For Last K Gene has posted the right Approach. For First K Hint : Logarithms log(N^N) = NlgN
On Tue, Oct 4, 2011 at 1:14 AM, Gene <[email protected]> wrote: > I have not done this, so I'm not sure. But there are some tricks. > > You can first break up the computation to exploit repeated squaring. > Rather than n-1 multiplications, you can get away with log_2 n by > computing > > n_1 = n^2 > n_2 = n_1^2 > n_3 = n_2^2 > so that n_i = n^{2^i} > for i=1..N where n_N <= n and n_{N+1} > n > > Let b_i be the i'th bit of n. > > Then n^n = product_{ i | b_i = 1 } ( n_i ) > > Now as you say you can't afford to do the full multiply. So you'll > need two arbitrary precision multiplication algorithms keeping k > digits of precision each. The first is easy. Compute n^n as above > modulo 10^k (always throwing away higher order digits) to get the last > k digits. > > The high order digits is the tricky part. I think the basic idea is > to implement floating point yourself. I.e. keep k+some extra digits > of mantissa plus an exponent to show where the decimal place is. The > problem is you always need to keep enough extra digits beyond k to be > sure rounding up won't affect to top k. There should be simple > algorithm to determine when you can stop. > > Or you can take a chance and count on the fact that the probability of > carry out is limited for each digit, so with about 30 extra digits the > chances are pretty close to zero. > > > On Oct 3, 8:18 pm, g4ur4v <[email protected]> wrote: > > can anyone please help me on how to approach this problem=> > http://www.codechef.com/problems/MARCHA4 > > -- > You received this message because you are subscribed to the Google Groups > "Algorithm Geeks" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/algogeeks?hl=en. > > -- Sunny Aggrawal B.Tech. V year,CSI Indian Institute Of Technology,Roorkee -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
