每值为0或n的矩阵的最大行列式-yiteyi-C++库

我们已经给出了一个正数n，我们必须找到一个3*3矩阵，它可以由0或n的组合构成，并且具有最大行列式。

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例如：

Input : n = 3 Output : Maximum determinant = 54Resultant Matrix :3 3 00 3 33 0 3Input : n = 13 Output : Maximum determinant = 4394Resultant Matrix :13 13  00  13 1313  0 13

说明： 对于元素为0或n的任何3*3矩阵，最大可能行列式为 2*（n^3）。 .此外，具有最大行列式的矩阵的形式为： n n 0 0 n n n 0 0

推荐：请尝试你的方法 {IDE} 首先，在进入解决方案之前。

C++

                         // C++ program to find  maximum possible determinant                       
                         // of 0/n matrix.                       
                         #include <bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         // Function for maximum determinant                       
                         int                                     maxDet(                                     int                                     n)                       
                         {                       
                                                 return                                     (2*n*n*n);                       
                         }                       
           
                         // Function to print resultant matrix                       
                         void                                     resMatrix (                                     int                                     n)                       
                         {                       
                                                 for                                     (                                     int                                     i = 0; i < 3; i++)                       
                                                 {                       
                                                 for                                     (                                     int                                     j = 0; j < 3; j++)                       
                                                 {                       
                                                 // three position where 0 appears                       
                                                 if                                     (i == 0 && j == 2)                       
                                                 cout <<                                     "0 "                                     ;                       
                                                 else                                     if                                     (i == 1 && j == 0)                       
                                                 cout <<                                     "0 "                                     ;                       
                                                 else                                     if                                     (i == 2 && j == 1)                       
                                                 cout <<                                     "0 "                                     ;                       
           
                                                 // position where n appears                       
                                                 else                       
                                                 cout << n <<                                     " "                                     ;                       
                                                 }                       
                                                 cout <<                                     ""                                     ;                       
                                                 }                       
                         }                       
           
                         // Driver code                       
                         int                                     main()                       
                         {                       
                                                 int                                     n = 15;                       
                                                 cout <<                                     "Maximum Determinant = "                                     << maxDet(n);                       
           
                                                 cout <<                                     "Resultant Matrix :"                                     ;                       
                                                 resMatrix(n);                       
           
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java program to find maximum possible                       
                         // determinant of 0/n matrix.                       
                         import                                     java.io.*;                       
           
                         public                                     class                                     GFG                       
                         {                       
                                   
                         // Function for maximum determinant                       
                         static                                     int                                     maxDet(                                     int                                     n)                       
                         {                       
                                                 return                                     (                                     2                                     * n * n * n);                       
                         }                       
           
           
                         // Function to print resultant matrix                       
                         void                                     resMatrix(                                     int                                     n)                       
                         {                       
                                                 for                                     (                                     int                                     i =                                     0                                     ; i <                                     3                                     ; i++)                       
                                                 {                       
                                                 for                                     (                                     int                                     j =                                     0                                     ; j <                                     3                                     ; j++)                       
                                                 {                       
                                                 // three position where 0 appears                       
                                                 if                                     (i ==                                     0                                     && j ==                                     2                                     )                       
                                                 System.out.print(                                     "0 "                                     );                       
                                                 else                                     if                                     (i ==                                     1                                     && j ==                                     0                                     )                       
                                                 System.out.print(                                     "0 "                                     );                       
                                                 else                                     if                                     (i ==                                     2                                     && j ==                                     1                                     )                       
                                                 System.out.print(                                     "0 "                                     );                       
           
                                                 // position where n appears                       
                                                 else                       
                                                 System.out.print(n +                                     " "                                     );                       
                                                 }                       
                                                 System.out.println(                                     ""                                     );                       
                                                 }                       
                         }                       
           
                                                 // Driver code                       
                                                 static                                     public                                     void                                     main (String[] args)                       
                                                 {                       
                                                 int                                     n =                                     15                                     ;                       
                                                 GFG geeks=                                     new                                     GFG();                       
                                                 System.out.println(                                     "Maximum Determinant = "                       
                                                 + maxDet(n));                       
           
                                                 System.out.println(                                     "Resultant Matrix :"                                     );                       
                                                 geeks.resMatrix(n);                       
           
                                                 }                       
                         }                       
           
                         // This code is contributed by vt_m.                       

