基于python 的 分治算法 解决 大数乘法问题 -- 浅浅记录

分治方法 总的来说 还是递归的调用,将大的问题分解为小的问题

#通过分治 计算 n个0的字符串
def zero(n):
    if n==0:
        return ""
    if n==1:
        return "0"
    return zero(n//2)+zero(n//2)+zero(n%2)

#计算大数加法
def  add(a,b):
    if len(a)<=8 and len(b)<=8:
        return str( int(a)+int(b) )
    a1="0"
    a2=a
    if len(a)>8:
        a1=a[0:len(a)-8]
        a2=a[len(a)-8:]
                                         
    b1="0"
    b2=b
    if len(b)>8:
        b1=b[0:len(b)-8]
        b2=b[len(b)-8:]

    k=add(a2,b2)
    while(len(k)<8):
        k="0"+k
    if len(k)>8:
        return add( add(a1,b1),"1")+k[1:]
    return add(a1,b1)+k

def chengfa(a,b):
    if len(a)<=4 and len(b)<=4:
        return str( int(a)*int(b) )
    if len(a)>4:
        k=len(a)//2  #分治的中间值
        #通过计算超过长度4 下分解
        return  add( chengfa(a[0:k],b)+zero(len(a[k:] )),chengfa(a[k:],b) )
    return chengfa(b,a)
print(chengfa("999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999","999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999"))

运行结果;

== RESTART: C:\Users\Administrator\AppData\Local\Programs\Python\Python38\w.py =
999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001