102981: [Atcoder]ABC298 B - Coloring Matrix
Description
Score : $200$ points
Problem Statement
You are given $N$-by-$N$ matrices $A$ and $B$ where each element is $0$ or $1$.
Let $A_{i,j}$ and $B_{i,j}$ denote the element at the $i$-th row and $j$-th column of $A$ and $B$, respectively.
Determine whether it is possible to rotate $A$ so that $B_{i,j} = 1$ for every pair of integers $(i, j)$ such that $A_{i,j} = 1$.
Here, to rotate $A$ is to perform the following operation zero or more times:
- for every pair of integers $(i, j)$ such that $1 \leq i, j \leq N$, simultaneously replace $A_{i,j}$ with $A_{N + 1 - j,i}$.
Constraints
- $1 \leq N \leq 100$
- Each element of $A$ and $B$ is $0$ or $1$.
- All values in the input are integers.
Input
The input is given from Standard Input in the following format:
$N$
$A_{1,1}$ $A_{1,2}$ $\ldots$ $A_{1,N}$
$\vdots$
$A_{N,1}$ $A_{N,2}$ $\ldots$ $A_{N,N}$
$B_{1,1}$ $B_{1,2}$ $\ldots$ $B_{1,N}$
$\vdots$
$B_{N,1}$ $B_{N,2}$ $\ldots$ $B_{N,N}$
Output
If it is possible to rotate $A$ so that $B_{i,j} = 1$ for every pair of integers $(i, j)$ such that $A_{i,j} = 1$, print Yes; otherwise, print No.
Sample Input 1
3 0 1 1 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1
Sample Output 1
Yes
Initially, $A$ is :
0 1 1 1 0 0 0 1 0
After performing the operation once, $A$ is :
0 1 0 1 0 1 0 0 1
After performing the operation once again, $A$ is :
0 1 0 0 0 1 1 1 0
Here, $B_{i,j} = 1$ for every pair of integers $(i, j)$ such that $A_{i,j} = 1$, so you should print Yes.
Sample Input 2
2 0 0 0 0 1 1 1 1
Sample Output 2
Yes
Sample Input 3
5 0 0 1 1 0 1 0 0 1 0 0 0 1 0 1 0 1 0 1 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0
Sample Output 3
No
Input
题意翻译
给定两个 $N\times N$ 的矩阵 $A$ 和 $B$，都由 $0$ 和 $1$ 组成。 你可以将 $A$ 顺时针旋转 $0\degree,90\degree,180\degree$ 或 $270\degree$（任选其一）。 判断旋转后的 $A$ 能否满足： - 对于每个 $A_{i,j}=1$ 的 $(i,j)$，$B_{i,j}=1$。 $1\le N\le 100$Output
分数：$200$分
问题描述
给你一个$N$乘$N$的矩阵$A$和$B$，每个元素为0或1。
设$A_{i,j}$和$B_{i,j}$分别表示矩阵$A$和$B$的第$i$行第$j$列的元素。
判断是否有可能通过旋转$A$，使得对于所有满足$A_{i,j}=1$的整数对$(i, j)$，有$B_{i,j}=1$。
这里，旋转$A$是指执行以下操作0次或多次：
- 对于所有满足$1 \leq i, j \leq N$的整数对$(i, j)$，同时将$A_{i,j}$替换为$A_{N + 1 - j,i}$。
约束
- $1 \leq N \leq 100$
- $A$和$B$的每个元素为0或1。
- 输入中的所有值都是整数。
输入
输入从标准输入中以以下格式给出：
$N$
$A_{1,1}$ $A_{1,2}$ $\ldots$ $A_{1,N}$
$\vdots$
$A_{N,1}$ $A_{N,2}$ $\ldots$ $A_{N,N}$
$B_{1,1}$ $B_{1,2}$ $\ldots$ $B_{1,N}$
$\vdots$
$B_{N,1}$ $B_{N,2}$ $\ldots$ $B_{N,N}$
输出
如果有可能通过旋转$A$，使得对于所有满足$A_{i,j}=1$的整数对$(i, j)$，有$B_{i,j}=1$，则输出Yes；否则，输出No。
样例输入1
3 0 1 1 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1
样例输出1
Yes
最初，$A$为：
0 1 1 1 0 0 0 1 0
执行一次操作后，$A$为：
0 1 0 1 0 1 0 0 1
再次执行一次操作后，$A$为：
0 1 0 0 0 1 1 1 0
这里，对于所有满足$A_{i,j}=1$的整数对$(i, j)$，有$B_{i,j}=1$，所以你应该输出Yes。
样例输入2
2 0 0 0 0 1 1 1 1
样例输出2
Yes
样例输入3
5 0 0 1 1 0 1 0 0 1 0 0 0 1 0 1 0 1 0 1 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0
样例输出3
No