Python3

                         # Python 3 program to find maximum                       
                         # possible determinant of 0/n matrix.                       
                         # Function for maximum determinant                       
                         def                                     maxDet(n):                       
                                                 return                                     2                                     *                                     n                                     *                                     n                                     *                                     n                       
           
                         # Function to print resultant matrix                       
                         def                                     resMatrix(n):                       
                                                 for                                     i                                     in                                     range                                     (                                     3                                     ):                       
                                                 for                                     j                                     in                                     range                                     (                                     3                                     ):                       
           
                                                 # three position where 0 appears                       
                                                 if                                     i                                     =                                     =                                     0                                     and                                     j                                     =                                     =                                     2                                     :                       
                                                 print                                     (                                     "0"                                     , end                                     =                                     " "                                     )                       
                                                 elif                                     i                                     =                                     =                                     1                                     and                                     j                                     =                                     =                                     0                                     :                       
                                                 print                                     (                                     "0"                                     , end                                     =                                     " "                                     )                       
                                                 elif                                     i                                     =                                     =                                     2                                     and                                     j                                     =                                     =                                     1                                     :                       
                                                 print                                     (                                     "0"                                     , end                                     =                                     " "                                     )                       
           
                                                 # position where n appears                       
                                                 else                                     :                       
                                                 print                                     (n, end                                     =                                     " "                                     )                       
                                                 print                                     (                                     ""                                     )                       
                                   
                         # Driver code                       
                         n                                     =                                     15                       
                         print                                     (                                     "Maximum Detrminat="                                     , maxDet(n))                       
                         print                                     (                                     "Resultant Matrix:"                                     )                       
                         resMatrix(n)                       
           
                         # This code is contributed by Shrikant13                       

C#

                         // C# program to find maximum possible                       
                         // determinant of 0/n matrix.                       
                         using                                     System;                       
           
                         public                                     class                                     GFG                       
                         {                       
                                   
                         // Function for maximum determinant                       
                         static                                     int                                     maxDet(                                     int                                     n)                       
                         {                       
                                                 return                                     (2 * n * n * n);                       
                         }                       
           
           
                         // Function to print resultant matrix                       
                         void                                     resMatrix(                                     int                                     n)                       
                         {                       
                                                 for                                     (                                     int                                     i = 0; i < 3; i++)                       
                                                 {                       
                                                 for                                     (                                     int                                     j = 0; j < 3; j++)                       
                                                 {                       
                                                 // three position where 0 appears                       
                                                 if                                     (i == 0 && j == 2)                       
                                                 Console.Write(                                     "0 "                                     );                       
                                                 else                                     if                                     (i == 1 && j == 0)                       
                                                 Console.Write(                                     "0 "                                     );                       
                                                 else                                     if                                     (i == 2 && j == 1)                       
                                                 Console.Write(                                     "0 "                                     );                       
           
                                                 // position where n appears                       
                                                 else                       
                                                 Console.Write(n +                                     " "                                     );                       
                                                 }                       
                                                 Console.WriteLine(                                     ""                                     );                       
                                                 }                       
                         }                       
           
                                                 // Driver code                       
                                                 static                                     public                                     void                                     Main (String []args)                       
                                                 {                       
                                                 int                                     n = 15;                       
                                                 GFG geeks=                                     new                                     GFG();                       
                                                 Console.WriteLine(                                     "Maximum Determinant = "                       
                                                 + maxDet(n));                       
           
                                                 Console.WriteLine(                                     "Resultant Matrix :"                                     );                       
                                                 geeks.resMatrix(n);                       
           
                                                 }                       
                         }                       
           
                         // This code is contributed by vt_m.                       

