Merge branch 'master' into add-sudoku-solver

Author: DenizAltunkapan

pom.xml

@@ -71,8 +71,7 @@
                 <artifactId>maven-compiler-plugin</artifactId>
                 <version>3.14.1</version>
                 <configuration>
-                    <source>21</source>
-                    <target>21</target>
+                    <release>21</release>
                     <compilerArgs>
                         <arg>-Xlint:all</arg>
                         <arg>-Xlint:-auxiliaryclass</arg>
@@ -128,7 +127,7 @@
                         <plugin>
                             <groupId>com.mebigfatguy.fb-contrib</groupId>
                             <artifactId>fb-contrib</artifactId>
-                            <version>7.6.14</version>
+                            <version>7.6.15</version>
                         </plugin>
                         <plugin>
                             <groupId>com.h3xstream.findsecbugs</groupId>

src/main/java/com/thealgorithms/conversions/CoordinateConverter.java

@@ -0,0 +1,57 @@
+package com.thealgorithms.conversions;
+
+/**
+ * A utility class to convert between Cartesian and Polar coordinate systems.
+ *
+ * <p>This class provides methods to perform the following conversions:
+ * <ul>
+ *   <li>Cartesian to Polar coordinates</li>
+ *   <li>Polar to Cartesian coordinates</li>
+ * </ul>
+ *
+ * <p>The class is final and cannot be instantiated.
+ */
+public final class CoordinateConverter {
+
+    private CoordinateConverter() {
+        // Prevent instantiation
+    }
+
+    /**
+     * Converts Cartesian coordinates to Polar coordinates.
+     *
+     * @param x the x-coordinate in the Cartesian system; must be a finite number
+     * @param y the y-coordinate in the Cartesian system; must be a finite number
+     * @return an array where the first element is the radius (r) and the second element is the angle (theta) in degrees
+     * @throws IllegalArgumentException if x or y is not a finite number
+     */
+    public static double[] cartesianToPolar(double x, double y) {
+        if (!Double.isFinite(x) || !Double.isFinite(y)) {
+            throw new IllegalArgumentException("x and y must be finite numbers.");
+        }
+        double r = Math.sqrt(x * x + y * y);
+        double theta = Math.toDegrees(Math.atan2(y, x));
+        return new double[] {r, theta};
+    }
+
+    /**
+     * Converts Polar coordinates to Cartesian coordinates.
+     *
+     * @param r the radius in the Polar system; must be non-negative
+     * @param thetaDegrees the angle (theta) in degrees in the Polar system; must be a finite number
+     * @return an array where the first element is the x-coordinate and the second element is the y-coordinate in the Cartesian system
+     * @throws IllegalArgumentException if r is negative or thetaDegrees is not a finite number
+     */
+    public static double[] polarToCartesian(double r, double thetaDegrees) {
+        if (r < 0) {
+            throw new IllegalArgumentException("Radius (r) must be non-negative.");
+        }
+        if (!Double.isFinite(thetaDegrees)) {
+            throw new IllegalArgumentException("Theta (angle) must be a finite number.");
+        }
+        double theta = Math.toRadians(thetaDegrees);
+        double x = r * Math.cos(theta);
+        double y = r * Math.sin(theta);
+        return new double[] {x, y};
+    }
+}

src/main/java/com/thealgorithms/dynamicprogramming/PartitionProblem.java

@@ -1,3 +1,5 @@
+package com.thealgorithms.dynamicprogramming;
+import java.util.Arrays;
 /**
  * @author Md Asif Joardar
  *
@@ -13,11 +15,6 @@
  *
  * The time complexity of the solution is O(n × sum) and requires O(n × sum) space
  */
-
-package com.thealgorithms.dynamicprogramming;
-
-import java.util.Arrays;
-
 public final class PartitionProblem {
     private PartitionProblem() {
     }

