106 lines
2.4 KiB
Java
106 lines
2.4 KiB
Java
import java.util.*;
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// https://en.wikipedia.org/wiki/Partial_permutation
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public class Arrangements {
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public static boolean nextArrangement(int[] a, int n) {
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boolean[] used = new boolean[n];
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for (int x : a)
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used[x] = true;
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int m = a.length;
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for (int i = m - 1; i >= 0; i--) {
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used[a[i]] = false;
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for (int j = a[i] + 1; j < n; j++) {
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if (!used[j]) {
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a[i++] = j;
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used[j] = true;
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for (int k = 0; i < m; k++) {
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if (!used[k]) {
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a[i++] = k;
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}
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}
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return true;
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}
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}
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}
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return false;
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}
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public static int[] arrangementByNumber(int n, int m, long number) {
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int[] a = new int[m];
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int[] free = new int[n];
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for (int i = 0; i < n; i++) {
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free[i] = i;
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}
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for (int i = 0; i < m; i++) {
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long cnt = countOfArrangements(n - 1 - i, m - 1 - i);
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int pos = (int) (number / cnt);
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a[i] = free[pos];
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System.arraycopy(free, pos + 1, free, pos, n - 1 - pos);
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number %= cnt;
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}
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return a;
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}
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public static long numberByArrangement(int[] a, int n) {
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int m = a.length;
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long res = 0;
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boolean[] used = new boolean[n];
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for (int i = 0; i < m; i++) {
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int cnt = 0;
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for (int j = 0; j < a[i]; j++) {
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if (!used[j]) {
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++cnt;
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}
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}
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res += cnt * countOfArrangements(n - i - 1, m - i - 1);
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used[a[i]] = true;
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}
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return res;
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}
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public static long countOfArrangements(int n, int m) {
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long res = 1;
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for (int i = 0; i < m; i++) {
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res *= n - i;
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}
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return res;
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}
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public static boolean nextArrangementWithRepeats(int[] a, int n) {
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for (int i = a.length - 1; i >= 0; i--) {
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if (a[i] < n - 1) {
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++a[i];
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Arrays.fill(a, i + 1, a.length, 0);
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return true;
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}
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}
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return false;
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}
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// Usage example
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public static void main(String[] args) {
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// print all arrangements
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int[] a = {0, 1, 2};
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int cnt = 0;
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int n = 4;
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do {
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System.out.println(Arrays.toString(a));
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if (!Arrays.equals(a, arrangementByNumber(n, a.length, numberByArrangement(a, n))) ||
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cnt != numberByArrangement(arrangementByNumber(n, a.length, cnt), n))
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throw new RuntimeException();
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++cnt;
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} while (nextArrangement(a, n));
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// print all arrangements with repeats
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a = new int[]{0, 0};
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do {
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System.out.println(Arrays.toString(a));
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} while (nextArrangementWithRepeats(a, 2));
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a = new int[]{2, 3, 4};
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System.out.println(32 == numberByArrangement(a, 5));
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System.out.println(Arrays.equals(a, arrangementByNumber(5, a.length, 32)));
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}
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}
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