Elegant.. I think it can't be better than this. Identifying that each of them are on different sides of S/2 was the key!
On Tue, Aug 4, 2009 at 10:05 AM, Prunthaban Kanthakumar < pruntha...@gmail.com> wrote: > Here is the right answer: > > Find the sum of missing numbers. Call it S (this is a easy to do). > Now the two missing numbers are such that one is <=S/2 and the other is > > S/2 > Have two variables S1 and S2, traverse the array and add everything <= S/2 > to S1 and > S/2 to S2. > Now > First number = (Sum of numbers from 1 to S/2) - S1 > Second Number = (Sum of numbers from [S/2 + 1] to n+2) - S2 > > O(n) time and O(1) space. > > > On Tue, Aug 4, 2009 at 3:28 AM, Karthik Singaram Lakshmanan < > karthiksinga...@gmail.com> wrote: > >> >> well..will this work? >> >> x + y = SUM(1:N+2) - SUM(array) = a >> x^2 + y^2 = SUM(1^2:(N+2)^2) - SUM(array.^2) = b >> so (a^2 - b) = 2xy >> >> so xy = (a^2-b)/2 = k (say) >> >> now, >> >> x + (k/x) = a >> >> x^2 + k = ax >> (x, y) = (a +/- sqrt(a^2-4k))/2 >> >> I may not have written the equations correctly (need coffee !!!) >> but you get the general idea... >> solve a quadratic equation to solve for (x+y) = a and (x^2 + y^2) = b >> >> - Karthik >> >> >> > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/algogeeks -~----------~----~----~----~------~----~------~--~---
