[英]Q: Solving the following recurrence: T(n) = 8T(n/8) + n log n
I am trying to solve the following recurrence: 我正在尝试解决以下重复问题:
T(n) = 8T(n/8) + n* log n.
I currently have done the following but am not sure if I am on the right track: 我目前已经完成了以下工作,但不确定自己是否步入正轨:
1. T(n)= 8 T(n/8) + n log n;
2. T(n)= 8^2 T(n/8^2) + n log (n/8) + n log n
3. T(n)= 8^3 T(n/8^3) + n log (n/8^2) + n log (n/8) + n log n
So the general formula came up for me as: 因此,我得出的一般公式为:
T(n)= 8^k T(n/8^k) + n log(n* n/8 * n/8^2 * ... * n/8^k).
And i am not sure how to continue this. 而且我不确定如何继续进行。 I tried to rewrite the log
as n^k / 8^(k*(k+1)/2)
, but I still don't see the solution. 我试图将log
重写为n^k / 8^(k*(k+1)/2)
,但是仍然看不到解决方案。
You are almost there. 你快到了 Set k = log_8(n)
then you can solve for T(n)
设置k = log_8(n)
则可以求解T(n)
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