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| 1 | +// Java program to find Determinant of a matrix |
| 2 | +class GFG { |
| 3 | + |
| 4 | + // Dimension of input square matrix |
| 5 | + static final int N = 4; |
| 6 | + |
| 7 | + // Function to get determinant of matrix |
| 8 | + static int determinantOfMatrix(int mat[][], int n) |
| 9 | + { |
| 10 | + int num1, num2, det = 1, index, |
| 11 | + total = 1; // Initialize result |
| 12 | + |
| 13 | + // temporary array for storing row |
| 14 | + int[] temp = new int[n + 1]; |
| 15 | + |
| 16 | + // loop for traversing the diagonal elements |
| 17 | + for (int i = 0; i < n; i++) { |
| 18 | + index = i; // initialize the index |
| 19 | + |
| 20 | + // finding the index which has non zero value |
| 21 | + while (mat[index][i] == 0 && index < n) { |
| 22 | + index++; |
| 23 | + } |
| 24 | + if (index == n) // if there is non zero element |
| 25 | + { |
| 26 | + // the determinant of matrix as zero |
| 27 | + continue; |
| 28 | + } |
| 29 | + if (index != i) { |
| 30 | + // loop for swaping the diagonal element row |
| 31 | + // and index row |
| 32 | + for (int j = 0; j < n; j++) { |
| 33 | + swap(mat, index, j, i, j); |
| 34 | + } |
| 35 | + // determinant sign changes when we shift |
| 36 | + // rows go through determinant properties |
| 37 | + det = (int)(det * Math.pow(-1, index - i)); |
| 38 | + } |
| 39 | + |
| 40 | + // storing the values of diagonal row elements |
| 41 | + for (int j = 0; j < n; j++) { |
| 42 | + temp[j] = mat[i][j]; |
| 43 | + } |
| 44 | + |
| 45 | + // traversing every row below the diagonal |
| 46 | + // element |
| 47 | + for (int j = i + 1; j < n; j++) { |
| 48 | + num1 = temp[i]; // value of diagonal element |
| 49 | + num2 = mat[j] |
| 50 | + [i]; // value of next row element |
| 51 | + |
| 52 | + // traversing every column of row |
| 53 | + // and multiplying to every row |
| 54 | + for (int k = 0; k < n; k++) { |
| 55 | + // multiplying to make the diagonal |
| 56 | + // element and next row element equal |
| 57 | + mat[j][k] = (num1 * mat[j][k]) |
| 58 | + - (num2 * temp[k]); |
| 59 | + } |
| 60 | + total = total * num1; // Det(kA)=kDet(A); |
| 61 | + } |
| 62 | + } |
| 63 | + |
| 64 | + // multiplying the diagonal elements to get |
| 65 | + // determinant |
| 66 | + for (int i = 0; i < n; i++) { |
| 67 | + det = det * mat[i][i]; |
| 68 | + } |
| 69 | + return (det / total); // Det(kA)/k=Det(A); |
| 70 | + } |
| 71 | + |
| 72 | + static int[][] swap(int[][] arr, int i1, int j1, int i2, |
| 73 | + int j2) |
| 74 | + { |
| 75 | + int temp = arr[i1][j1]; |
| 76 | + arr[i1][j1] = arr[i2][j2]; |
| 77 | + arr[i2][j2] = temp; |
| 78 | + return arr; |
| 79 | + } |
| 80 | + |
| 81 | + // Driver code |
| 82 | + public static void main(String[] args) |
| 83 | + { |
| 84 | + int mat[][] = { { 1, 0, 2, -1 }, |
| 85 | + { 3, 0, 0, 5 }, |
| 86 | + { 2, 1, 4, -3 }, |
| 87 | + { 1, 0, 5, 0 } }; |
| 88 | + |
| 89 | + // Function call |
| 90 | + System.out.printf( |
| 91 | + "Determinant of the matrix is : %d", |
| 92 | + determinantOfMatrix(mat, N)); |
| 93 | + } |
| 94 | +} |
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