中心对称矩阵-yiteyi-C++库

给定一个矩阵的大小 n×n .任务是检查给定的矩阵是否为中心对称矩阵。在数学中，a 中心对称矩阵对三角分裂是一个关于中心对称的矩阵。

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图片[1]-中心对称矩阵-yiteyi-C++库

例如：

Input : n = 3,        m[][] = { { 1, 3, 5 },                  { 6, 8, 6 },                  { 5, 3, 1 } };Output : YesInput : n = 3,         m[][] = { { 1, 3, 5 },                  { 6, 8, 6 },                  { 5, 3, 0 } };Output : No

推荐：请尝试你的方法 {IDE} 首先，在进入解决方案之前。

其思想是检查每个元素的m[i][j]是否等于m[n-i-1][n-j-1]。如果任何元素不满足上述条件，则打印“否”，否则打印“是”。以下是上述方法的实施情况：

C++

                         // CPP Program to check whether given                       
                         // matrix is centrosymmetric or not.                       
                         #include <bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
                         #define N 3                       
           
                         bool                                     checkCentrosymmetricted(                                     int                                     n,                                     int                                     m[N][N])                       
                         {                       
                                                 int                                     mid_row;                       
           
                                                 // Finding the middle row of the matrix                       
                                                 if                                     (n & 1)                       
                                                 mid_row = n / 2 + 1;                       
                                                 else                       
                                                 mid_row = n / 2;                       
           
                                                 // for each row upto middle row.                       
                                                 for                                     (                                     int                                     i = 0; i < mid_row; i++) {                       
           
                                                 // If each element and its corresponding                       
                                                 // element is not equal then return false.                       
                                                 for                                     (                                     int                                     j = 0; j < n; j++) {                       
                                                 if                                     (m[i][j] != m[n - i - 1][n - j - 1])                       
                                                 return                                     false                                     ;                       
                                                 }                       
                                                 }                       
           
                                                 return                                     true                                     ;                       
                         }                       
           
                         // Driven Program                       
                         int                                     main()                       
                         {                       
                                                 int                                     n = 3;                       
                                                 int                                     m[N][N] = { { 1, 3, 5 },                       
                                                 { 6, 8, 6 },                       
                                                 { 5, 3, 1 } };                       
           
                                                 (checkCentrosymmetricted(n, m) ?                       
                                                 (cout <<                                     "Yes"                                     ) : (cout <<                                     "No"                                     ));                       
           
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java Program to check whether given                       
                         // matrix is centrosymmetric or not.                       
                         import                                     java.io.*;                       
           
                         class                                     GFG {                       
                                   
                                                 static                                     int                                     N =                                     3                                     ;                       
                                   
                                                 static                                     boolean                                     checkCentrosymmetricted(                       
                                                 int                                     n,                                     int                                     m[][])                       
                                                 {                       
                                                 int                                     mid_row;                       
                                   
                                                 // Finding the middle row of the                       
                                                 // matrix                       
                                                 if                                     ((n &                                     1                                     )>                                     0                                     )                       
                                                 mid_row = n /                                     2                                     +                                     1                                     ;                       
                                                 else                       
                                                 mid_row = n /                                     2                                     ;                       
                                   
                                                 // for each row upto middle row.                       
                                                 for                                     (                                     int                                     i =                                     0                                     ; i < mid_row; i++)                       
                                                 {                       
                                   
                                                 // If each element and its                       
                                                 // corresponding element is                       
                                                 // not equal then return false.                       
                                                 for                                     (                                     int                                     j =                                     0                                     ; j < n; j++)                       
                                                 {                       
                                                 if                                     (m[i][j] !=                       
                                                 m[n - i -                                     1                                     ][n - j -                                     1                                     ])                       
                                                 return                                     false                                     ;                       
                                                 }                       
                                                 }                       
                                   
                                                 return                                     true                                     ;                       
                                                 }                       
                                   
