Added Freivalds' Algorithm for randomized matrix multiplication verification

Author: aditya-7562

src/main/java/com/thealgorithms/randomized/RandomizedMatrixMultiplicationVerification.java

@@ -0,0 +1,60 @@
+package com.thealgorithms.randomized;
+
+import java.util.Random;
+
+public class RandomizedMatrixMultiplicationVerification {
+
+    /**
+     * Verifies whether A × B == C using Freivalds' algorithm.
+     * @param A Left matrix
+     * @param B Right matrix
+     * @param C Product matrix to verify
+     * @param iterations Number of randomized checks
+     * @return true if likely A×B == C; false if definitely not
+     */
+    public static boolean verify(int[][] A, int[][] B, int[][] C, int iterations) {
+        int n = A.length;
+        Random random = new Random();
+
+        for (int iter = 0; iter < iterations; iter++) {
+            // Step 1: Generate random 0/1 vector
+            int[] r = new int[n];
+            for (int i = 0; i < n; i++) {
+                r[i] = random.nextInt(2);
+            }
+
+            // Step 2: Compute Br = B × r
+            int[] Br = new int[n];
+            for (int i = 0; i < n; i++) {
+                for (int j = 0; j < n; j++) {
+                    Br[i] += B[i][j] * r[j];
+                }
+            }
+
+            // Step 3: Compute A(Br)
+            int[] ABr = new int[n];
+            for (int i = 0; i < n; i++) {
+                for (int j = 0; j < n; j++) {
+                    ABr[i] += A[i][j] * Br[j];
+                }
+            }
+
+            // Step 4: Compute Cr = C × r
+            int[] Cr = new int[n];
+            for (int i = 0; i < n; i++) {
+                for (int j = 0; j < n; j++) {
+                    Cr[i] += C[i][j] * r[j];
+                }
+            }
+
+            // Step 5: Compare ABr and Cr
+            for (int i = 0; i < n; i++) {
+                if (ABr[i] != Cr[i]) {
+                    return false;
+                }
+            }
+        }
+
+        return true;
+    }
+}

src/test/java/com/thealgorithms/randomized/RandomizedMatrixMultiplicationVerificationTest.java

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+package com.thealgorithms.randomized;
+
+import org.junit.jupiter.api.Test;
+import static org.junit.jupiter.api.Assertions.*;
+
+class RandomizedMatrixMultiplicationVerificationTest {
+
+    @Test
+    void testCorrectMultiplication() {
+        int[][] A = {{ 1, 2 },{ 3, 4 }};
+        int[][] B = {{ 5, 6 }, { 7, 8 }};
+        int[][] C = {{ 19, 22 }, { 43, 50 }};
+        assertTrue(RandomizedMatrixMultiplicationVerification.verify(A, B, C, 10));
+    }
+
+    @Test
+    void testIncorrectMultiplication() {
+        int[][] A = {{ 1, 2 }, { 3, 4 }};
+        int[][] B = {{ 5, 6 }, { 7, 8 }};
+        int[][] wrongC = {{ 20, 22 }, { 43, 51 }};
+        assertFalse(RandomizedMatrixMultiplicationVerification.verify(A, B, wrongC, 10));
+    }
+
+    @Test
+    void testLargeMatrix() {
+        int size = 100;
+        int[][] A = new int[size][size];
+        int[][] B = new int[size][size];
+        int[][] C = new int[size][size];
+
+        for (int i = 0; i < size; i++) {
+            A[i][i] = 1;
+            B[i][i] = 1;
+            C[i][i] = 1;
+        }
+
+        assertTrue(RandomizedMatrixMultiplicationVerification.verify(A, B, C, 15));
+    }
+}