Merge branch 'master' into remove-stars-complex-mult

Author: SwarritSrivastava

src/main/java/com/thealgorithms/graph/ZeroOneBfs.java

@@ -0,0 +1,77 @@
+package com.thealgorithms.graph;
+
+import java.util.ArrayDeque;
+import java.util.Arrays;
+import java.util.Deque;
+import java.util.List;
+
+/**
+ * 0-1 BFS for shortest paths on graphs with edges weighted 0 or 1.
+ *
+ * <p>Time Complexity: O(V + E). Space Complexity: O(V).
+ *
+ * <p>References:
+ * <ul>
+ *   <li>https://cp-algorithms.com/graph/01_bfs.html</li>
+ * </ul>
+ */
+public final class ZeroOneBfs {
+
+    private ZeroOneBfs() {
+        // Utility class; do not instantiate.
+    }
+
+    /**
+     * Computes shortest distances from {@code src} in a graph whose edges have weight 0 or 1.
+     *
+     * @param n the number of vertices, labeled {@code 0..n-1}
+     * @param adj adjacency list; for each vertex u, {@code adj.get(u)} is a list of pairs
+     *            {@code (v, w)} where {@code v} is a neighbor and {@code w} is 0 or 1
+     * @param src the source vertex
+     * @return an array of distances; {@code Integer.MAX_VALUE} denotes unreachable
+     * @throws IllegalArgumentException if {@code n < 0}, {@code src} is out of range,
+     *                                  or any edge has weight other than 0 or 1
+     */
+    public static int[] shortestPaths(int n, List<List<int[]>> adj, int src) {
+        if (n < 0 || src < 0 || src >= n) {
+            throw new IllegalArgumentException("Invalid n or src");
+        }
+        int[] dist = new int[n];
+        Arrays.fill(dist, Integer.MAX_VALUE);
+        Deque<Integer> dq = new ArrayDeque<>();
+
+        dist[src] = 0;
+        dq.addFirst(src);
+
+        while (!dq.isEmpty()) {
+            int u = dq.pollFirst();
+            List<int[]> edges = adj.get(u);
+            if (edges == null) {
+                continue;
+            }
+            for (int[] e : edges) {
+                if (e == null || e.length < 2) {
+                    continue;
+                }
+                int v = e[0];
+                int w = e[1];
+                if (v < 0 || v >= n) {
+                    continue; // ignore bad edges
+                }
+                if (w != 0 && w != 1) {
+                    throw new IllegalArgumentException("Edge weight must be 0 or 1");
+                }
+                int nd = dist[u] + w;
+                if (nd < dist[v]) {
+                    dist[v] = nd;
+                    if (w == 0) {
+                        dq.addFirst(v);
+                    } else {
+                        dq.addLast(v);
+                    }
+                }
+            }
+        }
+        return dist;
+    }
+}

