Codeforces 977D Editorial

Revision en11, by aMitkvikram, 2018-06-21 20:00:24

977D — Divide by three, multiply by two

  1. We can see that all numbers in given sequence are distinct. since all numbers in sequence are of the form . Hence if ai = aj then = = 2x - m = 3y - n which is not possible because any power of 2 will be an even number and any power of 3 will be an odd number.

  2. if there exists in sequence then 2 * ai can not be in sequence and vice versa. We can prove it using contradiction. Suppose there is a number ai such that both and 2 * ai exists in sequence. by little bit of tricks this = , this again is not possible by same argument as above, we just have to change the order of exponents.

  3. Hence for each ai in sequence we see if or 2 * ai is present(remember that only one of them can be present). Now if there is any ai such that both and 2 * ai is not in sequence then this should be an. if there is any such ai that for all 0 ≤  j ≤ n:   ≠  ai AND 2 * ai  ≠  ai, then this is a1.

  4. Once you have got a1, you keep on producing sequence just by doing binary search for and 2 * ai (remember only one of them is present so once you find it you print it).

Tags dfs and similar, #sorting, #binary search

History

 
 
 
 
Revisions
 
 
  Rev. Lang. By When Δ Comment
en11 English aMitkvikram 2018-06-21 20:00:24 13
en10 English aMitkvikram 2018-06-21 19:59:23 14
en9 English aMitkvikram 2018-06-21 19:58:14 46 Tiny change: '^m}{3^n}$ which is n' -> '^m}{3^n}$ $\implies$ $2^{x - m} = 3^{y - n}$which is n'
en8 English aMitkvikram 2018-05-07 16:44:43 2 (published)
en7 English aMitkvikram 2018-05-07 16:43:12 2 Tiny change: 'eq$ $j\leq$ $\dfrac{' -> 'eq$ $j\leqn:$ $\dfrac{'
en6 English aMitkvikram 2018-05-07 16:42:31 5
en5 English aMitkvikram 2018-05-07 16:41:49 3 Tiny change: 'l $0\leq$ j $ $\leq$ $\' -> 'l $0\leq$ $j $\leq$ $\'
en4 English aMitkvikram 2018-05-07 16:41:03 17
en3 English aMitkvikram 2018-05-07 16:39:32 5
en2 English aMitkvikram 2018-05-07 16:37:18 1244 Tiny change: 'n4. Once yuou have go' -> 'n4. Once you have go'
en1 English aMitkvikram 2018-05-07 16:17:24 339 Initial revision (saved to drafts)