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A顺序定义如下:
Start with the natural numbers 1,2,3,...
Initialize count = 1;
while(there are uncrossed numbers)
{
pick the first uncrossed number say n.
set A[count] = n.
Cross out the number count+n.
Cross out the number n
Increment count.
}
快速算法确定A[n],考虑到N.。
Try 获取一种算法,该算法在原体中是多功能的。
询问这一问题。
显然,这是一种称为Wythoff序列的著名顺序,A[n] = [n*phi]对A[n]规定了一种划线公式,其中[x] = 食物和营养的有机组成部分是黄金比率。
为了计算[n],我们可以将营养作为连续的菲克斯数字的比例,给出奥(logn logn)算法(O(logn)时间对奥(log n)的比值做算法。
在这方面,它是如何开始的。
1 2 3 4 5 6 7 8 ... A[1] = 1, cross 2
1 X 3 4 5 6 7 8 ... A[2] = 1, cross 3
1 X X 4 5 6 7 8 ... A[3] = 1, cross 4
...
第1号从未跨越,因为可以跨越的最少数量是1+1=2。
因此,时间算法不变: A[n] = 1
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