PHP

                         <?php                       
                         // PHP program to find maximum                       
                         // possible determinant of 0/n matrix.                       
           
                         // Function for maximum determinant                       
                         function                                     maxDet(                                     $n                                     )                       
                         {                       
                                                 return                                     (2 *                                     $n                                     *                                     $n                                     *                                     $n                                     );                       
                         }                       
           
                         // Function to print                       
                         // resultant matrix                       
                         function                                     resMatrix (                                     $n                                     )                       
                         {                       
                                                 for                                     (                                     $i                                     = 0;                                     $i                                     < 3;                                     $i                                     ++)                       
                                                 {                       
                                                 for                                     (                                     $j                                     = 0;                                     $j                                     < 3;                                     $j                                     ++)                       
                                                 {                       
                                                 // three position                       
                                                 // where 0 appears                       
                                                 if                                     (                                     $i                                     == 0 &&                                     $j                                     == 2)                       
                                                 echo                                     "0 "                                     ;                       
                                                 else                                     if                                     (                                     $i                                     == 1 &&                                     $j                                     == 0)                       
                                                 echo                                     "0 "                                     ;                       
                                                 else                                     if                                     (                                     $i                                     == 2 &&                                     $j                                     == 1)                       
                                                 echo                                     "0 "                                     ;                       
           
                                                 // position where n appears                       
                                                 else                       
                                                 echo                                     $n                                     ,                                     " "                                     ;                       
                                                 }                       
                                                 echo                                     ""                                     ;                       
                                                 }                       
                         }                       
           
                         // Driver code                       
                         $n                                     = 15;                       
                         echo                                     "Maximum Determinant = "                                     ,                       
                                                 maxDet(                                     $n                                     );                       
           
                         echo                                     "Resultant Matrix :"                                     ;                       
                         resMatrix(                                     $n                                     );                       
           
                         // This code is contributed                       
                         // by nitin mittal.                       
                         ?>                       

Javascript

                         <script>                       
           
                         // Java script program to find maximum possible                       
                         // determinant of 0/n matrix.                       
                                   
                         // Function for maximum determinant                       
                         function                                     maxDet(n)                       
                         {                       
                                                 return                                     (2 * n * n * n);                       
                         }                       
           
                         // Function to print resultant matrix                       
                         function                                     resMatrix(n)                       
                         {                       
                                                 for                                     (let i = 0; i < 3; i++)                       
                                                 {                       
                                                 for                                     (let j = 0; j < 3; j++)                       
                                                 {                       
                                   
                                                 // Three position where 0 appears                       
                                                 if                                     (i == 0 && j == 2)                       
                                                 document.write(                                     "0 "                                     );                       
                                                 else                                     if                                     (i == 1 && j == 0)                       
                                                 document.write(                                     "0 "                                     );                       
                                                 else                                     if                                     (i == 2 && j == 1)                       
                                                 document.write(                                     "0 "                                     );                       
           
                                                 // Position where n appears                       
                                                 else                       
                                                 document.write(n +                                     " "                                     );                       
                                                 }                       
                                                 document.write(                                     "<br>"                                     );                       
                                                 }                       
                         }                       
           
                         // Driver code                       
                         let n = 15;                       
           
                         document.write(                                     "Maximum Determinant = "                                     +                       
                                                 maxDet(n) +                                     "<br>"                                     );                       
           
                         document.write(                                     "Resultant Matrix :<br>"                                     );                       
                                                 resMatrix(n);                       
                                   
                         // This code is contributed by sravan kumar                       
           
                         </script>                       

输出：

Maximum Determinant = 6750Resultant Matrix :15 15  00  15 1515 0  15

练习： 将上述解推广到广义k×k矩阵。

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