每个值为 0 或n的矩阵的最大行列式
原文： https://www.geeksforgeeks.org/maximum-determinant-matrix-every-values-either-0-n/
我们给定一个正数n，我们必须找到一个x3 * 3矩阵，该矩阵可以由 0 或n的组合形成，并且具有最大的行列式。
示例：
Input : n = 3
Output : Maximum determinant = 54
Resultant Matrix :
3 3 0
0 3 3
3 0 3
Input : n = 13
Output : Maximum determinant = 4394
Resultant Matrix :
13 13 0
0 13 13
13 0 13
解释：
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)。 具有最大行列式的矩阵的形式也为：
n n 0
0 n n
n 0 0
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 resulatant 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 << "\n";
}
}
// Driver code
int main()
{
int n = 15;
cout << "Maximum Determinant = " << maxDet(n);
cout << "\nResultant Matrix :\n";
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 resulatant 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 resulatant 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("\n")
# 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 resulatant 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
// resulatant 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 "\n";
}
}
// Driver code
$n = 15;
echo "Maximum Determinant = " ,
maxDet($n);
echo "\nResultant Matrix :\n";
resMatrix($n);
// This code is contributed
// by nitin mittal.
?>
输出：
Maximum Determinant = 6750
Resultant Matrix :
15 15 0
0 15 15
15 0 15
练习：将上述解扩展为广义的k x k矩阵。
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