Add Monte Carlo's Integral Approximation (#6235)

src/test/java/com/thealgorithms/randomized/MonteCarloIntegrationTest.java

@@ -0,0 +1,91 @@
+package com.thealgorithms.randomized;
+
+import static com.thealgorithms.randomized.MonteCarloIntegration.approximate;
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertNotNull;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import java.util.function.Function;
+import org.junit.jupiter.api.Test;
+
+class MonteCarloIntegrationTest {
+
+    private static final double EPSILON = 0.03; // Allow 3% error margin
+
+    @Test
+    void testConstantFunction() {
+        // Integral of f(x) = 2 from 0 to 1 is 2
+        Function<Double, Double> constant = x -> 2.0;
+        double result = approximate(constant, 0, 1, 10000);
+        assertEquals(2.0, result, EPSILON);
+    }
+
+    @Test
+    void testLinearFunction() {
+        // Integral of f(x) = x from 0 to 1 is 0.5
+        Function<Double, Double> linear = Function.identity();
+        double result = approximate(linear, 0, 1, 10000);
+        assertEquals(0.5, result, EPSILON);
+    }
+
+    @Test
+    void testQuadraticFunction() {
+        // Integral of f(x) = x^2 from 0 to 1 is 1/3
+        Function<Double, Double> quadratic = x -> x * x;
+        double result = approximate(quadratic, 0, 1, 10000);
+        assertEquals(1.0 / 3.0, result, EPSILON);
+    }
+
+    @Test
+    void testLargeSampleSize() {
+        // Integral of f(x) = x^2 from 0 to 1 is 1/3
+        Function<Double, Double> quadratic = x -> x * x;
+        double result = approximate(quadratic, 0, 1, 50000000);
+        assertEquals(1.0 / 3.0, result, EPSILON / 2); // Larger sample size, smaller error margin
+    }
+
+    @Test
+    void testReproducibility() {
+        Function<Double, Double> linear = Function.identity();
+        double result1 = approximate(linear, 0, 1, 10000, 42L);
+        double result2 = approximate(linear, 0, 1, 10000, 42L);
+        assertEquals(result1, result2, 0.0); // Exactly equal
+    }
+
+    @Test
+    void testNegativeInterval() {
+        // Integral of f(x) = x from -1 to 1 is 0
+        Function<Double, Double> linear = Function.identity();
+        double result = approximate(linear, -1, 1, 10000);
+        assertEquals(0.0, result, EPSILON);
+    }
+
+    @Test
+    void testNullFunction() {
+        Exception exception = assertThrows(IllegalArgumentException.class, () -> approximate(null, 0, 1, 1000));
+        assertNotNull(exception);
+    }
+
+    @Test
+    void testInvalidInterval() {
+        Function<Double, Double> linear = Function.identity();
+        Exception exception = assertThrows(IllegalArgumentException.class, () -> {
+            approximate(linear, 2, 1, 1000); // b <= a
+        });
+        assertNotNull(exception);
+    }
+
+    @Test
+    void testZeroSampleSize() {
+        Function<Double, Double> linear = Function.identity();
+        Exception exception = assertThrows(IllegalArgumentException.class, () -> approximate(linear, 0, 1, 0));
+        assertNotNull(exception);
+    }
+
+    @Test
+    void testNegativeSampleSize() {
+        Function<Double, Double> linear = Function.identity();
+        Exception exception = assertThrows(IllegalArgumentException.class, () -> approximate(linear, 0, 1, -100));
+        assertNotNull(exception);
+    }
+}