
     12 
     13 char s1[N],s2[N];
     14 int len,res[N];
     15 
     16 struct Complex
     17 {
     18     double r,i;
     19     Complex(double r=0,double i=0):r(r),i(i) {};
     20     Complex operator+(const Complex &rhs)
     21     {
     22         return Complex(r + rhs.r,i + rhs.i);
     23     }
     24     Complex operator-(const Complex &rhs)
     25     {
     26         return Complex(r - rhs.r,i - rhs.i);
     27     }
     28     Complex operator*(const Complex &rhs)
     29     {
     30         return Complex(r*rhs.r - i*rhs.i,i*rhs.r + r*rhs.i);
     31     }
     32 } va[N],vb[N];
     33 
     34 void rader(Complex F[],int len) //len = 2^M,reverse F[i] with  F[j] j为i二进制反转
     35 {
     36     int j = len >> 1;
     37     for(int i = 1;i < len - 1;++i)
     38     {
     39         if(i < j) swap(F[i],F[j]);  // reverse
     40         int k = len>>1;
     41         while(j>=k)
     42         {
     43             j -= k;
     44             k >>= 1;
     45         }
     46         if(j < k) j += k;
     47     }
     48 }
     49 
     50 void FFT(Complex F[],int len,int t)
     51 {
     52     rader(F,len);
     53     for(int h=2;h<=len;h<<=1)
     54     {
     55         Complex wn(cos(-t*2*pi/h),sin(-t*2*pi/h));
     56         for(int j=0;j<len;j+=h)
     57         {
     58             Complex E(1,0); //旋转因子
     59             for(int k=j;k<j+h/2;++k)
     60             {
     61                 Complex u = F[k];
     62                 Complex v = E*F[k+h/2];
     63                 F[k] = u+v;
     64                 F[k+h/2] = u-v;
     65                 E=E*wn;
     66             }
     67         }
     68     }
     69     if(t==-1)   //IDFT
     70         for(int i=0;i<len;++i)
     71             F[i].r/=len;
     72 }
     73 
     74 void Conv(Complex a[],Complex b[],int len) //求卷积
     75 {
     76     FFT(a,len,1);
     77     FFT(b,len,1);
     78     for(int i=0;i<len;++i) a[i] = a[i]*b[i];
     79     FFT(a,len,-1);
     80 }
     81 
     82 void init(char *s1,char *s2)
     83 {
     84     int n1 = strlen(s1),n2 = strlen(s2);
     85     len = 1;
     86     while(len < 2*n1 || len < 2*n2) len <<= 1;
     87     int i;
     88     for(i=0;i<n1;++i)
     89     {
     90         va[i].r = s1[n1-i-1]-'0';
     91         va[i].i = 0;
     92     }
     93     while(i<len)
     94     {
     95         va[i].r = va[i].i = 0;
     96         ++i;
     97     }
     98     for(i=0;i<n2;++i)
     99     {
    100         vb[i].r = s2[n2-i-1]-'0';
    101         vb[i].i = 0;
    102     }
    103     while(i<len)
    104     {
    105         vb[i].r = vb[i].i = 0;
    106         ++i;
    107     }
    108 }
    109 
    110 void gao()
    111 {
    112     Conv(va,vb,len);
    113     memset(res,0,sizeof res);
    114     for(int i=0;i<len;++i)
    115     {
    116         res[i]=va[i].r + 0.5;
    117     }
    118     for(int i=0;i<len;++i)
    119     {
    120         res[i+1]+=res[i]/10;
    121         res[i]%=10;
    122     }
    123     int high = 0;
    124     for(int i=len-1;i>=0;--i)
    125     {
    126         if(res[i])
    127         {
    128             high = i;
    129             break;
    130         }
    131     }
    132     for(int i=high;i>=0;--i) putchar('0'+res[i]);
    133     puts("");
    134 }
    135 
    136 
    137 int main()
    138 {
    139     while(scanf("%s%s",s1,s2)==2)
    140     {
    141         init(s1,s2);
    142         gao();
    143     }
    144     return 0;
    145 }
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  • 原文地址:https://www.cnblogs.com/cshg/p/5919583.html
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