Add Freivalds' Algorithm for randomized matrix multiplication verification (#6340)

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;
+    }
+}