CODE[VS] 3123 super-large integer multiplication of high-precision exercises

FFT makes high-precision multiplication

1#include <bits/stdc++.h>2 3 Const DoublePI = ACOs (-1);4 5 structComplex6 {7     DoubleA, B;8     9 Inline Complex (Ten         Double_a =0, One         Double_b =0)  A     { -A =_a; -b =_b; the     } -      -Inline friend complexoperator+ -(ConstComplex &a,ConstComplex &b) +     { -         returnComplex (A.A + B.A, a.b +b.b); +     } A      atInline friend complexoperator- -(ConstComplex &a,ConstComplex &b) -     { -         returnComplex (A.A-B.A, A.B-b.b); -     } -      inInline friend complexoperator* -(ConstComplex &a,ConstComplex &b) to     { +         returnComplex (a.a*b.a-a.b*b.b, a.a*b.b + a.b*B.A); -     } the      *Inline Friend Complex &operator+= $(Complex &a,ConstComplex &b)Panax Notoginseng     { -         returnA = a +b; the     } +      AInline Friend Complex &operator-= the(Complex &a,ConstComplex &b) +     { -         returnA = A-b; $     } $      -Inline Friend Complex &operator*= -(Complex &a,ConstComplex &b) the     { -         returnA = A *b;Wuyi     } the }; -  WuInline Complex Alpha (Doublea) - { About     returnComplex (cos (a), sin (a)); $ } -  -typedef std::vector<complex>Vec; -  AVEC FFT (ConstVEC &a) + { the     intn =a.size (); -      $     if(n = =1)returnA; the      theComplex W_k (1,0); theComplex w_n = Alpha (pi*2/n); the      -VEC ar[2], yr[2], y (n); in      the      for(inti =0; I < n; ++i) theAr[i &1].push_back (A[i]); About          the      for(inti =0; I <2; ++i) theYr[i] =FFT (Ar[i]); the          +      for(inti =0; I < n/2; ++i, W_k *=w_n) -     { theY[i] = yr[0][i] + w_k * yr[1][i];BayiY[i + n/2] = yr[0][i]-W_k * yr[1][i]; the     } the          -     returny; - } the  theVEC IFFT (ConstVEC &a) the { the     intn =a.size (); -      the     if(n = =1)returnA; the      theComplex W_k (1,0);94Complex w_n = Alpha (-pi*2/n); the      theVEC ar[2], yr[2], y (n); the     98      for(inti =0; I < n; ++i) AboutAr[i &1].push_back (A[i]); -         101      for(inti =0; I <2; ++i)102Yr[i] =IFFT (Ar[i]);103         104      for(inti =0; I < n/2; ++i, W_k *=w_n) the     {106Y[i] = yr[0][i] + w_k * yr[1][i];107Y[i + n/2] = yr[0][i]-W_k * yr[1][i];108     }109          the     returny;111 } the 113 Chars1[100005];intlen1; the Chars2[100005];intLen2; the  the VEC v1, v2, p1, p2, mul, ans;117 118Signed Main (void)119 { -scanf"%s", S1); Len1 =strlen (S1);121scanf"%s", S2); Len2 =strlen (S2);122     123     intLen = len1 +Len2;124      the      while(Len! = (Len&-len)) + +Len;126     127      for(inti = len1-1; ~i; I.) V1.push_back (Complex (S1[i)-'0',0)); -      for(inti = len2-1; ~i; I.) V2.push_back (Complex (S2[i)-'0',0));129      the      while((int) V1.size () <len) V1.push_back (complex ());131      while((int) V2.size () <len) V2.push_back (complex ()); the     133P1 =FFT (v1);134P2 =FFT (v2);135     136      for(inti =0; i < Len; ++i)137Mul.push_back (P1[i] *p2[i]);138         139Ans =IFFT (mul); $     141std::vector<int>ret;142     143      for(inti =0; i < Len; ++i)144Ret.push_back ((int) Round (ANS[I].A/len));145         146      for(inti =0; i < Len; ++i)147         if(Ret[i] >=Ten)148         {149Ret[i +1] + = Ret[i]/Ten; MaxRet[i]%=Ten;151         } the         153      while(Ret.size ()! =1&&!ret[ret.size ()-1])154 Ret.pop_back ();155         156      for(inti = ret.size ()-1; I >=0; --i)157Putchar ('0'+ret[i]);158Putchar ('\ n');159}

@Author: Yousiki

CODE[VS] 3123 super-large integer multiplication of high-precision exercises