USACO 2018 Open Contest Silver, Problem 1.

Revision en2, by algo3rythm, 2019-06-25 14:11:34

Hello everyone,

Since yesterday I have been reading the above stated problem but am not still able to come up with a solution, I have seen the editorial but i don't understand the proof for the algorithm.

LINK TO PROBLEM: http://usaco.org/index.php?page=viewproblem2&cpid=834

EDITORIAL: http://usaco.org/current/data/sol_sort_silver_open18.html

PROBLEM STATEMENT

Keeping an eye on long term career possibilities beyond the farm, Bessie the cow has started learning algorithms from various on-line coding websites. Her favorite algorithm thus far is "bubble sort". Here is Bessie's implementation, in cow-code, for sorting an array A of length N.

sorted = false
while (not sorted):
   sorted = true
   moo
   for i = 0 to N-2:
      if A[i+1] < A[i]:
         swap A[i], A[i+1]
         sorted = false

Apparently, the "moo" command in cow-code does nothing more than print out "moo". Strangely, Bessie seems to insist on including it at various points in her code.

Given an input array, please predict how many times "moo" will be printed by Bessie's code.

N<=100,000, each element being an integer in the range 0…10^9. Input elements are not guaranteed to be distinct.

Please help me find an easier to understand solution to the problem, Thanks.

Tags usaco

History

 
 
 
 
Revisions
 
 
  Rev. Lang. By When Δ Comment
en2 English algo3rythm 2019-06-25 14:11:34 72
en1 English algo3rythm 2019-06-25 14:00:36 1345 Initial revision (published)