A13702 | Circle Coloring
时间限制1s
内存限制256MB
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题目描述
You are given three sequences: $a_1, a_2, \ldots, a_n$ ; $b_1, b_2, \ldots, b_n$ ; $c_1, c_2, \ldots, c_n$ .
For each $i$ , $a_i \neq b_i$ , $a_i \neq c_i$ , $b_i \neq c_i$ .
Find a sequence $p_1, p_2, \ldots, p_n$ , that satisfy the following conditions:
- $p_i \in \{a_i, b_i, c_i\}$
- $p_i \neq p_{(i \mod n) + 1}$ .
In other words, for each element, you need to choose one of the three possible values, such that no two adjacent elements (where we consider elements $i,i+1$ adjacent for $i<n$ and also elements $1$ and $n$ ) will have equal value.
It can be proved that in the given constraints solution always exists. You don't need to minimize/maximize anything, you need to find any proper sequence.
For each $i$ , $a_i \neq b_i$ , $a_i \neq c_i$ , $b_i \neq c_i$ .
Find a sequence $p_1, p_2, \ldots, p_n$ , that satisfy the following conditions:
- $p_i \in \{a_i, b_i, c_i\}$
- $p_i \neq p_{(i \mod n) + 1}$ .
In other words, for each element, you need to choose one of the three possible values, such that no two adjacent elements (where we consider elements $i,i+1$ adjacent for $i<n$ and also elements $1$ and $n$ ) will have equal value.
It can be proved that in the given constraints solution always exists. You don't need to minimize/maximize anything, you need to find any proper sequence.
输入格式
The first line of input contains one integer $t$ ( $1 \leq t \leq 100$ ): the number of test cases.
The first line of each test case contains one integer $n$ ( $3 \leq n \leq 100$ ): the number of elements in the given sequences.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \leq a_i \leq 100$ ).
The third line contains $n$ integers $b_1, b_2, \ldots, b_n$ ( $1 \leq b_i \leq 100$ ).
The fourth line contains $n$ integers $c_1, c_2, \ldots, c_n$ ( $1 \leq c_i \leq 100$ ).
It is guaranteed that $a_i \neq b_i$ , $a_i \neq c_i$ , $b_i \neq c_i$ for all $i$ .
The first line of each test case contains one integer $n$ ( $3 \leq n \leq 100$ ): the number of elements in the given sequences.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \leq a_i \leq 100$ ).
The third line contains $n$ integers $b_1, b_2, \ldots, b_n$ ( $1 \leq b_i \leq 100$ ).
The fourth line contains $n$ integers $c_1, c_2, \ldots, c_n$ ( $1 \leq c_i \leq 100$ ).
It is guaranteed that $a_i \neq b_i$ , $a_i \neq c_i$ , $b_i \neq c_i$ for all $i$ .
输出格式
For each test case, print $n$ integers: $p_1, p_2, \ldots, p_n$ ( $p_i \in \{a_i, b_i, c_i\}$ , $p_i \neq p_{i \mod n + 1}$ ).
If there are several solutions, you can print any.
If there are several solutions, you can print any.
输入输出样例
输入 #1
5 3 1 1 1 2 2 2 3 3 3 4 1 2 1 2 2 1 2 1 3 4 3 4 7 1 3 3 1 1 1 1 2 4 4 3 2 2 4 4 2 2 2 4 4 2 3 1 2 1 2 3 3 3 1 2 10 1 1 1 2 2 2 3 3 3 1 2 2 2 3 3 3 1 1 1 2 3 3 3 1 1 1 2 2 2 3
输出 #1
1 2 3 1 2 1 2 1 3 4 3 2 4 2 1 3 2 1 2 3 1 2 3 1 2 3 2
In the first test case $p = [1, 2, 3]$ .
It is a correct answer, because:
- $p_1 = 1 = a_1$ , $p_2 = 2 = b_2$ , $p_3 = 3 = c_3$
- $p_1 \neq p_2 $ , $p_2 \neq p_3 $ , $p_3 \neq p_1$
All possible correct answers to this test case are: $[1, 2, 3]$ , $[1, 3, 2]$ , $[2, 1, 3]$ , $[2, 3, 1]$ , $[3, 1, 2]$ , $[3, 2, 1]$ .
In the second test case $p = [1, 2, 1, 2]$ .
In this sequence $p_1 = a_1$ , $p_2 = a_2$ , $p_3 = a_3$ , $p_4 = a_4$ . Also we can see, that no two adjacent elements of the sequence are equal.
In the third test case $p = [1, 3, 4, 3, 2, 4, 2]$ .
In this sequence $p_1 = a_1$ , $p_2 = a_2$ , $p_3 = b_3$ , $p_4 = b_4$ , $p_5 = b_5$ , $p_6 = c_6$ , $p_7 = c_7$ . Also we can see, that no two adjacent elements of the sequence are equal.
It is a correct answer, because:
- $p_1 = 1 = a_1$ , $p_2 = 2 = b_2$ , $p_3 = 3 = c_3$
- $p_1 \neq p_2 $ , $p_2 \neq p_3 $ , $p_3 \neq p_1$
All possible correct answers to this test case are: $[1, 2, 3]$ , $[1, 3, 2]$ , $[2, 1, 3]$ , $[2, 3, 1]$ , $[3, 1, 2]$ , $[3, 2, 1]$ .
In the second test case $p = [1, 2, 1, 2]$ .
In this sequence $p_1 = a_1$ , $p_2 = a_2$ , $p_3 = a_3$ , $p_4 = a_4$ . Also we can see, that no two adjacent elements of the sequence are equal.
In the third test case $p = [1, 3, 4, 3, 2, 4, 2]$ .
In this sequence $p_1 = a_1$ , $p_2 = a_2$ , $p_3 = b_3$ , $p_4 = b_4$ , $p_5 = b_5$ , $p_6 = c_6$ , $p_7 = c_7$ . Also we can see, that no two adjacent elements of the sequence are equal.
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