Bessie and Elsie are helping Farmer John wash the dishes, a more complicated
process than one might think due to their lack of opposable thumbs.

The two cows decide that Bessie will apply soap, and Elsie will rinse. Bessie is
given a dirty stack of plates labeled \(1\) through \(N\) (\(1 \leq N \leq 10^5\))
Elsie has an empty stack, where clean plates will go. There is a counter in
between Bessie and Elsie for soapy stacks.

At each step, either:

• Bessie takes a plate from the top of the dirty stack, applies soap, and then places it on the counter. When placing a soapy plate on the counter, Bessie must either (i) place the plate on top of an existing non-empty soapy stack or (ii) create a new soapy stack to the right of all existing soapy stacks.
• Elsie takes a plate from the top of the leftmost soapy stack. Elsie rinses the plate, then places it on top of the clean stack.

The goal is for the clean stack to have all plates in order, with the smallest
label on the bottom and the largest label on the top. It may not be possible
for the cows to achieve this goal for the entire stack of plates, so please
determine the length of the largest prefix of the input ordering for which the
goal is achievable.

Problem credits: George Xing

Problem credits: George Xing

The first line of input contains \(N\). The next \(N\) lines specify the order of
the dishes in Bessie's stack, with the first number being the dish on top of the
stack.

Please output the length of the longest prefix of the input stack that can be
successfully washed so that the plates end up ordered properly in the clean
stack.

riseoj 작성

출처 올림피아드 > USACO > 2018-2019 > February > Gold