src/main/java/com/thealgorithms/geometry/Haversine.java

@@ -0,0 +1,49 @@
+package com.thealgorithms.geometry;
+/**
+ * This Class implements the Haversine formula to calculate the distance between two points on a sphere (like Earth) from their latitudes and longitudes.
+ *
+ * The Haversine formula is used in navigation and mapping to find the great-circle distance,
+ * which is the shortest distance between two points along the surface of a sphere. It is often
+ * used to calculate the "as the crow flies" distance between two geographical locations.
+ *
+ * The formula is reliable for all distances, including small ones, and avoids issues with
+ * numerical instability that can affect other methods.
+ *
+ * @see "https://en.wikipedia.org/wiki/Haversine_formula" - Wikipedia
+ */
+public final class Haversine {
+
+    // Average radius of Earth in kilometers
+    private static final double EARTH_RADIUS_KM = 6371.0;
+
+    /**
+     * Private constructor to prevent instantiation of this utility class.
+     */
+    private Haversine() {
+    }
+
+    /**
+     * Calculates the great-circle distance between two points on the earth
+     * (specified in decimal degrees).
+     *
+     * @param lat1 Latitude of the first point in decimal degrees.
+     * @param lon1 Longitude of the first point in decimal degrees.
+     * @param lat2 Latitude of the second point in decimal degrees.
+     * @param lon2 Longitude of the second point in decimal degrees.
+     * @return The distance between the two points in kilometers.
+     */
+    public static double haversine(double lat1, double lon1, double lat2, double lon2) {
+        // Convert latitude and longitude from degrees to radians
+        double dLat = Math.toRadians(lat2 - lat1);
+        double dLon = Math.toRadians(lon2 - lon1);
+
+        double lat1Rad = Math.toRadians(lat1);
+        double lat2Rad = Math.toRadians(lat2);
+
+        // Apply the Haversine formula
+        double a = Math.pow(Math.sin(dLat / 2), 2) + Math.pow(Math.sin(dLon / 2), 2) * Math.cos(lat1Rad) * Math.cos(lat2Rad);
+        double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
+
+        return EARTH_RADIUS_KM * c;
+    }
+}

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/main/java/com/thealgorithms/recursion/SylvesterSequence.java

@@ -0,0 +1,50 @@
+package com.thealgorithms.recursion;
+
+import java.math.BigInteger;
+
+/**
+ * A utility class for calculating numbers in Sylvester's sequence.
+ *
+ * <p>Sylvester's sequence is a sequence of integers where each term is calculated
+ * using the formula:
+ * <pre>
+ * a(n) = a(n-1) * (a(n-1) - 1) + 1
+ * </pre>
+ * with the first term being 2.
+ *
+ * <p>This class is final and cannot be instantiated.
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Sylvester_sequence">Wikipedia: Sylvester sequence</a>
+ */
+public final class SylvesterSequence {
+
+    // Private constructor to prevent instantiation
+    private SylvesterSequence() {
+    }
+
+    /**
+     * Calculates the nth number in Sylvester's sequence.
+     *
+     * <p>The sequence is defined recursively, with the first term being 2:
+     * <pre>
+     * a(1) = 2
+     * a(n) = a(n-1) * (a(n-1) - 1) + 1 for n > 1
+     * </pre>
+     *
+     * @param n the position in the sequence (must be greater than 0)
+     * @return the nth number in Sylvester's sequence
+     * @throws IllegalArgumentException if n is less than or equal to 0
+     */
+    public static BigInteger sylvester(int n) {
+        if (n <= 0) {
+            throw new IllegalArgumentException("sylvester() does not accept negative numbers or zero.");
+        }
+        if (n == 1) {
+            return BigInteger.valueOf(2);
+        } else {
+            BigInteger prev = sylvester(n - 1);
+            // Sylvester sequence formula: a(n) = a(n-1) * (a(n-1) - 1) + 1
+            return prev.multiply(prev.subtract(BigInteger.ONE)).add(BigInteger.ONE);
+        }
+    }
+}