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Java example source code file (CombinatoricsUtilsTest.java)

This example Java source code file (CombinatoricsUtilsTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

arraylist, combinatoricsutilstest, double, expecting, hashmap, list, long, matharithmeticexception, mathillegalargumentexception, test, util

The CombinatoricsUtilsTest.java Java example source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math3.util;

import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

import org.apache.commons.math3.exception.MathArithmeticException;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.NotPositiveException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.junit.Assert;
import org.junit.Test;

/**
 * Test cases for the {@link CombinatoricsUtils} class.
 *
 */
public class CombinatoricsUtilsTest {

    /** cached binomial coefficients */
    private static final List<Map binomialCache = new ArrayList>();

    /** Verify that b(0,0) = 1 */
    @Test
    public void test0Choose0() {
        Assert.assertEquals(CombinatoricsUtils.binomialCoefficientDouble(0, 0), 1d, 0);
        Assert.assertEquals(CombinatoricsUtils.binomialCoefficientLog(0, 0), 0d, 0);
        Assert.assertEquals(CombinatoricsUtils.binomialCoefficient(0, 0), 1);
    }

    @Test
    public void testBinomialCoefficient() {
        long[] bcoef5 = {
            1,
            5,
            10,
            10,
            5,
            1 };
        long[] bcoef6 = {
            1,
            6,
            15,
            20,
            15,
            6,
            1 };
        for (int i = 0; i < 6; i++) {
            Assert.assertEquals("5 choose " + i, bcoef5[i], CombinatoricsUtils.binomialCoefficient(5, i));
        }
        for (int i = 0; i < 7; i++) {
            Assert.assertEquals("6 choose " + i, bcoef6[i], CombinatoricsUtils.binomialCoefficient(6, i));
        }

        for (int n = 1; n < 10; n++) {
            for (int k = 0; k <= n; k++) {
                Assert.assertEquals(n + " choose " + k, binomialCoefficient(n, k), CombinatoricsUtils.binomialCoefficient(n, k));
                Assert.assertEquals(n + " choose " + k, binomialCoefficient(n, k), CombinatoricsUtils.binomialCoefficientDouble(n, k), Double.MIN_VALUE);
                Assert.assertEquals(n + " choose " + k, FastMath.log(binomialCoefficient(n, k)), CombinatoricsUtils.binomialCoefficientLog(n, k), 10E-12);
            }
        }

        int[] n = { 34, 66, 100, 1500, 1500 };
        int[] k = { 17, 33, 10, 1500 - 4, 4 };
        for (int i = 0; i < n.length; i++) {
            long expected = binomialCoefficient(n[i], k[i]);
            Assert.assertEquals(n[i] + " choose " + k[i], expected,
                CombinatoricsUtils.binomialCoefficient(n[i], k[i]));
            Assert.assertEquals(n[i] + " choose " + k[i], expected,
                CombinatoricsUtils.binomialCoefficientDouble(n[i], k[i]), 0.0);
            Assert.assertEquals("log(" + n[i] + " choose " + k[i] + ")", FastMath.log(expected),
                CombinatoricsUtils.binomialCoefficientLog(n[i], k[i]), 0.0);
        }
    }

    @Test
    public void testBinomialCoefficientFail() {
        try {
            CombinatoricsUtils.binomialCoefficient(4, 5);
            Assert.fail("expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // ignored
        }

        try {
            CombinatoricsUtils.binomialCoefficientDouble(4, 5);
            Assert.fail("expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // ignored
        }

        try {
            CombinatoricsUtils.binomialCoefficientLog(4, 5);
            Assert.fail("expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // ignored
        }

        try {
            CombinatoricsUtils.binomialCoefficient(-1, -2);
            Assert.fail("expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // ignored
        }
        try {
            CombinatoricsUtils.binomialCoefficientDouble(-1, -2);
            Assert.fail("expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // ignored
        }
        try {
            CombinatoricsUtils.binomialCoefficientLog(-1, -2);
            Assert.fail("expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // ignored
        }

        try {
            CombinatoricsUtils.binomialCoefficient(67, 30);
            Assert.fail("expecting MathArithmeticException");
        } catch (MathArithmeticException ex) {
            // ignored
        }
        try {
            CombinatoricsUtils.binomialCoefficient(67, 34);
            Assert.fail("expecting MathArithmeticException");
        } catch (MathArithmeticException ex) {
            // ignored
        }
        double x = CombinatoricsUtils.binomialCoefficientDouble(1030, 515);
        Assert.assertTrue("expecting infinite binomial coefficient", Double
            .isInfinite(x));
    }

