benjaminaaron · May 28, 2018 21:15 · benjaminaaron · May 28, 2018
diff --git a/Main.java b/Main.java
 import java.util.ArrayList;
 import java.util.Arrays;
 import java.util.List;
 import java.util.stream.Collectors;

 public class Main {

    static List<List<Integer>> partitions = new ArrayList<>();

    static void partition(int n, int max, String prefix) {
        // from https://introcs.cs.princeton.edu/java/23recursion/Partition.java
        if (n == 0) {
            partitions.add(Arrays.stream(prefix.trim().split(" ")).map(Integer::valueOf).collect(Collectors.toList()));
            return;
        }
        for (int i = Math.min(max, n); i >= 1; i--) {
            partition(n-i, i, prefix + " " + i);
        }
    }

    static long faculty(int val) {
        long faculty = 1;
        for (int i = 1; i <= val; i ++) {
            faculty *= i;
        }
        return faculty;
    }

    static long binomialCoefficient(int n, int k) { // n over k
        return faculty(n) / (faculty(k) * faculty(n - k));
    }

    public static void main(String[] args) {
        int n = 13; // group of size n
        boolean oneMemberPerSubgroup = true; // false means a group member can be in multiple subgroups

        partition(n, n, "");

        System.out.println(partitions.size() + " subgroup constellations are possible with a group of " + n + ":");
        System.out.println(partitions);

        long summedOptions = 0;
        for (List<Integer> row : partitions) {
            long options = 1;
            int n_left = n;
            for (Integer groupSize : row) {
                long binom = binomialCoefficient(n_left, groupSize);
                options *= binom;
                if (oneMemberPerSubgroup) {
                    n_left -= groupSize;
                }
            }
            System.out.println(options + " ways to arrange " + n + " in this subgroup constellations: " + row);
            summedOptions += options;
        }

        System.out.println("\n --> " + summedOptions + " ways to create subgroup constellations from a group of " + n
                + " with members" + (oneMemberPerSubgroup ? " NOT " : " ") + "being allowed in more than one subgroup");
    }
 }
	import java.util.ArrayList;
	import java.util.Arrays;
	import java.util.List;
	import java.util.stream.Collectors;

	public class Main {

	static List<List<Integer>> partitions = new ArrayList<>();

	static void partition(int n, int max, String prefix) {
	// from https://introcs.cs.princeton.edu/java/23recursion/Partition.java
	if (n == 0) {
	partitions.add(Arrays.stream(prefix.trim().split(" ")).map(Integer::valueOf).collect(Collectors.toList()));
	return;
	}
	for (int i = Math.min(max, n); i >= 1; i--) {
	partition(n-i, i, prefix + " " + i);
	}
	}

	static long faculty(int val) {
	long faculty = 1;
	for (int i = 1; i <= val; i ++) {
	faculty *= i;
	}
	return faculty;
	}

	static long binomialCoefficient(int n, int k) { // n over k
	return faculty(n) / (faculty(k) * faculty(n - k));
	}

	public static void main(String[] args) {
	int n = 13; // group of size n
	boolean oneMemberPerSubgroup = true; // false means a group member can be in multiple subgroups

	partition(n, n, "");

	System.out.println(partitions.size() + " subgroup constellations are possible with a group of " + n + ":");
	System.out.println(partitions);

	long summedOptions = 0;
	for (List<Integer> row : partitions) {
	long options = 1;
	int n_left = n;
	for (Integer groupSize : row) {
	long binom = binomialCoefficient(n_left, groupSize);
	options *= binom;
	if (oneMemberPerSubgroup) {
	n_left -= groupSize;
	}
	}
	System.out.println(options + " ways to arrange " + n + " in this subgroup constellations: " + row);
	summedOptions += options;
	}

	System.out.println("\n --> " + summedOptions + " ways to create subgroup constellations from a group of " + n
	+ " with members" + (oneMemberPerSubgroup ? " NOT " : " ") + "being allowed in more than one subgroup");
	}
	}