src/main/java/com/thealgorithms/maths/EulerPseudoprime.java

@@ -0,0 +1,108 @@
+package com.thealgorithms.maths;
+
+import java.math.BigInteger;
+import java.util.Random;
+
+/**
+ * The {@code EulerPseudoprime} class implements the Euler primality test.
+ *
+ * It is based on Euler’s criterion:
+ * For an odd prime number {@code n} and any integer {@code a} coprime to {@code n}:
+ *   a^((n-1)/2) ≡ (a/n) (mod n)
+ * where (a/n) is the Jacobi symbol.
+ *
+ * This algorithm is a stronger probabilistic test than Fermat’s test.
+ * It may still incorrectly identify a composite as “probably prime” (Euler pseudoprime),
+ * but such cases are rare.
+ */
+public final class EulerPseudoprime {
+
+    private EulerPseudoprime() {
+        // Private constructor to prevent instantiation.
+    }
+
+    private static final Random RANDOM = new Random(1);
+
+    /**
+     * Performs the Euler primality test for a given number.
+     *
+     * @param n     number to test (must be > 2 and odd)
+     * @param trials number of random bases to test
+     * @return {@code true} if {@code n} passes all Euler tests (probably prime),
+     *         {@code false} if composite.
+     */
+    public static boolean isProbablePrime(BigInteger n, int trials) {
+        if (n.compareTo(BigInteger.TWO) < 0) {
+            return false;
+        }
+        if (n.equals(BigInteger.TWO) || n.equals(BigInteger.valueOf(3))) {
+            return true;
+        }
+        if (n.mod(BigInteger.TWO).equals(BigInteger.ZERO)) {
+            return false;
+        }
+
+        for (int i = 0; i < trials; i++) {
+            BigInteger a = uniformRandom(BigInteger.TWO, n.subtract(BigInteger.TWO));
+            BigInteger jacobi = BigInteger.valueOf(jacobiSymbol(a, n));
+            if (jacobi.equals(BigInteger.ZERO)) {
+                return false;
+            }
+
+            BigInteger exp = n.subtract(BigInteger.ONE).divide(BigInteger.TWO);
+            BigInteger modExp = a.modPow(exp, n);
+
+            // Euler's criterion: a^((n-1)/2) ≡ (a/n) (mod n)
+            if (!modExp.equals(jacobi.mod(n))) {
+                return false; // definitely composite
+            }
+        }
+        return true; // probably prime
+    }
+
+    /**
+     * Computes the Jacobi symbol (a/n).
+     * Assumes n is positive and odd.
+     */
+    public static int jacobiSymbol(BigInteger a, BigInteger n) {
+        if (n.signum() <= 0 || n.mod(BigInteger.TWO).equals(BigInteger.ZERO)) {
+            throw new IllegalArgumentException("n must be positive and odd.");
+        }
+
+        int result = 1;
+        a = a.mod(n);
+
+        while (a.compareTo(BigInteger.ZERO) != 0) {
+            while (a.mod(BigInteger.TWO).equals(BigInteger.ZERO)) {
+                a = a.divide(BigInteger.TWO);
+                BigInteger nMod8 = n.mod(BigInteger.valueOf(8));
+                if (nMod8.equals(BigInteger.valueOf(3)) || nMod8.equals(BigInteger.valueOf(5))) {
+                    result = -result;
+                }
+            }
+
+            BigInteger temp = a;
+            a = n;
+            n = temp;
+
+            if (a.mod(BigInteger.valueOf(4)).equals(BigInteger.valueOf(3)) && n.mod(BigInteger.valueOf(4)).equals(BigInteger.valueOf(3))) {
+                result = -result;
+            }
+
+            a = a.mod(n);
+        }
+
+        return n.equals(BigInteger.ONE) ? result : 0;
+    }
+
+    /**
+     * Generates a random BigInteger between {@code min} and {@code max}, inclusive.
+     */
+    private static BigInteger uniformRandom(BigInteger min, BigInteger max) {
+        BigInteger result;
+        do {
+            result = new BigInteger(max.bitLength(), RANDOM);
+        } while (result.compareTo(min) < 0 || result.compareTo(max) > 0);
+        return result;
+    }
+}

src/test/java/com/thealgorithms/graph/ZeroOneBfsTest.java

@@ -0,0 +1,68 @@
+package com.thealgorithms.graph;
+
+import static org.junit.jupiter.api.Assertions.assertArrayEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import java.util.ArrayList;
+import java.util.List;
+import org.junit.jupiter.api.Test;
+
+class ZeroOneBfsTest {
+
+    // Helper to build adjacency list with capacity n
+    private static List<List<int[]>> makeAdj(int n) {
+        List<List<int[]>> adj = new ArrayList<>(n);
+        for (int i = 0; i < n; i++) {
+            adj.add(new ArrayList<>());
+        }
+        return adj;
+    }
+
+    @Test
+    void simpleLineGraph() {
+        int n = 4;
+        List<List<int[]>> adj = makeAdj(n);
+        // 0 --0--> 1 --1--> 2 --0--> 3
+        adj.get(0).add(new int[] {1, 0});
+        adj.get(1).add(new int[] {2, 1});
+        adj.get(2).add(new int[] {3, 0});
+
+        int[] dist = ZeroOneBfs.shortestPaths(n, adj, 0);
+        assertArrayEquals(new int[] {0, 0, 1, 1}, dist);
+    }
+
+    @Test
+    void parallelEdgesPreferZero() {
+        int n = 3;
+        List<List<int[]>> adj = makeAdj(n);
+        // Two edges 0->1: weight 1 and weight 0. Algorithm should choose 0.
+        adj.get(0).add(new int[] {1, 1});
+        adj.get(0).add(new int[] {1, 0});
+        adj.get(1).add(new int[] {2, 1});
+
+        int[] dist = ZeroOneBfs.shortestPaths(n, adj, 0);
+        assertArrayEquals(new int[] {0, 0, 1}, dist);
+    }
+
+    @Test
+    void unreachableNodes() {
+        int n = 3;
+        List<List<int[]>> adj = makeAdj(n);
+        adj.get(0).add(new int[] {1, 0});
+        int[] dist = ZeroOneBfs.shortestPaths(n, adj, 0);
+        // node 2 unreachable -> Integer.MAX_VALUE
+        assertArrayEquals(new int[] {0, 0, Integer.MAX_VALUE}, dist);
+    }
+
+    @Test
+    void invalidArgs() {
+        int n = 2;
+        List<List<int[]>> adj = makeAdj(n);
+        // invalid weight
+        adj.get(0).add(new int[] {1, 2});
+        assertThrows(IllegalArgumentException.class, () -> ZeroOneBfs.shortestPaths(n, adj, 0));
+        // invalid src
+        assertThrows(IllegalArgumentException.class, () -> ZeroOneBfs.shortestPaths(n, adj, -1));
+        assertThrows(IllegalArgumentException.class, () -> ZeroOneBfs.shortestPaths(n, adj, 2));
+    }
+}

