A16341. Neutral Tonality
编程题
普及/提高-
知识点
题目描述
You are given an array $a$ consisting of $n$ integers, as well as an array $b$ consisting of $m$ integers.
Let $\text{LIS}(c)$ denote the length of the [longest increasing subsequence](https://en.wikipedia.org/wiki/Longest_increasing_subsequence) of array $c$ . For example, $\text{LIS}([2, \underline{1}, 1, \underline{3}])$ = $2$ , $\text{LIS}([\underline{1}, \underline{7}, \underline{9}])$ = $3$ , $\text{LIS}([3, \underline{1}, \underline{2}, \underline{4}])$ = $3$ .
You need to insert the numbers $b_1, b_2, \ldots, b_m$ into the array $a$ , at any positions, in any order. Let the resulting array be $c_1, c_2, \ldots, c_{n+m}$ . You need to choose the positions for insertion in order to minimize $\text{LIS}(c)$ .
Formally, you need to find an array $c_1, c_2, \ldots, c_{n+m}$ that simultaneously satisfies the following conditions:
- The array $a_1, a_2, \ldots, a_n$ is a subsequence of the array $c_1, c_2, \ldots, c_{n+m}$ .
- The array $c_1, c_2, \ldots, c_{n+m}$ consists of the numbers $a_1, a_2, \ldots, a_n, b_1, b_2, \ldots, b_m$ , possibly rearranged.
- The value of $\text{LIS}(c)$ is the minimum possible among all suitable arrays $c$ .
Let $\text{LIS}(c)$ denote the length of the [longest increasing subsequence](https://en.wikipedia.org/wiki/Longest_increasing_subsequence) of array $c$ . For example, $\text{LIS}([2, \underline{1}, 1, \underline{3}])$ = $2$ , $\text{LIS}([\underline{1}, \underline{7}, \underline{9}])$ = $3$ , $\text{LIS}([3, \underline{1}, \underline{2}, \underline{4}])$ = $3$ .
You need to insert the numbers $b_1, b_2, \ldots, b_m$ into the array $a$ , at any positions, in any order. Let the resulting array be $c_1, c_2, \ldots, c_{n+m}$ . You need to choose the positions for insertion in order to minimize $\text{LIS}(c)$ .
Formally, you need to find an array $c_1, c_2, \ldots, c_{n+m}$ that simultaneously satisfies the following conditions:
- The array $a_1, a_2, \ldots, a_n$ is a subsequence of the array $c_1, c_2, \ldots, c_{n+m}$ .
- The array $c_1, c_2, \ldots, c_{n+m}$ consists of the numbers $a_1, a_2, \ldots, a_n, b_1, b_2, \ldots, b_m$ , possibly rearranged.
- The value of $\text{LIS}(c)$ is the minimum possible among all suitable arrays $c$ .
输入格式
Each test contains multiple test cases. The first line contains a single integer $t$ $(1 \leq t \leq 10^4)$ — the number of test cases. The description of the test cases follows.
The first line of each test case contains two integers $n, m$ $(1 \leq n \leq 2 \cdot 10^5, 1 \leq m \leq 2 \cdot 10^5)$ — the length of array $a$ and the length of array $b$ .
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ $(1 \leq a_i \leq 10^9)$ — the elements of the array $a$ .
The third line of each test case contains $m$ integers $b_1, b_2, \ldots, b_m$ $(1 \leq b_i \leq 10^9)$ — the elements of the array $b$ .
It is guaranteed that the sum of $n$ over all test cases does not exceed $2\cdot 10^5$ , and the sum of $m$ over all test cases does not exceed $2\cdot 10^5$ .
The first line of each test case contains two integers $n, m$ $(1 \leq n \leq 2 \cdot 10^5, 1 \leq m \leq 2 \cdot 10^5)$ — the length of array $a$ and the length of array $b$ .
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ $(1 \leq a_i \leq 10^9)$ — the elements of the array $a$ .
The third line of each test case contains $m$ integers $b_1, b_2, \ldots, b_m$ $(1 \leq b_i \leq 10^9)$ — the elements of the array $b$ .
It is guaranteed that the sum of $n$ over all test cases does not exceed $2\cdot 10^5$ , and the sum of $m$ over all test cases does not exceed $2\cdot 10^5$ .
输出格式
For each test case, output $n + m$ numbers — the elements of the final array $c_1, c_2, \ldots, c_{n+m}$ , obtained after the insertion, such that the value of $\text{LIS}(c)$ is minimized. If there are several answers, you can output any of them.
输入输出样例
输入 #1
7 2 1 6 4 5 5 5 1 7 2 4 5 5 4 1 2 7 1 9 7 1 2 3 4 5 6 7 8 9 3 2 1 3 5 2 4 10 5 1 9 2 3 8 1 4 7 2 9 7 8 5 4 6 2 1 2 2 1 6 1 1 1 1 1 1 1 777
输出 #1
6 5 4 1 1 7 7 2 2 4 4 5 5 9 8 7 7 6 5 4 3 2 1 1 3 5 2 4 1 9 2 3 8 8 1 4 4 7 7 2 9 6 5 2 2 1 777 1 1 1 1 1 1
说明/提示
In the first test case, $\text{LIS}(a) = \text{LIS}([6, 4]) = 1$ . We can insert the number $5$ between $6$ and $4$ , then $\text{LIS}(c) = \text{LIS}([6, 5, 4]) = 1$ .
In the second test case, $\text{LIS}([\underline{1}, 7, \underline{2}, \underline{4}, \underline{5}])$ = $4$ . After the insertion, $c = [1, 1, 7, 7, 2, 2, 4, 4, 5, 5]$ . It is easy to see that $\text{LIS}(c) = 4$ . It can be shown that it is impossible to achieve $\text{LIS}(c)$ less than $4$ .
In the second test case, $\text{LIS}([\underline{1}, 7, \underline{2}, \underline{4}, \underline{5}])$ = $4$ . After the insertion, $c = [1, 1, 7, 7, 2, 2, 4, 4, 5, 5]$ . It is easy to see that $\text{LIS}(c) = 4$ . It can be shown that it is impossible to achieve $\text{LIS}(c)$ less than $4$ .