#P13021. [GCJ 2021 Qualification] Reversort

    ID: 12806 Type: RemoteJudge 10000ms 1024MiB Tried: 0 Accepted: 0 Difficulty: 2 Uploaded By: Tags>模拟2021Google Code Jam

[GCJ 2021 Qualification] Reversort

题目描述

Note: The main parts of the statements of the problems "Reversort" and "Reversort Engineering" are identical, except for the last paragraph. The problems can otherwise be solved independently.

Reversort is an algorithm to sort a list of distinct integers in increasing order. The algorithm is based on the "Reverse" operation. Each application of this operation reverses the order of some contiguous part of the list.

The pseudocode of the algorithm is the following:

Reversort(L):
  for i := 1 to length(L) - 1
    j := position with the minimum value in L between i and length(L), inclusive
    Reverse(L[i..j])

After i1i-1 iterations, the positions 1,2,,i11, 2, \ldots, i-1 of the list contain the i1i-1 smallest elements of LL, in increasing order. During the ii-th iteration, the process reverses the sublist going from the ii-th position to the current position of the ii-th minimum element. That makes the ii-th minimum element end up in the ii-th position.

For example, for a list with 4 elements, the algorithm would perform 3 iterations. Here is how it would process L=[4,2,1,3]L = [4, 2, 1, 3]:

  1. i=1i = 1, j=3L=[1,2,4,3]j = 3 \longrightarrow L = [1, 2, 4, 3]
  2. i=2i = 2, j=2L=[1,2,4,3]j = 2 \longrightarrow L = [1, 2, 4, 3]
  3. i=3i = 3, j=4L=[1,2,3,4]j = 4 \longrightarrow L = [1, 2, 3, 4]

The most expensive part of executing the algorithm on our architecture is the Reverse operation. Therefore, our measure for the cost of each iteration is simply the length of the sublist passed to Reverse, that is, the value ji+1j - i + 1. The cost of the whole algorithm is the sum of the costs of each iteration.

In the example above, the iterations cost 3, 1, and 2, in that order, for a total of 6.

Given the initial list, compute the cost of executing Reversort on it.

输入格式

The first line of the input gives the number of test cases, T\mathbf{T}. T\mathbf{T} test cases follow. Each test case consists of 2 lines. The first line contains a single integer N\mathbf{N}, representing the number of elements in the input list. The second line contains N\mathbf{N} distinct integers $\mathbf{L}_{1}, \mathbf{L}_{2}, \ldots, \mathbf{L}_{\mathbf{N}}$, representing the elements of the input list LL, in order.

输出格式

For each test case, output one line containing Case #xx: yy, where xx is the test case number (starting from 1) and yy is the total cost of executing Reversort on the list given as input.

3
4
4 2 1 3
2
1 2
7
7 6 5 4 3 2 1
Case #1: 6
Case #2: 1
Case #3: 12

提示

Sample Explanation

Sample Case #1 is described in the statement above.

In Sample Case #2, there is a single iteration, in which Reverse is applied to a sublist of size 1. Therefore, the total cost is 1.

In Sample Case #3, the first iteration reverses the full list, for a cost of 7. After that, the list is already sorted, but there are 5 more iterations, each of which contributes a cost of 1.

Limits

Test Set 1 (7 Pts, Visible Verdict)

  • 1T1001 \leq \mathbf{T} \leq 100.
  • 2N1002 \leq \mathbf{N} \leq 100.
  • 1LiN1 \leq \mathbf{L}_{i} \leq N, for all ii.
  • LiLj\mathbf{L}_{i} \neq \mathbf{L}_{j}, for all iji \neq j.