시간 제한 | 메모리 제한 | 제출 | 정답 | 맞힌 사람 | 정답 비율 |
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2 초 (추가 시간 없음) | 2048 MB | 8 | 8 | 8 | 100.000% |
There are $n$ people, numbered from $1$ to $n$, sitting at a round table. Person $i + 1$ is sitting to the right of person $i$ (with person $1$ sitting to the right of person $n$).
You have come up with a better seating arrangement, which is given as a permutation $p_1$, $p_2$, $\dots$, $p_n$. More specifically, you want to change the seats of the people so that at the end person $p_{i+1}$ is sitting to the right of person $p_i$ (with person $p_1$ sitting to the right of person $p_n$). Notice that for each seating arrangement there are $n$ permutations that describe it (which can be obtained by rotations).
In order to achieve that, you can swap two people sitting at adjacent places; but there is a catch: for all $1 ≤ x ≤ n - 1$ you cannot swap person $x$ and person $x + 1$ (notice that you can swap person $n$ and person $1$). What is the minimum number of swaps necessary? It can be proven that any arrangement can be achieved.
Each test contains multiple test cases. The first line contains an integer $t$ ($1 ≤ t ≤ 10\,000$) — the number of test cases. The descriptions of the $t$ test cases follow.
The first line of each test case contains a single integer $n$ ($3 ≤ n ≤ 200\,000$) — the number of people sitting at the table.
The second line contains $n$ distinct integers $p_1$, $p_2$, $\dots$, $p_n$ ($1 ≤ p_i ≤ n$, $p_i \ne p_j$ for $i \ne j$) — the desired final order of the people around the table.
The sum of the values of $n$ over all test cases does not exceed $200\,000$.
For each test case, print the minimum number of swaps necessary to achieve the desired order.
3 4 2 3 1 4 5 5 4 3 2 1 7 4 1 6 5 3 7 2
1 10 22
Explanation of sample 1.
In the first test case, we can swap person $4$ and person $1$ (who are adjacent) in the initial configuration and get the order $[4, 2, 3, 1]$ which is equivalent to the desired one. Hence in this case a single swap is sufficient.
ICPC > Regionals > Europe > Southwestern European Regional Contest > SWERC 2021-2022 G번