                                                 // Driven Program                       
                                                 public                                     static                                     void                                     main (String[] args)                       
                                                 {                       
                                                 int                                     n =                                     3                                     ;                       
                                                 int                                     m[][] = { {                                     1                                     ,                                     3                                     ,                                     5                                     },                       
                                                 {                                     6                                     ,                                     8                                     ,                                     6                                     },                       
                                                 {                                     5                                     ,                                     3                                     ,                                     1                                     } };                       
           
                                                 if                                     (checkCentrosymmetricted(n, m))                       
                                                 System.out.println(                                     "Yes"                                     );                       
                                                 else                       
                                                 System.out.println(                                     "No"                                     );                       
                                                 }                       
                         }                       
           
                         // This code is contributed by anuj_67.                       

Python3

                         # Python3 Program to check whether given                       
                         # matrix is centrosymmetric or not.                       
           
                         def                                     checkCentrosymmetricted( n, m):                       
           
                                                 mid_row                                     =                                     0                                     ;                       
           
                                                 # Finding the middle row                       
                                                 # of the matrix                       
                                                 if                                     ((n &                                     1                                     ) >                                     0                                     ):                       
                                                 mid_row                                     =                                     n                                     /                                     2                                     +                                     1                                     ;                       
                                                 else                                     :                       
                                                 mid_row                                     =                                     n                                     /                                     2                                     ;                       
           
                                                 # for each row upto middle row.                       
                                                 for                                     i                                     in                                     range                                     (                                     int                                     (mid_row)):                       
           
                                                 # If each element and                       
                                                 # its corresponding                       
                                                 # element is not equal                       
                                                 # then return false.                       
                                                 for                                     j                                     in                                     range                                     (n):                       
                                                 if                                     (m[i][j] !                                     =                                     m[n                                     -                                     i                                     -                                     1                                     ][n                                     -                                     j                                     -                                     1                                     ]):                       
                                                 return                                     False                                     ;                       
           
                                                 return                                     True                                     ;                       
                                   
                         # Driver Code                       
                         n                                     =                                     3                                     ;                       
                         m                                     =                                     [[                                     1                                     ,                                     3                                     ,                                     5                                     ],                       
                                                 [                                     6                                     ,                                     8                                     ,                                     6                                     ],                       
                                                 [                                     5                                     ,                                     3                                     ,                                     1                                     ]];                       
           
                         if                                     (checkCentrosymmetricted(n, m)):                       
                                                 print                                     (                                     "Yes"                                     );                       
                         else                                     :                       
                                                 print                                     (                                     "No"                                     );                       
                                   
                         # This code is contributed by mits                       

C#

                         // C# Program to check whether given                       
                         // matrix is centrosymmetric or not.                       
                         using                                     System;                       
           
                         class                                     GFG {                       
                                   
                                                 ///static int N = 3;                       
                                   
                                                 static                                     bool                                     checkCentrosymmetricted(                       
                                                 int                                     n,                                     int                                     [,]m)                       
                                                 {                       
                                                 int                                     mid_row;                       
                                   
                                                 // Finding the middle row of the                       
                                                 // matrix                       
                                                 if                                     ((n & 1)>0)                       
                                                 mid_row = n / 2 + 1;                       
                                                 else                       
                                                 mid_row = n / 2;                       
                                   
                                                 // for each row upto middle row.                       
                                                 for                                     (                                     int                                     i = 0; i < mid_row; i++)                       
                                                 {                       
                                   
                                                 // If each element and its                       
                                                 // corresponding element is                       
                                                 // not equal then return false.                       
                                                 for                                     (                                     int                                     j = 0; j < n; j++)                       
                                                 {                       
                                                 if                                     (m[i,j] !=                       
                                                 m[n - i - 1,n - j - 1])                       
                                                 return                                     false                                     ;                       
                                                 }                       
                                                 }                       
                                   
                                                 return                                     true                                     ;                       
                                                 }                       
                                   
                                                 // Driven Program                       
                                                 public                                     static                                     void                                     Main()                       
                                                 {                       
                                                 int                                     n = 3;                       
                                                 int                                     [,]m = { { 1, 3, 5 },                       
                                                 { 6, 8, 6 },                       
                                                 { 5, 3, 1 } };                       
           
                                                 if                                     (checkCentrosymmetricted(n, m))                       
                                                 Console.WriteLine(                                     "Yes"                                     );                       
                                                 else                       
                                                 Console.WriteLine(                                     "No"                                     );                       
                                                 }                       
                         }                       
           
                         // This code is contributed by anuj_67.                       

