96 lines
2.4 KiB
Java
96 lines
2.4 KiB
Java
import java.util.ArrayList;
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import java.util.Arrays;
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import java.util.List;
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public class Derangement {
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public static void main(String[] args) {
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System.out.println("derangements for n = 4\n");
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for (Object d : (ArrayList)(derangements(4, false)[0])) {
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System.out.println(Arrays.toString((int[])d));
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}
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System.out.println("\ntable of n vs counted vs calculated derangements\n");
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for (int i = 0; i < 10; i++) {
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int d = ((Integer)derangements(i, true)[1]).intValue();
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System.out.printf("%d %-7d %-7d\n", i, d, subfact(i));
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}
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System.out.printf ("\n!20 = %20d\n", subfact(20L));
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}
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static Object[] derangements(int n, boolean countOnly) {
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int[] seq = iota(n);
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int[] ori = Arrays.copyOf(seq, n);
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long tot = fact(n);
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List<int[]> all = new ArrayList<int[]>();
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int cnt = n == 0 ? 1 : 0;
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while (--tot > 0) {
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int j = n - 2;
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while (seq[j] > seq[j + 1]) {
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j--;
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}
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int k = n - 1;
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while (seq[j] > seq[k]) {
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k--;
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}
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swap(seq, k, j);
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int r = n - 1;
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int s = j + 1;
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while (r > s) {
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swap(seq, s, r);
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r--;
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s++;
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}
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j = 0;
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while (j < n && seq[j] != ori[j]) {
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j++;
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}
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if (j == n) {
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if (countOnly) {
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cnt++;
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} else {
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all.add(Arrays.copyOf(seq, n));
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}
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}
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}
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return new Object[]{all, cnt};
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}
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static long fact(long n) {
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long result = 1;
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for (long i = 2; i <= n; i++) {
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result *= i;
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}
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return result;
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}
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static long subfact(long n) {
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if (0 <= n && n <= 2) {
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return n != 1 ? 1 : 0;
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}
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return (n - 1) * (subfact(n - 1) + subfact(n - 2));
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}
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static void swap(int[] arr, int lhs, int rhs) {
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int tmp = arr[lhs];
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arr[lhs] = arr[rhs];
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arr[rhs] = tmp;
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}
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static int[] iota(int n) {
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if (n < 0) {
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throw new IllegalArgumentException("iota cannot accept < 0");
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}
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int[] r = new int[n];
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for (int i = 0; i < n; i++) {
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r[i] = i;
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}
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return r;
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}
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}
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