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前者用分制,比较简单;后者用傅立叶变换

Posted by hawk at 2003-10-18 10:48:57 on Problem 1405
In Reply To:老大讲解一下吧:) Posted by:gz2001 at 2003-10-18 10:38:08
具体资料网上有,自己查一下看:)
下面简略说一下分制,估计大多数都也都知道的:
用分制比如就把乘数分为两部分(可以按照高位,低位分也可以按照奇数位偶数位分)
X=A*2^k+B;Y=C*2^k+D
然后有X*Y=A*B*2^(2k)+(A*D+B*C)*2^k+C*D;
这里只要计算3次n/2(设原来的X和Y都是n位的)乘法
K1=A*B;
K2=C*D;
K3=(A+B)*(C+D)-K1-K2=A*D+B*C;
时间复杂度就是T(n)=3T(n/2)+O(n);
就是n^lg3的复杂度

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