ACK-Ackermann, 阿克曼函数

A(m, n) = \begin{cases} n+1 & \mbox{if } m = 0 \\ A(m-1, 1) & \mbox{if } m > 0 \mbox{ and } n = 0 \\ A(m-1, A(m, n-1)) & \mbox{if } m > 0 \mbox{ and } n > 0. \end{cases}

以前好几次在学语言的使用都有实现这个ack函数的经历，今天读本算法书，偶尔又提到了这个，查了下wiki来头好大

 

Values of A(m, n)
m\n01234n
0 1 2 3 4 5 n + 1
1 2 3 4 5 6 n + 2 = 2 + (n + 3) - 3
2 3 5 7 9 11 2n + 3 = 2\cdot(n + 3) - 3
3 5 13 29 61 125 2^{(n+3)} - 3
4 13

={2^{2^{2}}}-3		 65533

={2^{2^{2^{2}}}}-3		 265536 − 3

={2^{2^{2^{2^{2}}}}}-3		 {2^{2^{65536}}} - 3

={2^{2^{2^{2^{2^{2}}}}}}-3		 {2^{2^{2^{65536}}}} - 3

={2^{2^{2^{2^{2^{2^{2}}}}}}}-3		 \begin{matrix}\underbrace{{2^2}^{{\cdot}^{{\cdot}^{{\cdot}^2}}}} - 3 \\n\mbox{ + 3}\end{matrix}
posted @ 2014-03-06 15:13  卖程序的小歪  阅读(768)  评论(0)    收藏  举报