Permutation Minimization by Deque

2000ms

262144K

Description:

In fact, the problems E1 and E2 do not have much in common. You should probably think of them as two separate problems.

A permutation $$$p$$$ of size $$$n$$$ is given. A permutation of size $$$n$$$ is an array of size $$$n$$$ in which each integer from $$$1$$$ to $$$n$$$ occurs exactly once. For example, $$$[1, 4, 3, 2]$$$ and $$$[4, 2, 1, 3]$$$ are correct permutations while $$$[1, 2, 4]$$$ and $$$[1, 2, 2]$$$ are not.

Let us consider an empty deque (double-ended queue). A deque is a data structure that supports adding elements to both the beginning and the end. So, if there are elements $$$[1, 5, 2]$$$ currently in the deque, adding an element $$$4$$$ to the beginning will produce the sequence $$$[\color{red}{4}, 1, 5, 2]$$$, and adding same element to the end will produce $$$[1, 5, 2, \color{red}{4}]$$$.

The elements of the permutation are sequentially added to the initially empty deque, starting with $$$p_1$$$ and finishing with $$$p_n$$$. Before adding each element to the deque, you may choose whether to add it to the beginning or the end.

For example, if we consider a permutation $$$p = [3, 1, 2, 4]$$$, one of the possible sequences of actions looks like this:

$$$\quad$$$ 1.	add $$$3$$$ to the end of the deque:	deque has a sequence $$$[\color{red}{3}]$$$ in it;
$$$\quad$$$ 2.	add $$$1$$$ to the beginning of the deque:	deque has a sequence $$$[\color{red}{1}, 3]$$$ in it;
$$$\quad$$$ 3.	add $$$2$$$ to the end of the deque:	deque has a sequence $$$[1, 3, \color{red}{2}]$$$ in it;
$$$\quad$$$ 4.	add $$$4$$$ to the end of the deque:	deque has a sequence $$$[1, 3, 2, \color{red}{4}]$$$ in it;

Find the lexicographically smallest possible sequence of elements in the deque after the entire permutation has been processed.

A sequence $$$[x_1, x_2, \ldots, x_n]$$$ is lexicographically smaller than the sequence $$$[y_1, y_2, \ldots, y_n]$$$ if there exists such $$$i \leq n$$$ that $$$x_1 = y_1$$$, $$$x_2 = y_2$$$, $$$\ldots$$$, $$$x_{i - 1} = y_{i - 1}$$$ and $$$x_i < y_i$$$. In other words, if the sequences $$$x$$$ and $$$y$$$ have some (possibly empty) matching prefix, and the next element of the sequence $$$x$$$ is strictly smaller than the corresponding element of the sequence $$$y$$$. For example, the sequence $$$[1, 3, 2, 4]$$$ is smaller than the sequence $$$[1, 3, 4, 2]$$$ because after the two matching elements $$$[1, 3]$$$ in the start the first sequence has an element $$$2$$$ which is smaller than the corresponding element $$$4$$$ in the second sequence.

Input:

The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 1000$$$) — the number of test cases.

The next $$$2t$$$ lines contain descriptions of the test cases.

The first line of each test case description contains an integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — permutation size. The second line of the description contains $$$n$$$ space-separated integers $$$p_i$$$ ($$$1 \le p_i \le n$$$; all $$$p_i$$$ are all unique) — elements of the permutation.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output:

Print $$$t$$$ lines, each line containing the answer to the corresponding test case. The answer to a test case should contain $$$n$$$ space-separated integer numbers — the elements of the lexicographically smallest permutation that is possible to find in the deque after executing the described algorithm.

Sample Input:

Sample Output:

Note:

One of the ways to get a lexicographically smallest permutation $$$[1, 3, 2, 4]$$$ from the permutation $$$[3, 1, 2, 4]$$$ (the first sample test case) is described in the problem statement.

Informação

Provedor Codeforces

Código CF1579E1