import java.io.File;
/*
* 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.
*
*
*/
public class Main {
/**
* Returns an exact representation of the
* Coefficient, "n choose k", the number of
* k-element subsets that can be selected from an
* n-element set.
*
* Preconditions:
*
* -
0 <= k <= n (otherwise
* IllegalArgumentException is thrown)
* - The result is small enough to fit into a
long. The
* largest value of n for which all coefficients are
* < Long.MAX_VALUE is 66. If the computed value exceeds
* Long.MAX_VALUE an ArithMeticException
* is
* thrown.
*
*
* @param n the size of the set
* @param k the size of the subsets to be counted
* @return n choose k
* @throws IllegalArgumentException if preconditions are not met.
* @throws ArithmeticException if the result is too large to be represented
* by a long integer.
*/
public static long binomialCoefficient(final int n, final int k) {
if (n < k) {
throw new IllegalArgumentException(
"must have n >= k for binomial coefficient (n,k)");
}
if (n < 0) {
throw new IllegalArgumentException(
"must have n >= 0 for binomial coefficient (n,k)");
}
if ((n == k) || (k == 0)) {
return 1;
}
if ((k == 1) || (k == n - 1)) {
return n;
}
long result = Math.round(binomialCoefficientDouble(n, k));
if (result == Long.MAX_VALUE) {
throw new ArithmeticException(
"result too large to represent in a long integer");
}
return result;
}
/**
* Returns a double representation of the
* Coefficient, "n choose k", the number of
* k-element subsets that can be selected from an
* n-element set.
*
* Preconditions:
*
* -
0 <= k <= n (otherwise
* IllegalArgumentException is thrown)
* - The result is small enough to fit into a
double. The
* largest value of n for which all coefficients are <
* Double.MAX_VALUE is 1029. If the computed value exceeds Double.MAX_VALUE,
* Double.POSITIVE_INFINITY is returned
*
*
* @param n the size of the set
* @param k the size of the subsets to be counted
* @return n choose k
* @throws IllegalArgumentException if preconditions are not met.
*/
public static double binomialCoefficientDouble(final int n, final int k) {
return Math.floor(Math.exp(binomialCoefficientLog(n, k)) + 0.5);
}
/**
* Returns the natural log of the
* Coefficient, "n choose k", the number of
* k-element subsets that can be selected from an
* n-element set.
*
* Preconditions:
*
* -
0 <= k <= n (otherwise
* IllegalArgumentException is thrown)
*
*
* @param n the size of the set
* @param k the size of the subsets to be counted
* @return n choose k
* @throws IllegalArgumentException if preconditions are not met.
*/
public static double binomialCoefficientLog(final int n, final int k) {
if (n < k) {
throw new IllegalArgumentException(
"must have n >= k for binomial coefficient (n,k)");
}
if (n < 0) {
throw new IllegalArgumentException(
"must have n >= 0 for binomial coefficient (n,k)");
}
if ((n == k) || (k == 0)) {
return 0;
}
if ((k == 1) || (k == n - 1)) {
return Math.log((double)n);
}
double logSum = 0;
// n!/k!
for (int i = k + 1; i <= n; i++) {
logSum += Math.log((double)i);
}
// divide by (n-k)!
for (int i = 2; i <= n - k; i++) {
logSum -= Math.log((double)i);
}
return logSum;
}
}