Merge branch 'master' into adfgvx_improve

Author: siriak

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

@@ -0,0 +1,85 @@
+package com.thealgorithms.geometry;
+
+import java.util.ArrayList;
+import java.util.Collection;
+import java.util.List;
+
+/**
+ * Class to represent the Midpoint Circle Algorithm.
+ * This algorithm calculates points on the circumference of a circle
+ * using integer arithmetic for efficient computation.
+ */
+public final class MidpointCircle {
+
+    private MidpointCircle() {
+        // Private Constructor to prevent instantiation.
+    }
+
+    /**
+     * Generates points on the circumference of a circle using the midpoint circle algorithm.
+     *
+     * @param centerX The x-coordinate of the circle's center.
+     * @param centerY The y-coordinate of the circle's center.
+     * @param radius  The radius of the circle.
+     * @return A list of points on the circle, each represented as an int[] with 2 elements [x, y].
+     */
+    public static List<int[]> generateCirclePoints(int centerX, int centerY, int radius) {
+        List<int[]> points = new ArrayList<>();
+
+        // Special case for radius 0, only the center point should be added.
+        if (radius == 0) {
+            points.add(new int[] {centerX, centerY});
+            return points;
+        }
+
+        // Start at (radius, 0)
+        int x = radius;
+        int y = 0;
+
+        // Decision parameter
+        int p = 1 - radius;
+
+        // Add the initial points in all octants
+        addSymmetricPoints(points, centerX, centerY, x, y);
+
+        // Iterate while x > y
+        while (x > y) {
+            y++;
+
+            if (p <= 0) {
+                // Midpoint is inside or on the circle
+                p = p + 2 * y + 1;
+            } else {
+                // Midpoint is outside the circle
+                x--;
+                p = p + 2 * y - 2 * x + 1;
+            }
+
+            // Add points for this (x, y)
+            addSymmetricPoints(points, centerX, centerY, x, y);
+        }
+
+        return points;
+    }
+
+    /**
+     * Adds the symmetric points in all octants of the circle based on the current x and y values.
+     *
+     * @param points  The list to which symmetric points will be added.
+     * @param centerX The x-coordinate of the circle's center.
+     * @param centerY The y-coordinate of the circle's center.
+     * @param x       The current x-coordinate on the circumference.
+     * @param y       The current y-coordinate on the circumference.
+     */
+    private static void addSymmetricPoints(Collection<int[]> points, int centerX, int centerY, int x, int y) {
+        // Octant symmetry points
+        points.add(new int[] {centerX + x, centerY + y});
+        points.add(new int[] {centerX - x, centerY + y});
+        points.add(new int[] {centerX + x, centerY - y});
+        points.add(new int[] {centerX - x, centerY - y});
+        points.add(new int[] {centerX + y, centerY + x});
+        points.add(new int[] {centerX - y, centerY + x});
+        points.add(new int[] {centerX + y, centerY - x});
+        points.add(new int[] {centerX - y, centerY - x});
+    }
+}

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

@@ -0,0 +1,39 @@
+package com.thealgorithms.maths;
+
+/**
+ * Calculate Catalan Numbers
+ */
+public final class CatalanNumbers {
+    private CatalanNumbers() {
+    }
+
+    /**
+     * Calculate the nth Catalan number using a recursive formula.
+     *
+     * @param n the index of the Catalan number to compute
+     * @return the nth Catalan number
+     */
+    public static long catalan(final int n) {
+        if (n < 0) {
+            throw new IllegalArgumentException("Index must be non-negative");
+        }
+        return factorial(2 * n) / (factorial(n + 1) * factorial(n));
+    }
+
+    /**
+     * Calculate the factorial of a number.
+     *
+     * @param n the number to compute the factorial for
+     * @return the factorial of n
+     */
+    private static long factorial(final int n) {
+        if (n == 0 || n == 1) {
+            return 1;
+        }
+        long result = 1;
+        for (int i = 2; i <= n; i++) {
+            result *= i;
+        }
+        return result;
+    }
+}

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

@@ -1,5 +1,7 @@
 package com.thealgorithms.maths;
 
+import java.util.Collections;
+import java.util.PriorityQueue;
 import java.util.Random;
 
 /**
@@ -62,4 +64,19 @@ private static void swap(int[] array, int i, int j) {
         array[i] = array[j];
         array[j] = temp;
     }
+
+    public static int findKthMaxUsingHeap(int[] array, int k) {
+        if (k <= 0 || k > array.length) {
+            throw new IllegalArgumentException("k must be between 1 and the size of the array");
+        }
+        PriorityQueue<Integer> maxHeap = new PriorityQueue<>(Collections.reverseOrder()); // using max-heap to store numbers.
+        for (int num : array) {
+            maxHeap.add(num);
+        }
+        while (k > 1) {
+            maxHeap.poll(); // removing max number from heap
+            k--;
+        }
+        return maxHeap.peek();
+    }
 }

