Merge branch 'master' into sliding_window_new_algo

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/geometry/MidpointEllipse.java

@@ -0,0 +1,131 @@
+package com.thealgorithms.geometry;
+
+import java.util.ArrayList;
+import java.util.Collection;
+import java.util.List;
+
+/**
+ * The MidpointEllipse class implements the Midpoint Ellipse Drawing Algorithm.
+ * This algorithm efficiently computes the points on an ellipse by dividing it into two regions
+ * and using decision parameters to determine the next point to plot.
+ */
+public final class MidpointEllipse {
+
+    private MidpointEllipse() {
+        // Private constructor to prevent instantiation
+    }
+
+    /**
+     * Draws an ellipse using the Midpoint Ellipse Algorithm.
+     *
+     * @param centerX the x-coordinate of the center of the ellipse
+     * @param centerY the y-coordinate of the center of the ellipse
+     * @param a the length of the semi-major axis (horizontal radius)
+     * @param b the length of the semi-minor axis (vertical radius)
+     * @return a list of points (represented as int arrays) that form the ellipse
+     */
+    public static List<int[]> drawEllipse(int centerX, int centerY, int a, int b) {
+        List<int[]> points = new ArrayList<>();
+
+        // Handle degenerate cases with early returns
+        if (a == 0 && b == 0) {
+            points.add(new int[] {centerX, centerY}); // Only the center point
+            return points;
+        }
+
+        if (a == 0) {
+            // Semi-major axis is zero, create a vertical line
+            for (int y = centerY - b; y <= centerY + b; y++) {
+                points.add(new int[] {centerX, y});
+            }
+            return points; // Early return
+        }
+
+        if (b == 0) {
+            // Semi-minor axis is zero, create a horizontal line
+            for (int x = centerX - a; x <= centerX + a; x++) {
+                points.add(new int[] {x, centerY});
+            }
+            return points; // Early return
+        }
+
+        // Normal case: Non-degenerate ellipse
+        computeEllipsePoints(points, centerX, centerY, a, b);
+
+        return points; // Return all calculated points of the ellipse
+    }
+
+    /**
+     * Computes points of a non-degenerate ellipse using the Midpoint Ellipse Algorithm.
+     *
+     * @param points    the list to which points will be added
+     * @param centerX  the x-coordinate of the center of the ellipse
+     * @param centerY  the y-coordinate of the center of the ellipse
+     * @param a        the length of the semi-major axis (horizontal radius)
+     * @param b        the length of the semi-minor axis (vertical radius)
+     */
+    private static void computeEllipsePoints(Collection<int[]> points, int centerX, int centerY, int a, int b) {
+        int x = 0; // Initial x-coordinate
+        int y = b; // Initial y-coordinate
+
+        // Region 1: Initial decision parameter
+        double d1 = (b * b) - (a * a * b) + (0.25 * a * a); // Decision variable for region 1
+        double dx = 2.0 * b * b * x; // Change in x
+        double dy = 2.0 * a * a * y; // Change in y
+
+        // Region 1: When the slope is less than 1
+        while (dx < dy) {
+            addEllipsePoints(points, centerX, centerY, x, y);
+
+            // Update decision parameter and variables
+            if (d1 < 0) {
+                x++;
+                dx += (2 * b * b); // Update x change
+                d1 += dx + (b * b); // Update decision parameter
+            } else {
+                x++;
+                y--;
+                dx += (2 * b * b); // Update x change
+                dy -= (2 * a * a); // Update y change
+                d1 += dx - dy + (b * b); // Update decision parameter
+            }
+        }
+
+        // Region 2: Initial decision parameter for the second region
+        double d2 = b * b * (x + 0.5) * (x + 0.5) + a * a * (y - 1) * (y - 1) - a * a * b * b;
+
+        // Region 2: When the slope is greater than or equal to 1
+        while (y >= 0) {
+            addEllipsePoints(points, centerX, centerY, x, y);
+
+            // Update decision parameter and variables
+            if (d2 > 0) {
+                y--;
+                dy -= (2 * a * a); // Update y change
+                d2 += (a * a) - dy; // Update decision parameter
+            } else {
+                y--;
+                x++;
+                dx += (2 * b * b); // Update x change
+                dy -= (2 * a * a); // Update y change
+                d2 += dx - dy + (a * a); // Update decision parameter
+            }
+        }
+    }
+
+    /**
+     * Adds points for all four quadrants of the ellipse based on symmetry.
+     *
+     * @param points    the list to which points will be added
+     * @param centerX  the x-coordinate of the center of the ellipse
+     * @param centerY  the y-coordinate of the center of the ellipse
+     * @param x        the x-coordinate relative to the center
+     * @param y        the y-coordinate relative to the center
+     */
+    private static void addEllipsePoints(Collection<int[]> points, int centerX, int centerY, int x, int 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 - x, centerY - y});
+    }
+}

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.");
+    }
+}