programming-examples/java/Data_Structures/Arrangements.java

import java.util.*;

// https://en.wikipedia.org/wiki/Partial_permutation
public class Arrangements {

	public static boolean nextArrangement(int[] a, int n) {
		boolean[] used = new boolean[n];
		for (int x : a)
			used[x] = true;
		int m = a.length;
		for (int i = m - 1; i >= 0; i--) {
			used[a[i]] = false;
			for (int j = a[i] + 1; j < n; j++) {
				if (!used[j]) {
					a[i++] = j;
					used[j] = true;
					for (int k = 0; i < m; k++) {
						if (!used[k]) {
							a[i++] = k;
						}
					}
					return true;
				}
			}
		}
		return false;
	}

	public static int[] arrangementByNumber(int n, int m, long number) {
		int[] a = new int[m];
		int[] free = new int[n];
		for (int i = 0; i < n; i++) {
			free[i] = i;
		}
		for (int i = 0; i < m; i++) {
			long cnt = countOfArrangements(n - 1 - i, m - 1 - i);
			int pos = (int) (number / cnt);
			a[i] = free[pos];
			System.arraycopy(free, pos + 1, free, pos, n - 1 - pos);
			number %= cnt;
		}
		return a;
	}

	public static long numberByArrangement(int[] a, int n) {
		int m = a.length;
		long res = 0;
		boolean[] used = new boolean[n];
		for (int i = 0; i < m; i++) {
			int cnt = 0;
			for (int j = 0; j < a[i]; j++) {
				if (!used[j]) {
					++cnt;
				}
			}
			res += cnt * countOfArrangements(n - i - 1, m - i - 1);
			used[a[i]] = true;
		}
		return res;
	}

	public static long countOfArrangements(int n, int m) {
		long res = 1;
		for (int i = 0; i < m; i++) {
			res *= n - i;
		}
		return res;
	}

	public static boolean nextArrangementWithRepeats(int[] a, int n) {
		for (int i = a.length - 1; i >= 0; i--) {
			if (a[i] < n - 1) {
				++a[i];
				Arrays.fill(a, i + 1, a.length, 0);
				return true;
			}
		}
		return false;
	}

	// Usage example
	public static void main(String[] args) {
		// print all arrangements
		int[] a = {0, 1, 2};
		int cnt = 0;
		int n = 4;
		do {
			System.out.println(Arrays.toString(a));
			if (!Arrays.equals(a, arrangementByNumber(n, a.length, numberByArrangement(a, n))) ||
					cnt != numberByArrangement(arrangementByNumber(n, a.length, cnt), n))
				throw new RuntimeException();
			++cnt;
		} while (nextArrangement(a, n));

		// print all arrangements with repeats
		a = new int[]{0, 0};
		do {
			System.out.println(Arrays.toString(a));
		} while (nextArrangementWithRepeats(a, 2));

		a = new int[]{2, 3, 4};
		System.out.println(32 == numberByArrangement(a, 5));
		System.out.println(Arrays.equals(a, arrangementByNumber(5, a.length, 32)));
	}
}