用Python做50道ACM之《Ackermann Function》

19.Ackermann Function

http://acm.fzu.edu.cn/problem.php?pid=1042

先编写递归函数，输入较小规模的数据观察输出结果，后利用规律编写函数直接获得结果。

# 编写递归函数，输入较小规模数据进行观察

def ackermann(m,n,dic):
    if str([m,n]) in dic.keys():
        return dic[str([m,n])]
    if m==0:
        result=n+1
        dic[str([m,n])]=result
        return result
    elif m>0 and n==0:
        result=ackermann(m-1,1,dic)
        dic[str([m,n])]=result
        return result
    else:
        result=ackermann(m-1,ackermann(m,n-1,dic),dic)
        dic[str([m,n])]=result
        return result

dic={}
for i in range(0,3):
    for j in range(0,1001):
        print(ackermann(i,j,dic),end=',')
    print()
    print('-'*55)
print()
for j in range(0,11):
    print(ackermann(3,j,dic),end=',')

def ackermann_quick(m,n):
    if m==0:
        return n+1
    elif m==1:
        return n+2
    elif m==2:
        return 2*(n+1)+1
    else:
        if n==0:
            return 5
        else:
            result=5
            for i in range(0,n):
                result=(result*2+3)
            return result

import sys

for read_in in sys.stdin.readlines():
    m,n=tuple([int(x) for x in read_in.rstrip().split(' ')])
    print(ackermann_quick(m,n))