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