Sleepy Cow Sorting
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Farmer John is attempting to sort his \(N\) cows (\(1 \leq N \leq 100\)),
conveniently numbered \(1 \dots N\), before they head out to the pastures for
breakfast.
Currently, the cows are standing in a line in the order
$p_1, p_2, p_3,
\dots, p_N\(, and\ Farmer\ John\ is\ standing\ in\ front\ of\ cow \)p_1$.
He wants to reorder the cows so that they are in the order \(1, 2, 3, \dots, N\),
with cow \(1\) next to Farmer John.
The cows are a bit sleepy today, so at any point in time the only cow who is
paying attention to Farmer John's instructions is the cow directly facing Farmer
John. In one time step, he can instruct this cow to move \(k\) paces down the
line, for any \(k\) in the range \(1 \ldots N-1\). The \(k\) cows whom she passes will
amble forward, making room for her to insert herself in the line after them.
For example, suppose that \(N=4\) and the cows start off in the following order:
FJ: 4, 3, 2, 1
The only cow paying attention to FJ is cow \(4\). If he instructs her to move \(2\)
paces down the line, the order will subsequently look like this:
FJ: 3, 2, 4, 1
Now the only cow paying attention to FJ is cow \(3\), so in the second time step
he may give cow \(3\) an instruction, and so forth until the cows are sorted.
Farmer John is eager to complete the sorting, so he can go back to the farmhouse
for his own breakfast. Help him find the minimum number of time steps required
to sort the cows.
Problem credits: Dhruv Rohatgi
Problem credits: Dhruv Rohatgi
The first line of input contains \(N\).
The second line contains \(N\) space-separated integers,
\(p_1, p_2, p_3, \dots, p_N\), indicating the starting order of the cows.
A single integer: the number of time steps before the \(N\) cows are in sorted
order, if Farmer John acts optimally.
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출처 올림피아드 > USACO > 2018-2019 > January > Bronze
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Sleepy Cow Sorting