    /**
     * Tests correctness for large n and sharpness of upper bound in API doc
     * JIRA: MATH-241
     */
    @Test
    public void testBinomialCoefficientLarge() throws Exception {
        // This tests all legal and illegal values for n <= 200.
        for (int n = 0; n <= 200; n++) {
            for (int k = 0; k <= n; k++) {
                long ourResult = -1;
                long exactResult = -1;
                boolean shouldThrow = false;
                boolean didThrow = false;
                try {
                    ourResult = CombinatoricsUtils.binomialCoefficient(n, k);
                } catch (MathArithmeticException ex) {
                    didThrow = true;
                }
                try {
                    exactResult = binomialCoefficient(n, k);
                } catch (MathArithmeticException ex) {
                    shouldThrow = true;
                }
                Assert.assertEquals(n + " choose " + k, exactResult, ourResult);
                Assert.assertEquals(n + " choose " + k, shouldThrow, didThrow);
                Assert.assertTrue(n + " choose " + k, (n > 66 || !didThrow));

                if (!shouldThrow && exactResult > 1) {
                    Assert.assertEquals(n + " choose " + k, 1.,
                        CombinatoricsUtils.binomialCoefficientDouble(n, k) / exactResult, 1e-10);
                    Assert.assertEquals(n + " choose " + k, 1,
                        CombinatoricsUtils.binomialCoefficientLog(n, k) / FastMath.log(exactResult), 1e-10);
                }
            }
        }

        long ourResult = CombinatoricsUtils.binomialCoefficient(300, 3);
        long exactResult = binomialCoefficient(300, 3);
        Assert.assertEquals(exactResult, ourResult);

        ourResult = CombinatoricsUtils.binomialCoefficient(700, 697);
        exactResult = binomialCoefficient(700, 697);
        Assert.assertEquals(exactResult, ourResult);

        // This one should throw
        try {
            CombinatoricsUtils.binomialCoefficient(700, 300);
            Assert.fail("Expecting MathArithmeticException");
        } catch (MathArithmeticException ex) {
            // Expected
        }

        int n = 10000;
        ourResult = CombinatoricsUtils.binomialCoefficient(n, 3);
        exactResult = binomialCoefficient(n, 3);
        Assert.assertEquals(exactResult, ourResult);
        Assert.assertEquals(1, CombinatoricsUtils.binomialCoefficientDouble(n, 3) / exactResult, 1e-10);
        Assert.assertEquals(1, CombinatoricsUtils.binomialCoefficientLog(n, 3) / FastMath.log(exactResult), 1e-10);

    }

    @Test
    public void testFactorial() {
        for (int i = 1; i < 21; i++) {
            Assert.assertEquals(i + "! ", factorial(i), CombinatoricsUtils.factorial(i));
            Assert.assertEquals(i + "! ", factorial(i), CombinatoricsUtils.factorialDouble(i), Double.MIN_VALUE);
            Assert.assertEquals(i + "! ", FastMath.log(factorial(i)), CombinatoricsUtils.factorialLog(i), 10E-12);
        }

        Assert.assertEquals("0", 1, CombinatoricsUtils.factorial(0));
        Assert.assertEquals("0", 1.0d, CombinatoricsUtils.factorialDouble(0), 1E-14);
        Assert.assertEquals("0", 0.0d, CombinatoricsUtils.factorialLog(0), 1E-14);
    }

    @Test
    public void testFactorialFail() {
        try {
            CombinatoricsUtils.factorial(-1);
            Assert.fail("expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // ignored
        }
        try {
            CombinatoricsUtils.factorialDouble(-1);
            Assert.fail("expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // ignored
        }
        try {
            CombinatoricsUtils.factorialLog(-1);
            Assert.fail("expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // ignored
        }
        try {
            CombinatoricsUtils.factorial(21);
            Assert.fail("expecting MathArithmeticException");
        } catch (MathArithmeticException ex) {
            // ignored
        }
        Assert.assertTrue("expecting infinite factorial value", Double.isInfinite(CombinatoricsUtils.factorialDouble(171)));
    }

    @Test
    public void testStirlingS2() {

        Assert.assertEquals(1, CombinatoricsUtils.stirlingS2(0, 0));

        for (int n = 1; n < 30; ++n) {
            Assert.assertEquals(0, CombinatoricsUtils.stirlingS2(n, 0));
            Assert.assertEquals(1, CombinatoricsUtils.stirlingS2(n, 1));
            if (n > 2) {
                Assert.assertEquals((1l << (n - 1)) - 1l, CombinatoricsUtils.stirlingS2(n, 2));
                Assert.assertEquals(CombinatoricsUtils.binomialCoefficient(n, 2),
                                    CombinatoricsUtils.stirlingS2(n, n - 1));
            }
            Assert.assertEquals(1, CombinatoricsUtils.stirlingS2(n, n));
        }
        Assert.assertEquals(536870911l, CombinatoricsUtils.stirlingS2(30, 2));
        Assert.assertEquals(576460752303423487l, CombinatoricsUtils.stirlingS2(60, 2));

