From b0f6b541c495889fbfeaaaf6380ccd90f97471a1 Mon Sep 17 00:00:00 2001
From: Shreya-1305 <paintershreya@gmail.com>
Date: Thu, 24 Oct 2024 09:51:15 +0530
Subject: [PATCH] Segmented Sieve Problem added

---
 .../maths/SegmentedSieveTest.java             | 87 +++++++++++++++++++
 1 file changed, 87 insertions(+)
 create mode 100644 src/main/java/com/thealgorithms/maths/SegmentedSieveTest.java

diff --git a/src/main/java/com/thealgorithms/maths/SegmentedSieveTest.java b/src/main/java/com/thealgorithms/maths/SegmentedSieveTest.java
new file mode 100644
index 000000000000..c57b3e835fca
--- /dev/null
+++ b/src/main/java/com/thealgorithms/maths/SegmentedSieveTest.java
@@ -0,0 +1,87 @@
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import java.util.*;
+import org.junit.jupiter.api.Test;
+
+public class SegmentedSieveTest {
+
+    // The segmented sieve algorithm implementation
+    public static void fillPrime(List<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 <= high; j = j + i) {
+                    ck[j] = false;
+                }
+            }
+        }
+        for (int i = 2; i <= high; i++) {
+            if (ck[i]) {
+                chprime.add(i);
+            }
+        }
+    }
+
+    public static List<Integer> segmentedSieve(int low, int high) {
+        if (low < 2) throw new IllegalArgumentException("Low must be greater than or equal to 2.");
+        if (low > high) throw new IllegalArgumentException("Low cannot be greater than high.");
+
+        List<Integer> chprime = new ArrayList<>();
+        fillPrime(chprime, (int) Math.sqrt(high));
+
+        boolean[] prime = new boolean[high - low + 1];
+        Arrays.fill(prime, true);
+
+        for (int primeNum : chprime) {
+            int lower = (low / primeNum) * primeNum;
+            if (lower < low) lower += primeNum;
+            if (lower == primeNum) lower += primeNum;
+
+            for (int j = lower; j <= high; j += primeNum) {
+                prime[j - low] = false;
+            }
+        }
+
+        List<Integer> primesInRange = new ArrayList<>();
+        for (int i = low; i <= high; i++) {
+            if (prime[i - low]) {
+                primesInRange.add(i);
+            }
+        }
+
+        return primesInRange;
+    }
+
+    // JUnit test cases
+    @Test
+    public void testSegmentedSieveSmallRange() {
+        List<Integer> expectedPrimes = Arrays.asList(2, 3, 5, 7);
+        assertEquals(expectedPrimes, segmentedSieve(2, 10));
+    }
+
+    @Test
+    public void testSegmentedSieveLargeRange() {
+        List<Integer> expectedPrimes = Arrays.asList(99991, 99997);
+        assertEquals(expectedPrimes, segmentedSieve(99990, 100000));
+    }
+
+    @Test
+    public void testSegmentedSieveSingleNumberRange() {
+        List<Integer> expectedPrime = Arrays.asList(7);
+        assertEquals(expectedPrime, segmentedSieve(7, 7));
+
+        List<Integer> expectedEmpty = new ArrayList<>();
+        assertEquals(expectedEmpty, segmentedSieve(8, 8));
+    }
+
+    @Test
+    public void testSegmentedSieveWithInvalidRange() {
+        assertThrows(IllegalArgumentException.class, () -> segmentedSieve(-10, 10));
+        assertThrows(IllegalArgumentException.class, () -> segmentedSieve(20, 10));
+    }
+}