src/test/java/com/thealgorithms/maths/EulerPseudoprimeTest.java

@@ -0,0 +1,93 @@
+package com.thealgorithms.maths;
+
+import static org.junit.jupiter.api.Assertions.assertFalse;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+import static org.mockito.ArgumentMatchers.any;
+
+import java.math.BigInteger;
+import org.junit.jupiter.api.Test;
+import org.mockito.MockedStatic;
+import org.mockito.Mockito;
+
+class EulerPseudoprimeTest {
+
+    @Test
+    void testPrimeNumbers() {
+        assertTrue(EulerPseudoprime.isProbablePrime(BigInteger.valueOf(7), 5));
+        assertTrue(EulerPseudoprime.isProbablePrime(BigInteger.valueOf(13), 5));
+        assertTrue(EulerPseudoprime.isProbablePrime(BigInteger.valueOf(101), 5));
+    }
+
+    @Test
+    void testCompositeNumbers() {
+        assertFalse(EulerPseudoprime.isProbablePrime(BigInteger.valueOf(9), 5));
+        assertFalse(EulerPseudoprime.isProbablePrime(BigInteger.valueOf(21), 5));
+        assertFalse(EulerPseudoprime.isProbablePrime(BigInteger.valueOf(221), 5));
+    }
+
+    @Test
+    void testEvenNumbers() {
+        assertFalse(EulerPseudoprime.isProbablePrime(BigInteger.valueOf(4), 5));
+        assertFalse(EulerPseudoprime.isProbablePrime(BigInteger.valueOf(100), 5));
+    }
+
+    @Test
+    void testEdgeCases() {
+        assertFalse(EulerPseudoprime.isProbablePrime(BigInteger.valueOf(0), 5));
+        assertFalse(EulerPseudoprime.isProbablePrime(BigInteger.valueOf(1), 5));
+        assertTrue(EulerPseudoprime.isProbablePrime(BigInteger.valueOf(2), 5));
+        assertTrue(EulerPseudoprime.isProbablePrime(BigInteger.valueOf(3), 5));
+    }
+
+    @Test
+    void testIsProbablePrimeWhenJacobiSymbolIsZero() {
+        try (MockedStatic<EulerPseudoprime> mockedPrimality = Mockito.mockStatic(EulerPseudoprime.class, Mockito.CALLS_REAL_METHODS)) {
+
+            // Mock jacobiSymbol to return 0 to test the branch
+            mockedPrimality.when(() -> EulerPseudoprime.jacobiSymbol(any(BigInteger.class), any(BigInteger.class))).thenReturn(0);
+
+            boolean result = EulerPseudoprime.isProbablePrime(BigInteger.valueOf(15), 1);
+
+            assertFalse(result);
+        }
+    }
+
+    @Test
+    void testJacobiSymbolThrowsForEvenOrNonPositiveN() throws Exception {
+        var method = EulerPseudoprime.class.getDeclaredMethod("jacobiSymbol", BigInteger.class, BigInteger.class);
+
+        // Helper lambda to unwrap InvocationTargetException
+        Runnable invokeJacobi = () -> {
+            try {
+                method.invoke(null, BigInteger.valueOf(2), BigInteger.valueOf(8));
+            } catch (Exception e) {
+                // unwrap
+                Throwable cause = e.getCause();
+                if (cause instanceof IllegalArgumentException) {
+                    throw (IllegalArgumentException) cause;
+                } else {
+                    throw new RuntimeException(e);
+                }
+            }
+        };
+
+        // Now check that it actually throws
+        assertThrows(IllegalArgumentException.class, invokeJacobi::run);
+
+        // Another case: non-positive n
+        Runnable invokeJacobi2 = () -> {
+            try {
+                method.invoke(null, BigInteger.valueOf(5), BigInteger.valueOf(-3));
+            } catch (Exception e) {
+                Throwable cause = e.getCause();
+                if (cause instanceof IllegalArgumentException) {
+                    throw (IllegalArgumentException) cause;
+                } else {
+                    throw new RuntimeException(e);
+                }
+            }
+        };
+        assertThrows(IllegalArgumentException.class, invokeJacobi2::run);
+    }
+}