Determinant of a Matrix
Problem Statement - link #
Given a square matrix of size N x N. The task is to find the determinant of this matrix.
Your Task: You don’t need to read input or print anything. Complete the function determinantOfMatrix() that takes matrix and its size n as input parameters and returns the determinant of the matrix.
Expected Time Complexity: O(N^4)
Expected Auxiliary Space: O(N^2)
Examples #
Example 1:
Input:
N = 4
matrix[][] = [[1, 0, 2, -1], [3, 0, 0, 5], [2, 1, 4, -3], [1, 0, 5, 0]]
Output: 30
Explanation:
Determinant of the given matrix is 30.
Example 2:
Input:
N = 3
matrix[][] = [[1, 2, 3], [4, 5, 6], [7, 10, 9]]
Output: 12
Explanation:
Determinant of the given matrix is 12.
Constraints #
1 <= N <=8-10 <= matrix[i][j] <= 10
Solutions #
class Solution{
public:
//Function for finding determinant of matrix.
void gcf(vector<vector<int>> matrix, vector<vector<int>> &cf, int n, int x){
for(int i=1; i<n; i++){
int j=0;
for(int k=0; k<n; k++){
if(x==k) continue;
cf[i-1][j++] = matrix[i][k];
}
}
}
int determinantOfMatrix(vector<vector<int> > matrix, int n){
// code here
if(n==1) return matrix[0][0];
if(n==2) return (matrix[0][0]*matrix[1][1] - matrix[0][1]*matrix[1][0]);
vector<vector<int>> cf(n-1,vector<int>(n-1));
int sum = 0, sign = 1;
for(int i=0; i<n; i++){
gcf(matrix, cf, n, i);
sum += sign*matrix[0][i]*determinantOfMatrix(cf, n-1);
sign *= -1;
}
return sum;
}
};