/*
* 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<Integer, Long>> binomialCache = new ArrayList<Map<Integer, Long>>();
/** 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;
}
}