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

@@ -18,4 +18,16 @@ public static boolean isPerfectSquare(final int number) {
         final int sqrt = (int) Math.sqrt(number);
         return sqrt * sqrt == number;
     }
+
+    /**
+     * Check if a number is perfect square or not
+     *
+     * @param number number to be checked
+     * @return {@code true} if {@code number} is perfect square, otherwise
+     * {@code false}
+     */
+    public static boolean isPerfectSquareUsingPow(long number) {
+        long a = (long) Math.pow(number, 1.0 / 2);
+        return a * a == number;
+    }
 }

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

@@ -21,6 +21,9 @@ private PronicNumber() {
      * @return true if input number is a pronic number, false otherwise
      */
     static boolean isPronic(int inputNumber) {
+        if (inputNumber == 0) {
+            return true;
+        }
         // Iterating from 0 to input_number
         for (int i = 0; i <= inputNumber; i++) {
             // Checking if product of i and (i+1) is equals input_number
@@ -34,4 +37,15 @@ static boolean isPronic(int inputNumber) {
         // equals input_number
         return false;
     }
+
+    /**
+     * This method checks if the given number is pronic number or non-pronic number using square root of number for finding divisors
+     *
+     * @param number Integer value which is to be checked if is a pronic number or not
+     * @return true if input number is a pronic number, false otherwise
+     */
+    public static boolean isPronicNumber(int number) {
+        int squareRoot = (int) Math.sqrt(number); // finding just smaller divisor of the number than its square root.
+        return squareRoot * (squareRoot + 1) == number;
+    }
 }

src/test/java/com/thealgorithms/geometry/MidpointCircleTest.java

@@ -0,0 +1,55 @@
+package com.thealgorithms.geometry;
+
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import java.util.List;
+import org.junit.jupiter.api.Test;
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.CsvSource;
+
+/**
+ * Test class for the {@code MidpointCircle} class
+ */
+class MidpointCircleTest {
+
+    /**
+     * Parameterized test to check the generated points for different circles.
+     * The points are checked based on the expected center and radius.
+     *
+     * @param centerX The x-coordinate of the circle's center.
+     * @param centerY The y-coordinate of the circle's center.
+     * @param radius  The radius of the circle.
+     */
+    @ParameterizedTest
+    @CsvSource({
+        "0, 0, 3", // Circle centered at (0, 0) with radius 3
+        "10, 10, 2" // Circle centered at (10, 10) with radius 2
+    })
+    void
+    testGenerateCirclePoints(int centerX, int centerY, int radius) {
+        List<int[]> points = MidpointCircle.generateCirclePoints(centerX, centerY, radius);
+
+        // Ensure that all points satisfy the circle equation (x - centerX)^2 + (y - centerY)^2 = radius^2
+        for (int[] point : points) {
+            int x = point[0];
+            int y = point[1];
+
+            int dx = x - centerX;
+            int dy = y - centerY;
+            int distanceSquared = dx * dx + dy * dy;
+
+            assertTrue(Math.abs(distanceSquared - radius * radius) <= 1, "Point (" + x + ", " + y + ") does not satisfy the circle equation.");
+        }
+    }
+
+    /**
+     * Test to ensure the algorithm generates points for a zero-radius circle.
+     */
+    @Test
+    void testZeroRadiusCircle() {
+        List<int[]> points = MidpointCircle.generateCirclePoints(0, 0, 0);
+
+        // A zero-radius circle should only have one point: (0, 0)
+        assertTrue(points.size() == 1 && points.get(0)[0] == 0 && points.get(0)[1] == 0, "Zero-radius circle did not generate the correct point.");
+    }
+}

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

@@ -0,0 +1,43 @@
+package com.thealgorithms.maths;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import java.util.stream.Stream;
+import org.junit.jupiter.api.Test;
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.MethodSource;
+
+/**
+ * Test class for CatalanNumbers
+ */
+class CatalanNumbersTest {
+
+    /**
+     * Provides test data for the parameterized Catalan number test.
+     * Each array contains two elements:
+     * [input number, expected Catalan number for that input]
+     */
+    static Stream<Object[]> catalanNumbersProvider() {
+        return Stream.of(new Object[] {0, 1}, new Object[] {1, 1}, new Object[] {2, 2}, new Object[] {3, 5}, new Object[] {4, 14}, new Object[] {5, 42}, new Object[] {6, 132}, new Object[] {7, 429}, new Object[] {8, 1430}, new Object[] {9, 4862}, new Object[] {10, 16796});
+    }
+
+    /**
+     * Parameterized test for checking the correctness of Catalan numbers.
+     * Uses the data from the provider method 'catalanNumbersProvider'.
+     */
+    @ParameterizedTest
+    @MethodSource("catalanNumbersProvider")
+    void testCatalanNumbers(int input, int expected) {
+        assertEquals(expected, CatalanNumbers.catalan(input), () -> String.format("Catalan number for input %d should be %d", input, expected));
+    }
+
+    /**
+     * Test for invalid inputs which should throw an IllegalArgumentException.
+     */
+    @Test
+    void testIllegalInput() {
+        assertThrows(IllegalArgumentException.class, () -> CatalanNumbers.catalan(-1));
+        assertThrows(IllegalArgumentException.class, () -> CatalanNumbers.catalan(-5));
+    }
+}

