Segmented sieve problem added

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

@@ -0,0 +1,65 @@
+package com.thealgorithms.maths;
+
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.List;
+
+public class SegmentedSieve {
+
+    // fillPrime function fills primes from 2 to sqrt of high in chprime ArrayList    
+    public static void fillPrime(ArrayList<Integer> chprime, int high) {
+        boolean[] ck = new boolean[high + 1];
+        Arrays.fill(ck, true);
+        ck[1] = false;
+        ck[0] = false;
+
+        for (int i = 2; (i * i) <= high; i++) {
+            if (ck[i]) {
+                for (int j = i * i; j <= Math.sqrt(high); j = j + i) {
+                    ck[j] = false;
+                }
+            }
+        }
+        for (int i = 2; i * i <= high; i++) {
+            if (ck[i]) {
+                chprime.add(i);
+            }
+        }
+    }
+
+    // in segmented sieve we check for prime from range [low, high]
+    public static List<Integer> segmentedSieve(int low, int high) {
+        if (low > high || low < 2) {
+            throw new IllegalArgumentException("Invalid range");
+        }
+
+        ArrayList<Integer> chprime = new ArrayList<>();
+        fillPrime(chprime, high);
+
+        boolean[] prime = new boolean[high - low + 1];
+        Arrays.fill(prime, true);
+
+        for (int i : chprime) {
+            int lower = (low / i);
+            if (lower <= 1) {
+                lower = i + i;
+            } else if (low % i != 0) {
+                lower = (lower * i) + i;
+            } else {
+                lower = (lower * i);
+            }
+            for (int j = lower; j <= high; j = j + i) {
+                prime[j - low] = false;
+            }
+        }
+
+        List<Integer> result = new ArrayList<>();
+        for (int i = low; i <= high; i++) {
+            if (prime[i - low]) {
+                result.add(i);
+            }
+        }
+
+        return result;
+    }
+}

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

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+package com.thealgorithms.maths;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+import java.util.ArrayList;
+import java.util.List;
+import org.junit.jupiter.api.Test;
+
+public class SegmentedSieveTest {
+
+    @Test
+    public void testPrimesInRange() {
+        List<Integer> expectedPrimes = List.of(2, 3, 5, 7);
+        assertEquals(expectedPrimes, SegmentedSieve.segmentedSieve(2, 10));
+
+        List<Integer> expectedPrimes2 = List.of(11, 13, 17, 19);
+        assertEquals(expectedPrimes2, SegmentedSieve.segmentedSieve(10, 20));
+    }
+
+    @Test
+    public void testLargeRange() {
+        List<Integer> expectedPrimes = List.of(99991, 99997);
+        assertEquals(expectedPrimes, SegmentedSieve.segmentedSieve(99990, 100000));
+    }
+
+    @Test
+    public void testSinglePrime() {
+        List<Integer> expectedPrime = List.of(7);
+        assertEquals(expectedPrime, SegmentedSieve.segmentedSieve(7, 7));
+
+        List<Integer> expectedEmpty = new ArrayList<>();
+        assertEquals(expectedEmpty, SegmentedSieve.segmentedSieve(8, 8));
+    }
+
+    @Test
+    public void testInvalidRange() {
+        assertThrows(IllegalArgumentException.class, () -> SegmentedSieve.segmentedSieve(-10, 10));
+        assertThrows(IllegalArgumentException.class, () -> SegmentedSieve.segmentedSieve(20, 10)); // Invalid range
+    }
+}