Tests.java

package com.fun;

import java.util.ArrayList;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class Tests{
    static TreeMap<Integer, ArrayList<String>> savedPartitions = new TreeMap<>();
    static{
        savedPartitions.put(1, new ArrayList<String>());
        savedPartitions.get(1).add("1");
        savedPartitions.put(2, new ArrayList<String>());
        savedPartitions.get(2).add("2");
        savedPartitions.get(2).add("1+1");
    }
    static int stringCount(String s, String target){
        int count = 0;
        while(true)
            if(s.indexOf(target) != -1){
                count++;
                s = s.substring(s.indexOf(target)+target.length(), s.length());
            }else
                break;
        return count;
    }
    static boolean caseEquals(String case1, String case2){
        StringTokenizer tokenizer = new StringTokenizer(case1, "+");
        while(tokenizer.hasMoreTokens()){
            String nextToken = tokenizer.nextToken();
            if( stringCount(case1, nextToken) != stringCount(case2, nextToken) )
                return false;
        }
        return true;
    }
    static ArrayList<String> partition(int n) {
        if (n <= 0)
            throw new IllegalArgumentException("Value given is either 0 or negative!");
        if(savedPartitions.containsKey(n))
            return savedPartitions.get(n);
        ArrayList<String> partitions = new ArrayList<>();
        partitions.add(n + "");
        for (int x = 1, y = n - 1; x != n; x++, y--) {
            ArrayList<String> p = partition(y);
            for (String eP : p) {
                StringBuilder builder = new StringBuilder(eP);
                for (int i = 1; i < builder.length(); i += 2)
                    if (builder.charAt(i) != '+' && (i+1 < builder.length() && builder.charAt(i+1) != '0'))
                        builder.insert(i, '+');
                partitions.add(x + "+" + builder.toString());
            }
        }
        savedPartitions.put(n, filter( partitions ));
        return savedPartitions.get(n);
    }

    private static ArrayList<String> filter(ArrayList<String> a) {
        for(int x = 0; x < a.size();x++)
            for(int y = x+1; y < a.size();y++)
                if( caseEquals( a.get(x), a.get(y) ) ){
                    a.remove(y);
                }
        return a;
    }

    public static void main(String[] args){
        System.out.printf("Java %d", 8);
    }
}