# Maximum determinant of a matrix with every values either 0 or n in C++

C++Server Side ProgrammingProgramming

## Problem statement

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 determinants.

## Example

If n = 15 then we can create matrix as follows −

{{15, 15, 0}{0, 15, 15}{15, 0, 0}}

For any 3*3 matrix having elements either 0 or n, the maximum possible determinant is 2 *(n)3. Hence answer is −

2 * (15)3 = 6750

## Algorithm

For any 3*3 matrix having elements either 0 or n, the maximum possible determinant is 2 *(n)3

## Example

Let us now see an example −

Live Demo

#include <bits/stdc++.h>
using namespace std;
int getMaxDeterminant(int n){
return (2 * n * n * n);
}
void printMatrix(int n){
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
if (i == 0 && j == 2) {
printf("%-5d", 0);
} else if (i == 1 && j == 0) {
printf("%-5d", 0);
} else if (i == 2 && j == 1) {
printf("%-5d", 0);
} else {
printf("%-5d", n);
}
}
printf("\n");
}
}
int main() {
int n = 15;
cout << "Matrix is:\n";
printMatrix(n);
cout << "\nMaximum determinant = " << getMaxDeterminant(n) << endl;
return 0;
}

## Output

Matrix is:
15150
0 15 15
15 015
Maximum determinant = 6750
Updated on 31-Dec-2019 12:22:55