Find determinant of matrix generated by array rotation

Given an array of three element. The task is to construct a matrix of order 3*3 by using all three rotation of array as row of matrix and find the determinant of resultant matrix.

Examples:

Input : arr[] = {1, 2, 3}
Output : 18

Input : arr[] = {1, 1, 1}
Output : 0

Approach: As per problem statement, construct a 3*3 matrix using the given array. If a1, a2, a3 are array elements then the corresponding matrix will be:



{{a1, a2, a3}, 
 {a3, a1, a2},
 {a2, a3, a1}}

The task is to calculate the determinant of the above matrix.

Determinant can be calculated by using proper method for this but on the other hand if resultant matrix is expanded for calculation, the result will be a13 + a23 + a33 – 3*a1*a2*a3. Hence, instead of calculating determinant by proper expansion use the above generated formula.

Therefore, Determinant of the above Matrix will be:

a13 + a23 + a33 - (3*a1*a2*a3)

Below is the implementation of the above approach:

C++

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// C++ program for finding determinant of generated matrix
  
#include <bits/stdc++.h>
#define N 3
using namespace std;
  
// Function to calculate determinant
int calcDeterminant(int arr[])
{
    int determinant = 0;
  
    for (int i = 0; i < N; i++) {
        determinant += pow(arr[i], 3);
    }
  
    determinant -= 3 * arr[0] * arr[1] * arr[2];
  
    return determinant;
}
  
// Driver code
int main()
{
    int arr[] = { 4, 5, 3 };
    cout << calcDeterminant(arr);
    return 0;
}

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Java

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// Java program for finding determinant
// of generated matrix 
import java.util.*;
import java.lang.*;
  
class GFG
{
static int N = 3;
  
// Function to calculate determinant 
static double calcDeterminant(int arr[]) 
    double determinant = 0
  
    for (int i = 0; i < N; i++) 
    
        determinant += Math.pow(arr[i], 3); 
    
  
    determinant -= 3 * arr[0] * 
                    arr[1] * arr[2]; 
  
    return determinant; 
  
// Driver code
static public void main (String args[])
{
    int []arr = { 4, 5, 3 }; 
    System.out.println(calcDeterminant(arr)); 
}
}
  
// This code is contributed 
// by Akanksha Rai

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Python3

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# Python3 program for finding determinant of generated matrix
  
# Function to calculate determinant
def calcDeterminant(arr,n):
    determinant =0
  
    for i in range(n):
        determinant+= pow(arr[i],3)
  
    determinant -= 3*arr[0]*arr[1]*arr[2]
  
    return determinant
  
# Driver code
arr = [4,5,3]
n = len(arr)
print(calcDeterminant(arr,n))
  
# This code is contributed by Shrikant13

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C#

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// C# program for finding determinant
// of generated matrix 
using System;
  
class GFG
{
static int N = 3;
  
// Function to calculate determinant 
static double calcDeterminant(int []arr) 
    double determinant = 0; 
  
    for (int i = 0; i < N; i++) 
    
        determinant += Math.Pow(arr[i], 3); 
    
  
    determinant -= 3 * arr[0] * 
                       arr[1] * arr[2]; 
  
    return determinant; 
  
// Driver code
static public void Main ()
{
    int []arr = { 4, 5, 3 }; 
    Console.WriteLine(calcDeterminant(arr)); 
}
}
  
// This code is contributed by akt_mit

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PHP

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<?php
// PHP program for finding determinant
// of generated matrix 
  
$N = 3; 
  
// Function to calculate determinant 
function calcDeterminant($arr
    global $N
    $determinant = 0; 
  
    for ($i = 0; $i < $N; $i++) 
    
        $determinant += pow($arr[$i], 3); 
    
  
    $determinant -= 3 * $arr[0] * 
                        $arr[1] * $arr[2]; 
  
    return $determinant
  
// Driver code 
$arr = array( 4, 5, 3 ); 
echo calcDeterminant($arr); 
  
// This code is contributed by ajit 
?>

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Output:

36


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