        Assert.assertEquals(   25, CombinatoricsUtils.stirlingS2( 5, 3));
        Assert.assertEquals(   90, CombinatoricsUtils.stirlingS2( 6, 3));
        Assert.assertEquals(   65, CombinatoricsUtils.stirlingS2( 6, 4));
        Assert.assertEquals(  301, CombinatoricsUtils.stirlingS2( 7, 3));
        Assert.assertEquals(  350, CombinatoricsUtils.stirlingS2( 7, 4));
        Assert.assertEquals(  140, CombinatoricsUtils.stirlingS2( 7, 5));
        Assert.assertEquals(  966, CombinatoricsUtils.stirlingS2( 8, 3));
        Assert.assertEquals( 1701, CombinatoricsUtils.stirlingS2( 8, 4));
        Assert.assertEquals( 1050, CombinatoricsUtils.stirlingS2( 8, 5));
        Assert.assertEquals(  266, CombinatoricsUtils.stirlingS2( 8, 6));
        Assert.assertEquals( 3025, CombinatoricsUtils.stirlingS2( 9, 3));
        Assert.assertEquals( 7770, CombinatoricsUtils.stirlingS2( 9, 4));
        Assert.assertEquals( 6951, CombinatoricsUtils.stirlingS2( 9, 5));
        Assert.assertEquals( 2646, CombinatoricsUtils.stirlingS2( 9, 6));
        Assert.assertEquals(  462, CombinatoricsUtils.stirlingS2( 9, 7));
        Assert.assertEquals( 9330, CombinatoricsUtils.stirlingS2(10, 3));
        Assert.assertEquals(34105, CombinatoricsUtils.stirlingS2(10, 4));
        Assert.assertEquals(42525, CombinatoricsUtils.stirlingS2(10, 5));
        Assert.assertEquals(22827, CombinatoricsUtils.stirlingS2(10, 6));
        Assert.assertEquals( 5880, CombinatoricsUtils.stirlingS2(10, 7));
        Assert.assertEquals(  750, CombinatoricsUtils.stirlingS2(10, 8));

    }

    @Test(expected=NotPositiveException.class)
    public void testStirlingS2NegativeN() {
        CombinatoricsUtils.stirlingS2(3, -1);
    }

    @Test(expected=NumberIsTooLargeException.class)
    public void testStirlingS2LargeK() {
        CombinatoricsUtils.stirlingS2(3, 4);
    }

    @Test(expected=MathArithmeticException.class)
    public void testStirlingS2Overflow() {
        CombinatoricsUtils.stirlingS2(26, 9);
    }

    @Test(expected=NotPositiveException.class)
    public void testCheckBinomial1() {
        // n < 0
        CombinatoricsUtils.checkBinomial(-1, -2);
    }

    @Test(expected=NumberIsTooLargeException.class)
    public void testCheckBinomial2() {
        // k > n
        CombinatoricsUtils.checkBinomial(4, 5);
    }

    @Test
    public void testCheckBinomial3() {
        // OK (no exception thrown)
        CombinatoricsUtils.checkBinomial(5, 4);
    }

    /**
     * Exact (caching) recursive implementation to test against
     */
    private long binomialCoefficient(int n, int k) throws MathArithmeticException {
        if (binomialCache.size() > n) {
            Long cachedResult = binomialCache.get(n).get(Integer.valueOf(k));
            if (cachedResult != null) {
                return cachedResult.longValue();
            }
        }
        long result = -1;
        if ((n == k) || (k == 0)) {
            result = 1;
        } else if ((k == 1) || (k == n - 1)) {
            result = n;
        } else {
            // Reduce stack depth for larger values of n
            if (k < n - 100) {
                binomialCoefficient(n - 100, k);
            }
            if (k > 100) {
                binomialCoefficient(n - 100, k - 100);
            }
            result = ArithmeticUtils.addAndCheck(binomialCoefficient(n - 1, k - 1),
                binomialCoefficient(n - 1, k));
        }
        if (result == -1) {
            throw new MathArithmeticException();
        }
        for (int i = binomialCache.size(); i < n + 1; i++) {
            binomialCache.add(new HashMap<Integer, Long>());
        }
        binomialCache.get(n).put(Integer.valueOf(k), Long.valueOf(result));
        return result;
    }

    /**
     * Exact direct multiplication implementation to test against
     */
    private long factorial(int n) {
        long result = 1;
        for (int i = 2; i <= n; i++) {
            result *= i;
        }
        return result;
    }
}

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