Codeforces Round 848 (Div. 2) |
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You are given a permutation $$$p$$$ of length $$$n$$$, an array of $$$m$$$ distinct integers $$$a_1, a_2, \ldots, a_m$$$ ($$$1 \le a_i \le n$$$), and an integer $$$d$$$.
Let $$$\mathrm{pos}(x)$$$ be the index of $$$x$$$ in the permutation $$$p$$$. The array $$$a$$$ is not good if
For example, with the permutation $$$p = [4, 2, 1, 3, 6, 5]$$$ and $$$d = 2$$$:
In one move, you can swap two adjacent elements of the permutation $$$p$$$. What is the minimum number of moves needed such that the array $$$a$$$ becomes good? It can be shown that there always exists a sequence of moves so that the array $$$a$$$ becomes good.
A permutation is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array) and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$, but there is $$$4$$$ in the array).
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.
The first line of each test case contains three integers $$$n$$$, $$$m$$$ and $$$d$$$ ($$$2\leq n \leq 10^5$$$, $$$2\leq m\leq n$$$, $$$1 \le d \le n$$$), the length of the permutation $$$p$$$, the length of the array $$$a$$$ and the value of $$$d$$$.
The second line contains $$$n$$$ integers $$$p_1, p_2, \ldots, p_n$$$ ($$$1\leq p_i \leq n$$$, $$$p_i \ne p_j$$$ for $$$i \ne j$$$).
The third line contains $$$m$$$ distinct integers $$$a_1, a_2, \ldots, a_m$$$ ($$$1\leq a_i \leq n$$$, $$$a_i \ne a_j$$$ for $$$i \ne j$$$).
The sum of $$$n$$$ over all test cases doesn't exceed $$$5 \cdot 10^5$$$.
For each test case, print the minimum number of moves needed such that the array $$$a$$$ becomes good.
54 2 21 2 3 41 35 2 45 4 3 2 15 25 3 33 4 1 5 23 1 22 2 11 22 16 2 41 2 3 4 5 62 5
1 3 2 0 2
In the first case, $$$pos(a_1)=1$$$, $$$pos(a_2)=3$$$. To make the array good, one way is to swap $$$p_3$$$ and $$$p_4$$$. After that, the array $$$a$$$ will be good because the condition $$$\mathrm{pos}(a_2) \le \mathrm{pos}(a_1) + d$$$ won't be satisfied.
In the second case, $$$pos(a_1)=1$$$, $$$pos(a_2)=4$$$. The $$$3$$$ moves could be:
In the third case, $$$pos(a_1)=1$$$, $$$pos(a_2)=3$$$, $$$pos(a_3)=5$$$. The $$$2$$$ moves can be:
In the fourth case, $$$pos(a_1)=2$$$, $$$pos(a_2)=1$$$. The array $$$a$$$ is already good.
In the fifth case, $$$pos(a_1)=2$$$, $$$pos(a_2)=5$$$. The $$$2$$$ moves are:
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