60 lines
1.4 KiB
Java
60 lines
1.4 KiB
Java
import java.math.BigInteger;
|
|
|
|
public class BinomialCoefficients {
|
|
|
|
public static long[][] binomialTable(int n) {
|
|
long[][] c = new long[n + 1][n + 1];
|
|
for (int i = 0; i <= n; i++)
|
|
for (int j = 0; j <= i; j++)
|
|
c[i][j] = (j == 0) ? 1 : c[i - 1][j - 1] + c[i - 1][j];
|
|
return c;
|
|
}
|
|
|
|
public static long binomial(long n, long m) {
|
|
m = Math.min(m, n - m);
|
|
long res = 1;
|
|
for (long i = 0; i < m; i++) {
|
|
res = res * (n - i) / (i + 1);
|
|
}
|
|
return res;
|
|
}
|
|
|
|
// for (int i = 1; i < f.length; i++) f[i] = f[i - 1] + Math.log(i);
|
|
public static double binomial(int n, int m, double[] f) {
|
|
if (m < 0 || m > n) return 0;
|
|
return Math.exp(f[n] - f[m] - f[n - m]);
|
|
}
|
|
|
|
// n! % mod
|
|
public static int factorial(int n, int mod) {
|
|
long res = 1;
|
|
for (int i = 2; i <= n; i++)
|
|
res = res * i % mod;
|
|
return (int) (res % mod);
|
|
}
|
|
|
|
// n! mod p, p - prime, O(p*log(n)) complexity
|
|
public static int factorial2(int n, int p) {
|
|
int res = 1;
|
|
while (n > 1) {
|
|
res = (res * ((n / p) % 2 == 1 ? p - 1 : 1)) % p;
|
|
for (int i = 2; i <= n % p; ++i)
|
|
res = (res * i) % p;
|
|
n /= p;
|
|
}
|
|
return res % p;
|
|
}
|
|
|
|
public static int binomial(int n, int m, int mod) {
|
|
m = Math.min(m, n - m);
|
|
long res = 1;
|
|
for (int i = n - m + 1; i <= n; i++)
|
|
res = res * i % mod;
|
|
return (int) (res * BigInteger.valueOf(factorial(m, mod)).modInverse(BigInteger.valueOf(mod)).intValue() % mod);
|
|
}
|
|
|
|
// Usage example
|
|
public static void main(String[] args) {
|
|
}
|
|
}
|