Contest analysis proves this by induction http://code.google.com/codejam/contest/dashboard?c=975485#s=a&a=3
On 18 May 2011 03:29, Steven Hao <[email protected]> wrote: > anyone have an inductive proof for Expected smashes = #elements in > wrong position? I tried to prove it after I finished the contest but I > couldn't figure it out. > > On May 16, 3:31 am, Bharath Raghavendran <[email protected]> wrote: >> Thanks Pedro ... I did not say you wrote so .. I was just asking if >> what I am saying is correct :) >> >> On 16 May 2011 15:51, Pedro Osório <[email protected]> wrote: >> >> > @Brats: >> > I didn't write E[n=a+1] = 1 + E(n=a), I wrote for the specific case of a=3 >> > (which is true for all a>1) that: >> > E[n=a] = 1+ sum( p(n=0) * E[n=0] + p(n=1) * E[n=1] + ... + p(n=a) * E[n=a]) >> > Where the n on the LHS is the number of elements in the wrong position >> > before hitting and on the RHS the same after hitting. >> > For a=3 the probabilities are trivial to compute, and hence I used it as an >> > example (because Eagle insisted that E[n=3] > 3), for bigger a this >> > computation is not so easy, but it's still correct. >> > I know the notation is strange, but relating to lemma 1, my E[n=a] is >> > simply >> > x(A), when A has 'a' elements out of place, and my p(n=b) is simply pb. >> >> > -- >> > You received this message because you are subscribed to the Google Groups >> > "google-codejam" 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/google-code?hl=en. > > -- > You received this message because you are subscribed to the Google Groups > "google-codejam" 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/google-code?hl=en. > > -- You received this message because you are subscribed to the Google Groups "google-codejam" 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/google-code?hl=en.
