每个值为 0 或 n 的矩阵的最大行列式 · GeeksForGeeks 中文系列教程

# 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/](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 3 * 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++ ```cpp // 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 // 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 ```py # 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# ```cs // 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 // 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。本文由 [**Shivam Pradhan（anuj_charm）**](https://www.facebook.com/anuj.charm) 提供。如果您喜欢 GeeksforGeeks 并希望做出贡献，则还可以使用 [tribution.geeksforgeeks.org](http://www.contribute.geeksforgeeks.org) 撰写文章，或将您的文章邮寄至 tribution@geeksforgeeks.org。查看您的文章出现在 GeeksforGeeks 主页上，并帮助其他 Geeks。