Let x = E[n=3]. We have an equation of the form x = 2 + x/3.
Solve for x. Paul Smith [email protected] On Mon, May 9, 2011 at 3:10 PM, Eagle <[email protected]> wrote: > @Pedro, > > In your last two steps, > >> E[n=3] = 2 + 1/3 * E[n=3] >> >> E[n=3] = 3 > > there is something wrong. How are you eliminating E[n=3] on the right > hand side of the equation? > > Eagle > > > > On May 9, 12:28 am, Pedro Osório <[email protected]> wrote: >> Hi Ricardo, >> >> For your example regarding 3, you have the following possibilities: >> >> 1 2 3 - perfect >> 1 3 2 - one correct >> 2 1 3 - one correct >> 2 3 1 - wrong >> 3 1 2 - wrong >> 3 2 1 - one correct >> >> As you can see, if goro hits without holding anything, 1/6 of the time >> it will be sorted, 1/2 of the time there will be 2 out of place and >> 1/3 of the time there will be 3 out of place. >> >> This means that: >> >> E[n=3] = 1 + (1/6 * 0 + 1/2 * E[n=2] + 1/3 * E[n=3]) >> >> As you have shown, E[n=2] = 2, so: >> >> E[n=3] = 2 + 1/3 * E[n=3] >> >> E[n=3] = 3 >> >> On May 8, 7:57 pm, werneckpaiva <[email protected]> wrote: >> >> > I read too and it doesn't make any sense for me. >> >> > I understand that this is a geometric distribution where if P(X)=p so >> > E(X)=1/p. So, if you have 2 numbers unsorted and Goro hits the table, >> > there is 0.5% chance to stay in the same position and 0.5% chance to >> > swap positions. But, if you have 3 unsorted elements, there are 6 >> > different permutations, so, P(X)=1/6 and the E(X)=6. My solution is >> > hold 1 number, swap the other 2; hold the sorted element and swap the >> > other 2 remaining, so 2 + 2 = 4 hits >> >> > 3 1 2 >> > 1 3 2 >> > 1 2 3 >> >> > But this doesn't seem to be the correct answer. The developers >> > solutions say that for 3 unsorted numbers needs only 3 hits. Anyone >> > knows how to explain that? >> >> > Regards, >> >> > Ricardo >> >> > On May 7, 8:24 pm, SwiftCoder <[email protected]> wrote: >> >> > > I looked at some of the solutions, as per that umber of hits are same >> > > as the count of numbers which are not at their correct sorted >> > > position. Is that so? > > -- > 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.
