Generates integer partitions in anti-lexicographic order - Java java.lang

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Description

Generates integer partitions in anti-lexicographic order

Demo Code

/* Copyright 2012-2015 SAP SE
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License./* w w w.  j  a  v  a 2  s.  c  o m*/
 */
//package com.java2s;
import java.util.ArrayList;
import java.util.List;

public class Main {
    /**
     * Generates integer partitions in anti-lexicographic order using the
     * algorithm ZS1 as described in Zoghbi, A. and Stojmenovic, I.
     * "Fast Algorithms for Generating Integer Partitions", published in 1998.
     * For each partition, the parts are provided in descending order.
     *
     * @param n
     *            The integer for which the partitions should be generated.
     * @return A List containing the integer partitions, each represented as a
     *         integer Array.
     */
    public static List<int[]> generateIntegerPartitions(int n) {

        List<int[]> res = new ArrayList<int[]>();

        int[] x = new int[n];

        for (int i = 1; i <= n; i++) {
            x[i - 1] = 1;
        }

        x[0] = n;
        int m = 1;
        int h = 1;

        res.add(copySubarray(x, 0, 1));

        while (x[0] != 1) {

            if (x[h - 1] == 2) {
                m = m + 1;
                x[h - 1] = 1;
                h = h - 1;
            } else {
                int r = x[h - 1] - 1;
                int t = m - h + 1;
                x[h - 1] = r;

                while (t >= r) {
                    h = h + 1;
                    x[h - 1] = r;
                    t = t - r;
                }

                if (t == 0) {
                    m = h;
                } else {
                    m = h + 1;

                    if (t > 1) {
                        h = h + 1;
                        x[h - 1] = t;
                    }
                }
            }
            res.add(copySubarray(x, 0, m));
        }

        return res;

    }

    /**
     * Copies a subarray of a given array and returns it.
     *
     * @param src
     *            The source array that should be used.
     * @param start
     *            The start index.
     * @param end
     *            The end index.
     * @return A subarray of the source array, including the value at the start
     *         index and excluding the value at the end index.
     */
    private static int[] copySubarray(int[] src, int start, int end) {

        int[] res = new int[end - start];
        int resPos = 0;

        for (int i = start; i < end; i++) {
            res[resPos] = src[i];
            resPos++;
        }

        return res;
    }
}

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