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)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.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 Binomial
* 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)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 returnedn 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 Binomial
* 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)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;
}
}