added program for lucky number

Author: TaranjeetSinghKalsi

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

@@ -0,0 +1,72 @@
+package com.thealgorithms.maths;
+
+/**
+ * In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve".
+ * This sieve is similar to the sieve of Eratosthenes that generates the primes,
+ * but it eliminates numbers based on their position in the remaining set,
+ * instead of their value (or position in the initial set of natural numbers).
+ *
+ * Wiki: https://en.wikipedia.org/wiki/Lucky_number
+ */
+public final class LuckyNumber {
+
+    private LuckyNumber() {
+    }
+
+    // Common validation method
+    private static void validatePositiveNumber(int number) {
+        if (number <= 0) {
+            throw new IllegalArgumentException("Number must be positive.");
+        }
+    }
+
+    // Function to check recursively for Lucky Number
+    private static boolean isLuckyRecursiveApproach(int n, int counter) {
+        // Base case: If counter exceeds n, number is lucky
+        if (counter > n) return true;
+
+        // If number is eliminated in this step, it's not lucky
+        if (n % counter == 0) return false;
+
+        // Calculate new position after removing every counter-th number
+        int newNumber = n - (n / counter);
+
+        // Recursive call for next round
+        return isLuckyRecursiveApproach(newNumber, counter + 1);
+    }
+
+    /**
+     * Check if {@code number} is a Lucky number or not using recursive approach
+     *
+     * @param number the number
+     * @return {@code true} if {@code number} is a Lucky number, otherwise false
+     */
+    public static boolean isLuckyNumber(int number) {
+        validatePositiveNumber(number);
+        int counterStarting = 2;
+        return isLuckyRecursiveApproach(number, counterStarting);
+    }
+
+    /**
+     * Check if {@code number} is a Lucky number or not using iterative approach
+     *
+     * @param number the number
+     * @return {@code true} if {@code number} is a Lucky number, otherwise false
+     */
+    public static boolean isLucky(int number) {
+        validatePositiveNumber(number);
+
+        int counter = 2; // Position starts from 2 (since first elimination happens at 2)
+        int position = number; // The position of the number in the sequence
+
+        while (counter <= position) {
+            if (position % counter == 0) return false; // Number is eliminated
+
+            // Update the position of n after removing every counter-th number
+            position = position - (position / counter);
+            counter++;
+        }
+
+        return true; // Survives all eliminations → Lucky Number
+    }
+}

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

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+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 org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.CsvSource;
+
+class LuckyNumberTest {
+
+    @ParameterizedTest
+    @CsvSource({"1", "3", "13", "49", "109", "459", "949"})
+    void luckyNumbersTest(int n) {
+        assertTrue(LuckyNumber.isLucky(n));
+        assertTrue(LuckyNumber.isLuckyNumber(n));
+    }
+
+    @ParameterizedTest
+    @CsvSource({"2", "17", "100", "300", "700"})
+    void nonLuckyNumbersTest(int n) {
+        assertFalse(LuckyNumber.isLucky(n));
+        assertFalse(LuckyNumber.isLuckyNumber(n));
+    }
+
+    @ParameterizedTest
+    @CsvSource({"0", "-1"})
+    void throwsNegativeNumbersNotAllowed(int n) {
+        assertThrows(IllegalArgumentException.class, () -> LuckyNumber.isLucky(n));
+        assertThrows(IllegalArgumentException.class, () -> LuckyNumber.isLuckyNumber(n));
+    }
+}