PHP

                         <?php                       
                         // PHP Program to check whether given                       
                         // matrix is centrosymmetric or not.                       
           
                         //$N = 3;                       
           
                         function                                     checkCentrosymmetricted(                                     $n                                     ,                                     $m                                     )                       
                         {                       
                                                 $mid_row                                     ;                       
           
                                                 // Finding the middle row                       
                                                 // of the matrix                       
                                                 if                                     (                                     $n                                     & 1)                       
                                                 $mid_row                                     =                                     $n                                     / 2 + 1;                       
                                                 else                       
                                                 $mid_row                                     =                                     $n                                     / 2;                       
           
                                                 // for each row upto middle row.                       
                                                 for                                     (                                     $i                                     = 0;                                     $i                                     <                                     $mid_row                                     ;                                     $i                                     ++)                       
                                                 {                       
           
                                                 // If each element and                       
                                                 // its corresponding                       
                                                 // element is not equal                       
                                                 // then return false.                       
                                                 for                                     (                                     $j                                     = 0;                                     $j                                     <                                     $n                                     ;                                     $j                                     ++) {                       
                                                 if                                     (                                     $m                                     [                                     $i                                     ][                                     $j                                     ] !=                                     $m                                     [                                     $n                                     -                                     $i                                     - 1]                       
                                                 [                                     $n                                     -                                     $j                                     - 1])                       
                                                 return                                     false;                       
                                                 }                       
                                                 }                       
           
                                                 return                                     true;                       
                         }                       
                                   
                                                 // Driver Code                       
                                                 $n                                     = 3;                       
                                                 $m                                     =                                     array                                     (                                     array                                     (1, 3, 5 ),                       
                                                 array                                     ( 6, 8, 6 ),                       
                                                 array                                     ( 5, 3, 1 ));                       
           
                                                 if                                     (checkCentrosymmetricted(                                     $n                                     ,                                     $m                                     ) )                       
                                                 echo                                     "Yes"                                     ;                       
                                                 else                       
                                                 echo                                     "No"                                     ;                       
                                   
                         // This code is contributed by anuj_67.                       
                         ?>                       

Javascript

                         <script>                       
           
           
                         // Javascript Program to check whether given                       
                         // matrix is centrosymmetric or not.                       
           
                         let N = 3                       
           
                         function                                     checkCentrosymmetricted( n,  m)                       
                         {                       
                                                 let mid_row;                       
           
                                                 // Finding the middle row of the matrix                       
                                                 if                                     (n & 1)                       
                                                 mid_row = Math.floor(n / 2) + 1;                       
                                                 else                       
                                                 mid_row = n / 2;                       
           
                                                 // for each row upto middle row.                       
                                                 for                                     (let i = 0; i < mid_row; i++) {                       
           
                                                 // If each element and its corresponding                       
                                                 // element is not equal then return false.                       
                                                 for                                     (let j = 0; j < n; j++) {                       
                                                 if                                     (m[i][j] != m[n - i - 1][n - j - 1])                       
                                                 return                                     false                                     ;                       
                                                 }                       
                                                 }                       
           
                                                 return                                     true                                     ;                       
                         }                       
           
                         // Driver Code                       
           
                         let n = 3;                       
                         let m = [ [ 1, 3, 5 ],                       
                                                 [ 6, 8, 6 ],                       
                                                 [ 5, 3, 1 ] ];                       
           
                         (checkCentrosymmetricted(n, m) ?                       
                                                 (document.write(                                     "Yes"                                     )) : document.write(                                     "No"                                     ));                       
           
                         // This code is contributed by jana_sayanta.                       
                         </script>                       

输出

Yes

复杂性： O（N） ^2. )

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