programming-examples/java/Data_Structures/Combinations.java

import java.util.*;

// https://en.wikipedia.org/wiki/Combination
public class Combinations {

	public static boolean nextCombination(int[] p, int n) {
		int m = p.length;
		for (int i = m - 1; i >= 0; i--) {
			if (p[i] < n - m + i) {
				++p[i];
				while (++i < m) {
					p[i] = p[i - 1] + 1;
				}
				return true;
			}
		}
		return false;
	}

	public static int[] combinationByNumber(int n, int m, long number) {
		int[] c = new int[m];
		int cnt = n;
		for (int i = 0; i < m; i++) {
			int j = 1;
			while (true) {
				long am = binomial(cnt - j, m - 1 - i);
				if (number < am)
					break;
				number -= am;
				++j;
			}
			c[i] = (i > 0) ? (c[i - 1] + j) : (j - 1);
			cnt -= j;
		}
		return c;
	}

	public static long numberByCombination(int[] c, int n) {
		int m = c.length;
		long res = 0;
		int prev = -1;
		for (int i = 0; i < m; i++) {
			for (int j = prev + 1; j < c[i]; j++) {
				res += binomial(n - 1 - j, m - 1 - i);
			}
			prev = c[i];
		}
		return res;
	}

	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;
	}

	public static boolean nextCombinationWithRepeats(int[] p, int n) {
		int m = p.length;
		for (int i = m - 1; i >= 0; i--) {
			if (p[i] < n - 1) {
				++p[i];
				while (++i < m) {
					p[i] = p[i - 1];
				}
				return true;
			}
		}
		return false;
	}

	// Usage example
	public static void main(String[] args) {
		int[] p = {0, 1};
		System.out.println(!nextCombination(p, 2));
		System.out.println(Arrays.equals(new int[]{0, 1}, p));

		p = new int[]{0, 0};
		System.out.println(nextCombinationWithRepeats(p, 2));
		System.out.println(Arrays.equals(new int[]{0, 1}, p));

		System.out.println(nextCombinationWithRepeats(p, 2));
		System.out.println(Arrays.equals(new int[]{1, 1}, p));

		System.out.println(!nextCombinationWithRepeats(p, 2));

		System.out.println(78 == numberByCombination(new int[]{1, 2, 3, 6, 8}, 9));
		System.out.println(Arrays.toString(combinationByNumber(9, 5, 78)));

		p = new int[]{0, 0, 0};
		do {
			System.out.println(Arrays.toString(p));
		} while (nextCombinationWithRepeats(p, 3));
	}
}