Determinant_of_Matrix

Author: dhirenkokal

Determinant_of_Matrix.java

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+// Java program to find Determinant of a matrix
+class GFG {
+ 
+    // Dimension of input square matrix
+    static final int N = 4;
+ 
+    // Function to get determinant of matrix
+    static int determinantOfMatrix(int mat[][], int n)
+    {
+        int num1, num2, det = 1, index,
+                        total = 1; // Initialize result
+ 
+        // temporary array for storing row
+        int[] temp = new int[n + 1];
+ 
+        // loop for traversing the diagonal elements
+        for (int i = 0; i < n; i++) {
+            index = i; // initialize the index
+ 
+            // finding the index which has non zero value
+            while (mat[index][i] == 0 && index < n) {
+                index++;
+            }
+            if (index == n) // if there is non zero element
+            {
+                // the determinant of matrix as zero
+                continue;
+            }
+            if (index != i) {
+                // loop for swaping the diagonal element row
+                // and index row
+                for (int j = 0; j < n; j++) {
+                    swap(mat, index, j, i, j);
+                }
+                // determinant sign changes when we shift
+                // rows go through determinant properties
+                det = (int)(det * Math.pow(-1, index - i));
+            }
+ 
+            // storing the values of diagonal row elements
+            for (int j = 0; j < n; j++) {
+                temp[j] = mat[i][j];
+            }
+ 
+            // traversing every row below the diagonal
+            // element
+            for (int j = i + 1; j < n; j++) {
+                num1 = temp[i]; // value of diagonal element
+                num2 = mat[j]
+                          [i]; // value of next row element
+ 
+                // traversing every column of row
+                // and multiplying to every row
+                for (int k = 0; k < n; k++) {
+                    // multiplying to make the diagonal
+                    // element and next row element equal
+                    mat[j][k] = (num1 * mat[j][k])
+                                - (num2 * temp[k]);
+                }
+                total = total * num1; // Det(kA)=kDet(A);
+            }
+        }
+ 
+        // multiplying the diagonal elements to get
+        // determinant
+        for (int i = 0; i < n; i++) {
+            det = det * mat[i][i];
+        }
+        return (det / total); // Det(kA)/k=Det(A);
+    }
+ 
+    static int[][] swap(int[][] arr, int i1, int j1, int i2,
+                        int j2)
+    {
+        int temp = arr[i1][j1];
+        arr[i1][j1] = arr[i2][j2];
+        arr[i2][j2] = temp;
+        return arr;
+    }
+ 
+    // Driver code
+    public static void main(String[] args)
+    {
+        int mat[][] = { { 1, 0, 2, -1 },
+                        { 3, 0, 0, 5 },
+                        { 2, 1, 4, -3 },
+                        { 1, 0, 5, 0 } };
+ 
+        // Function call
+        System.out.printf(
+            "Determinant of the matrix is : %d",
+            determinantOfMatrix(mat, N));
+    }
+}