From 58ac54cbdbc6d8f006e4fcb753f6ac416521702b Mon Sep 17 00:00:00 2001
From: Aditya <aditya.12114424@lpu.in>
Date: Fri, 4 Jul 2025 15:46:57 +0530
Subject: [PATCH] Add Freivalds' Algorithm for randomized matrix multiplication
 verification (#6340)

---
 ...mizedMatrixMultiplicationVerification.java | 64 +++++++++++++++++++
 ...dMatrixMultiplicationVerificationTest.java | 41 ++++++++++++
 2 files changed, 105 insertions(+)
 create mode 100644 src/main/java/com/thealgorithms/randomized/RandomizedMatrixMultiplicationVerification.java
 create mode 100644 src/test/java/com/thealgorithms/randomized/RandomizedMatrixMultiplicationVerificationTest.java

diff --git a/src/main/java/com/thealgorithms/randomized/RandomizedMatrixMultiplicationVerification.java b/src/main/java/com/thealgorithms/randomized/RandomizedMatrixMultiplicationVerification.java
new file mode 100644
index 000000000..b5ac7076b
--- /dev/null
+++ b/src/main/java/com/thealgorithms/randomized/RandomizedMatrixMultiplicationVerification.java
@@ -0,0 +1,64 @@
+package com.thealgorithms.randomized;
+
+import java.util.Random;
+
+public final class RandomizedMatrixMultiplicationVerification {
+
+    private RandomizedMatrixMultiplicationVerification() {
+        // Prevent instantiation of utility class
+    }
+
+    /**
+     * 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;
+    }
+}
diff --git a/src/test/java/com/thealgorithms/randomized/RandomizedMatrixMultiplicationVerificationTest.java b/src/test/java/com/thealgorithms/randomized/RandomizedMatrixMultiplicationVerificationTest.java
new file mode 100644
index 000000000..330662ac2
--- /dev/null
+++ b/src/test/java/com/thealgorithms/randomized/RandomizedMatrixMultiplicationVerificationTest.java
@@ -0,0 +1,41 @@
+package com.thealgorithms.randomized;
+
+import static org.junit.jupiter.api.Assertions.assertFalse;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import org.junit.jupiter.api.Test;
+
+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));
+    }
+}