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  • CODEVS3123 a*b problem plus (FFT)

     1 type xh=record
     2         x,y:double;
     3         end;
     4       arr=array[0..1000008] of xh;
     5 var n,m:longint;
     6     s1,s2:ansistring;
     7     a,b,g,w:arr;
     8     ch:char;
     9 operator -(a,b:xh) c:xh;
    10 begin
    11     c.x:=a.x-b.x;
    12     c.y:=a.y-b.y;
    13 end;
    14 operator +(a,b:xh) c:xh;
    15 begin
    16     c.x:=a.x+b.x;
    17     c.y:=a.y+b.y;
    18 end;
    19 operator *(a,b:xh) c:xh;
    20 begin
    21     c.x:=a.x*b.x-a.y*b.y;
    22     c.y:=a.x*b.y+a.y*b.x;
    23 end;
    24 procedure dft(var a:arr;s,t:longint);//a待处理数组 s初始位置 1<<t长度
    25 var i,p:longint;
    26     cnt:xh;
    27 begin
    28     if n>>t=1 then exit;
    29     dft(a,s,t+1); dft(a,s+1<<t,t+1);
    30     for i:=0 to n>>t>>1-1 do
    31     begin
    32         p:=i<<t<<1+s;
    33         cnt:=w[i<<t]*a[p+1<<t];
    34         g[i]:=a[p]+cnt;
    35         g[i+n>>t>>1]:=a[p]-cnt;
    36     end;
    37     for i:=0 to n>>t-1 do a[s+i<<t]:=g[i];
    38 end;
    39 procedure clr(var a:arr);
    40 begin
    41     fillchar(a,sizeof(a),0);
    42 end;
    43 procedure FFT;
    44 var i,len:longint;
    45     lx:longint;
    46 begin
    47     n:=1;
    48     while n<m<<1 do n:=n<<1;
    49     for i:=0 to n-1 do w[i].x:=cos(pi*2*i/n);
    50     for i:=0 to n-1 do w[i].y:=sin(pi*2*i/n);
    51     dft(a,0,0); dft(b,0,0);
    52     for i:=0 to n-1 do a[i]:=a[i]*b[i];
    53     for i:=0 to n-1 do w[i].y:=-w[i].y;  //!!!!
    54     dft(a,0,0);
    55     for i:=m<<1-1 downto 0 do a[i].x:=a[i].x/n;//!!!!
    56     for i:=0 to m<<1-1 do
    57     begin
    58         lx:=round(a[i].x);
    59         a[i+1].x:=a[i+1].x+lx div 10;
    60         a[i].x:=lx mod 10;
    61     end;
    62         len:=m<<1-1;
    63         while a[len].x<1e-12 do dec(len);
    64     for i:=len downto 0 do write(a[i].x:0:0);
    65     writeln;
    66 end;
    67 procedure main;
    68 var i:longint;
    69 begin
    70     read(ch);
    71     while ord(ch)>=48 do begin s1:=s1+ch; read(ch); end;
    72     readln(s2);
    73     clr(a); clr(b);
    74     for i:=length(s1) downto 1 do a[length(s1)-i].x:=ord(s1[i])-48;
    75     for i:=length(s2) downto 1 do b[length(s2)-i].x:=ord(s2[i])-48;
    76     if length(s1)>length(s2) then m:=length(s1) else m:=length(s2);
    77     FFT;
    78 end;
    79 begin
    80     main;
    81 end.
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  • 原文地址:https://www.cnblogs.com/rpSebastian/p/4330807.html
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