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

@@ -14,37 +14,50 @@ public void testFindKthMaxTypicalCases() {
         assertEquals(3, FindKthNumber.findKthMax(array1, 3));
         assertEquals(4, FindKthNumber.findKthMax(array1, 2));
         assertEquals(5, FindKthNumber.findKthMax(array1, 1));
+        assertEquals(3, FindKthNumber.findKthMaxUsingHeap(array1, 3));
+        assertEquals(4, FindKthNumber.findKthMaxUsingHeap(array1, 2));
+        assertEquals(5, FindKthNumber.findKthMaxUsingHeap(array1, 1));
 
         int[] array2 = {7, 5, 8, 2, 1, 6};
         assertEquals(5, FindKthNumber.findKthMax(array2, 4));
         assertEquals(6, FindKthNumber.findKthMax(array2, 3));
         assertEquals(8, FindKthNumber.findKthMax(array2, 1));
+        assertEquals(5, FindKthNumber.findKthMaxUsingHeap(array2, 4));
+        assertEquals(6, FindKthNumber.findKthMaxUsingHeap(array2, 3));
+        assertEquals(8, FindKthNumber.findKthMaxUsingHeap(array2, 1));
     }
 
     @Test
     public void testFindKthMaxEdgeCases() {
         int[] array1 = {1};
         assertEquals(1, FindKthNumber.findKthMax(array1, 1));
+        assertEquals(1, FindKthNumber.findKthMaxUsingHeap(array1, 1));
 
         int[] array2 = {5, 3};
         assertEquals(5, FindKthNumber.findKthMax(array2, 1));
         assertEquals(3, FindKthNumber.findKthMax(array2, 2));
+        assertEquals(5, FindKthNumber.findKthMaxUsingHeap(array2, 1));
+        assertEquals(3, FindKthNumber.findKthMaxUsingHeap(array2, 2));
     }
 
     @Test
     public void testFindKthMaxInvalidK() {
         int[] array = {1, 2, 3, 4, 5};
         assertThrows(IllegalArgumentException.class, () -> FindKthNumber.findKthMax(array, 0));
         assertThrows(IllegalArgumentException.class, () -> FindKthNumber.findKthMax(array, 6));
+        assertThrows(IllegalArgumentException.class, () -> FindKthNumber.findKthMaxUsingHeap(array, 0));
+        assertThrows(IllegalArgumentException.class, () -> FindKthNumber.findKthMaxUsingHeap(array, 6));
     }
 
     @Test
     public void testFindKthMaxLargeArray() {
         int[] array = generateArray(1000);
         int k = new Random().nextInt(1, array.length);
         int result = FindKthNumber.findKthMax(array, k);
+        int maxK = FindKthNumber.findKthMaxUsingHeap(array, k);
         Arrays.sort(array);
         assertEquals(array[array.length - k], result);
+        assertEquals(array[array.length - k], maxK);
     }
 
     public static int[] generateArray(int capacity) {

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

@@ -9,11 +9,13 @@ public class PerfectSquareTest {
     @ValueSource(ints = {0, 1, 2 * 2, 3 * 3, 4 * 4, 5 * 5, 6 * 6, 7 * 7, 8 * 8, 9 * 9, 10 * 10, 11 * 11, 123 * 123})
     void positiveTest(final int number) {
         Assertions.assertTrue(PerfectSquare.isPerfectSquare(number));
+        Assertions.assertTrue(PerfectSquare.isPerfectSquareUsingPow(number));
     }
 
     @ParameterizedTest
     @ValueSource(ints = {-1, -2, -3, -4, -5, -100, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 15, 17, 99, 101, 257, 999, 1001})
     void negativeTest(final int number) {
         Assertions.assertFalse(PerfectSquare.isPerfectSquare(number));
+        Assertions.assertFalse(PerfectSquare.isPerfectSquareUsingPow(number));
     }
 }