给定两个大小为 NxN 的矩阵 mat1[][] 和 mat2[][]。我们的任务是判断这两个给定矩阵是否互为镜像。如果是，则打印 “Yes”，否则打印 “No”。
> 如果对于矩阵的任意有效索引，大小为 N*N 的两个矩阵 mat1 和 mat2 满足以下条件，则称它们互为镜像：
>
>
> mat1[i][j] = mat2[i][N-j-1]
> >
> !image
示例：
> 输入：
> mat1[][] = {{1, 2, 3}, {3, 4, 5}, {6, 7, 8}},
> mat2[][] = {{3, 2, 1}, {5, 4, 3}, {8, 7, 6}}
> 输出： Yes
>
>
>
>
>
> 输入：
> mat1 = {{1, 2, 3}, {5, 4, 1}, {6, 7, 2}};
> mat2 = {{3, 2, 1}, {5, 4, 1}, {2, 7, 6}};
> 输出： No
方法： 这种方法基于我们的观察：一个矩阵只有在满足以下条件时才是另一个矩阵的镜像：第一个矩阵每一行的元素必须等于另一个矩阵对应行的元素逆序排列的结果。让我们按照以下步骤进行操作：
- 从头到尾按行遍历矩阵 mat1[][]，并从尾到头按行遍历 mat2[][]。
- 在遍历过程中，如果发现 mat1[][] 的任何元素与 mat2[][] 对应位置的元素不相等，则打印 "No"。
- 遍完两个矩阵后，如果发现所有元素都相等，则打印 "Yes"。
下面是上述方法的实现：
C++
// C++ implementation of
// the above approach
#include
using namespace std;
// Function to check whether the
// two matrices are mirror
// of each other
void mirrorMatrix(int mat1[][4],
int mat2[][4], int N)
{
// Initialising row and column of
// second matrix
int row = 0;
int col = 0;
bool isMirrorImage = true;
// Iterating over the matrices
for (int i = 0; i = 0; j--) {
// If the element is not equal
if (mat2[row][col] != mat1[i][j]) {
isMirrorImage = false;
}
// Increment column
col++;
}
// Reset column to 0
// for new row
col = 0;
// Increment row
row++;
}
if (isMirrorImage)
cout << "Yes";
else
cout << "No";
}
// Driver code
int main()
{
// Given 2 matrices
int N = 4;
int mat1[][4] = { { 1, 2, 3, 4 },
{ 0, 6, 7, 8 },
{ 9, 10, 11, 12 },
{ 13, 14, 15, 16 } };
int mat2[][4] = { { 4, 3, 2, 1 },
{ 8, 7, 6, 0 },
{ 12, 11, 10, 9 },
{ 16, 15, 14, 13 } };
// Function Call
mirrorMatrix(mat1, mat2, N);
}
Java
// Java implementation of
// the above approach
import java.util.*;
class GFG{
// Function to check whether the
// two matrices are mirror
// of each other
static void mirrorMatrix(int mat1[][],
int mat2[][], int N)
{
// Initialising row and column of
// second matrix
int row = 0;
int col = 0;
boolean isMirrorImage = true;
// Iterating over the matrices
for (int i = 0; i = 0; j--)
{
// If the element is not equal
if (mat2[row][col] != mat1[i][j])
{
isMirrorImage = false;
}
// Increment column
col++;
}
// Reset column to 0
// for new row
col = 0;
// Increment row
row++;
}
if (isMirrorImage)
System.out.print("Yes");
else
System.out.print("No");
}
// Driver code
public static void main(String[] args)
{
// Given 2 matrices
int N = 4;
int mat1[][] = {{1, 2, 3, 4},
{0, 6, 7, 8},
{9, 10, 11, 12},
{13, 14, 15, 16}};
int mat2[][] = {{4, 3, 2, 1},
{8, 7, 6, 0},
{12, 11, 10, 9},
{16, 15, 14, 13}};
// Function Call
mirrorMatrix(mat1, mat2, N);
}
}
// This code is contributed by 29AjayKumar
Python3
# Python3 implementation of
# the above approach
# Function to check whether the
# two matrices are mirror
# of each other
def mirrorMatrix(mat1, mat2, N):
# Initialising row and column of
# second matrix
row = 0
col = 0
isMirrorImage = True
# Iterating over the matrices
for i in range(N):
# Check row of first matrix with
# reversed row of second matrix
for j in range(N - 1, -1, -1):
# If the element is not equal
if (mat2[row][col] != mat1[i][j]):
isMirrorImage = False
# Increment column
col += 1
# Reset column to 0
# for new row
col = 0
# Increment row
row += 1
if (isMirrorImage):
print("Yes")
else:
print("No")
# Driver code
if __name__ == "__main__":
# Given 2 matrices
N = 4
mat1 = [ [ 1, 2, 3, 4 ],
[ 0, 6, 7, 8 ],
[ 9, 10, 11, 12 ],
[ 13, 14, 15, 16 ] ]
mat2 = [ [ 4, 3, 2, 1 ],
[ 8, 7, 6, 0 ],
[ 12, 11, 10, 9 ],
[ 16, 15, 14, 13 ] ]
# Function Call
mirrorMatrix(mat1, mat2, N)
C#
// C# implementation of
// the above approach
using System;
class GFG{
// Function to check whether the
// two matrices are mirror
// of each other
static void mirrorMatrix(int [,]mat1,
int [,]mat2, int N)
{
// Initialising row and column of
// second matrix
int row = 0;
int col = 0;
bool isMirrorImage = true;
// Iterating over the matrices
for (int i = 0; i = 0; j--)
{
// If the element is not equal
if (mat2[row,col] != mat1[i,j])
{
isMirrorImage = false;
}
// Increment column
col++;
}
// Reset column to 0
// for new row
col = 0;
// Increment row
row++;
}
if (isMirrorImage)
Console.Write("Yes");
else
Console.Write("No");
}
// Driver code
public static void Main(String[] args)
{
// Given 2 matrices
int N = 4;
int [,]mat1 = {{1, 2, 3, 4},
{0, 6, 7, 8},
{9, 10, 11, 12},
{13, 14, 15, 16}};
int [,]mat2 = {{4, 3, 2, 1},
{8, 7, 6, 0},
{12, 11, 10, 9},
{16, 15, 14, 13}};
// Function Call
mirrorMatrix(mat1, mat2, N);
}
}
// This code is contributed by Amit Katiyar
Javascript
// Javascript implementation of
// the above approach
// Function to check whether the
// two matrices are mirror
// of each other
function mirrorMatrix(mat1, mat2, N)
{
// Initialising row and column of
// second matrix
let row = 0;
let col = 0;
let isMirrorImage = true;
// Iterating over the matrices
for (let i = 0; i = 0; j--) {
// If the element is not equal
if (mat2[row][col] != mat1[i][j]) {
isMirrorImage = false;
}
// Increment column
col++;
}
// Reset column to 0
// for new row
col = 0;
// Increment row
row++;
}
if (isMirrorImage)
document.write("Yes");
else
document.write("No");
}
// Driver code
// Given 2 matrices
let N = 4;
let mat1 = [ [ 1, 2, 3, 4 ],
[ 0, 6, 7, 8 ],
[ 9, 10, 11, 12 ],
[ 13, 14, 15, 16 ] ];
let mat2 = [ [ 4, 3, 2, 1 ],
[ 8, 7, 6, 0 ],
[ 12, 11, 10, 9 ],
[ 16, 15, 14, 13 ] ];
// Function Call
mirrorMatrix(mat1, mat2, N);