We have given a positive number n, and we have to find a 3*3 matrix which can be formed with combination of 0 or n and has maximum determinant.
Examples :
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
Explanation:
For any 3*3 matrix having elements either 0 or n, the maximum possible determinant is 2*(n^3).. Also a matrix having maximum determinant is of form: n n 0 0 n n n 0 0
Implementation:
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 << "\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 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 neveropen=new GFG(); System.out.println("Maximum Determinant = " + maxDet(n)); System.out.println("Resultant Matrix :"); neveropen.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 = " ") else if i == 1 and j == 0: print("0", end = " ") else if i == 2 and j == 1: print("0", end = " ") # position where n appears else: print(n, end = " ") print("\n") # Driver code n = 15print("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 neveropen=new GFG(); Console.WriteLine("Maximum Determinant = " + maxDet(n)); Console.WriteLine("Resultant Matrix :"); neveropen.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 "\n"; } } // Driver code $n = 15; echo "Maximum Determinant = " , maxDet($n); echo "\nResultant Matrix :\n"; 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> |
Output
Maximum Determinant = 6750 Resultant Matrix : 15 15 0 0 15 15 15 0 15
Time complexity: O(1).
Auxiliary Space: O(1), since no extra space has been taken.
Exercise: Extend the above solution for a generalized k x k matrix.
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