【UOJ34】高精度乘法（FFT）

题意：

思路：FFT模板，自带10倍常数

  1 type cp=record
  2          x,y:double;
  3         end;
  4      arr=array[0..510000]of cp;
  5 var a,b,cur:arr;
  6     n,m,n1,n2,i,j:longint;
  7     x:double;
  8 
  9 function jia(a,b:cp;f:longint):cp;
 10 begin
 11  if f=-1 then
 12  begin
 13   b.x:=-b.x; b.y:=-b.y;
 14  end;
 15  jia.x:=a.x+b.x;
 16  jia.y:=a.y+b.y;
 17 end;
 18 
 19 function mult(a,b:cp):cp;
 20 begin
 21  mult.x:=a.x*b.x-a.y*b.y;
 22  mult.y:=a.x*b.y+a.y*b.x;
 23 end;
 24 
 25 procedure swap(var x,y:cp);
 26 var t:cp;
 27 begin
 28  t:=x; x:=y; y:=t;
 29 end;
 30 
 31 function max(x,y:longint):longint;
 32 begin
 33  if x>y then exit(x);
 34  exit(y);
 35 end;
 36 
 37 procedure fft(var a:arr;n,f:longint);
 38 var i,j,k,m:longint;
 39     w,u,v:cp;
 40 
 41 begin
 42  i:=n>>1; j:=1;
 43  while j<n do
 44  begin
 45   if i<j then swap(a[i],a[j]);
 46   k:=n>>1;
 47   while k and i>0 do
 48   begin
 49    i:=i xor k;
 50    k:=k>>1;
 51   end;
 52   i:=i xor k;
 53   inc(j);
 54  end;
 55  m:=2;
 56  while m<=n do
 57  begin
 58   w.x:=cos(2*pi*f/m); w.y:=sin(2*pi*f/m);
 59   cur[0].x:=1; cur[0].y:=0;
 60   for i:=1 to m-1 do cur[i]:=mult(cur[i-1],w);
 61   i:=0;
 62   while i<n do
 63   begin
 64    j:=i;
 65    while j<i+(m>>1) do
 66    begin
 67     u:=a[j]; v:=mult(a[j+(m>>1)],cur[j-i]);
 68     a[j]:=jia(u,v,1);
 69     a[j+(m>>1)]:=jia(u,v,-1);
 70     inc(j);
 71    end;
 72    i:=i+m;
 73   end;
 74   m:=m<<1;
 75  end;
 76 end;
 77 
 78 begin
 79  assign(input,'uoj34.in'); reset(input);
 80  assign(output,'uoj34.out'); rewrite(output);
 81  readln(n1,n2);
 82  inc(n1); inc(n2);
 83  for i:=0 to n1-1 do
 84  begin
 85   read(x); a[i].x:=x;
 86  end;
 87  for i:=0 to n2-1 do
 88  begin
 89   read(x); b[i].x:=x;
 90  end;
 91  n:=max(n1,n2);
 92  m:=1;
 93  while m<=(n<<1) do m:=m<<1;
 94  fft(a,m,1); fft(b,m,1);
 95  for i:=0 to m do a[i]:=mult(a[i],b[i]);
 96  fft(a,m,-1);
 97  for i:=0 to n1+n2-2 do write(round(a[i].x/m),' ');
 98  close(input);
 99  close(output);
100 end.

 

posted on 2017-04-19 17:05  myx12345  阅读(184)  评论(0)  编辑  收藏  举报

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