Add tests, improve docs in NewManShanksPrime (#5660)

src/test/java/com/thealgorithms/dynamicprogramming/NewManShanksPrimeTest.java

@@ -0,0 +1,80 @@
+package com.thealgorithms.dynamicprogramming;
+
+import static org.junit.jupiter.api.Assertions.assertFalse;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import org.junit.jupiter.api.Test;
+
+/**
+ * Unit tests for the NewManShanksPrime class.
+ * This test class verifies the correctness of the nthManShanksPrime method
+ * for various input cases.
+ */
+class NewManShanksPrimeTest {
+
+    /**
+     * Test case for the 1st New Man Shanks prime.
+     * The expected answer is 1.
+     */
+    @Test
+    void testNthManShanksPrime1() {
+        int n = 1;
+        int expectedAnswer = 1;
+        assertTrue(NewManShanksPrime.nthManShanksPrime(n, expectedAnswer), "The 1st New Man Shanks prime should be 1.");
+    }
+
+    /**
+     * Test case for the 2nd New Man Shanks prime.
+     * The expected answer is 3.
+     */
+    @Test
+    void testNthManShanksPrime2() {
+        int n = 2;
+        int expectedAnswer = 3;
+        assertTrue(NewManShanksPrime.nthManShanksPrime(n, expectedAnswer), "The 2nd New Man Shanks prime should be 3.");
+    }
+
+    /**
+     * Test case for the 3rd New Man Shanks prime.
+     * The expected answer is 7.
+     */
+    @Test
+    void testNthManShanksPrime3() {
+        int n = 3;
+        int expectedAnswer = 7;
+        assertTrue(NewManShanksPrime.nthManShanksPrime(n, expectedAnswer), "The 3rd New Man Shanks prime should be 7.");
+    }
+
+    /**
+     * Test case for the 4th New Man Shanks prime.
+     * The expected answer is 17.
+     */
+    @Test
+    void testNthManShanksPrime4() {
+        int n = 4;
+        int expectedAnswer = 17;
+        assertTrue(NewManShanksPrime.nthManShanksPrime(n, expectedAnswer), "The 4th New Man Shanks prime should be 17.");
+    }
+
+    /**
+     * Test case for the 5th New Man Shanks prime.
+     * The expected answer is 41.
+     */
+    @Test
+    void testNthManShanksPrime5() {
+        int n = 5;
+        int expectedAnswer = 41;
+        assertTrue(NewManShanksPrime.nthManShanksPrime(n, expectedAnswer), "The 5th New Man Shanks prime should be 41.");
+    }
+
+    /**
+     * Test case with an incorrect expected answer.
+     * For n = 2, the expected answer is 3.
+     */
+    @Test
+    void testNthManShanksPrimeIncorrectAnswer() {
+        int n = 2;
+        int expectedAnswer = 4; // Incorrect expected value
+        assertFalse(NewManShanksPrime.nthManShanksPrime(n, expectedAnswer), "The 2nd New Man Shanks prime should not be 4.");
+    }
+}