Split number into sum components

Question

Is there an efficient algorithm to split up a number into N subsections so that the sum of the numbers adds up to the original, with a base minimum? For example, if

Answer 1

Here is a java example of code creating the requested repartition of numbers. It is recursive approach, we decompose the problem into 2 subproblems : if we want to decompose a number in to a sum of components amongst n baskets, then we try to consider a subnumber at a time, and for each of them delegate the finding out of the remaining decomposition to the recursive call for the repartition amongst (n-1) baskets. The requested threshold is considered when processing a particular subnumber (in the for loop).

import java.util.ArrayList;
import java.util.List;

public class TestFigures {

    public static List> computeRepartitionNumber(int number_to_decompose, int number_of_subnumbers, int threshold_number) {
        List> resultRec = new ArrayList<>();

        if (number_of_subnumbers == 1) {
            List> resultEnd = new ArrayList<>();
            ArrayList unitary = new ArrayList<>();
            resultEnd.add(unitary);
            unitary.add(number_to_decompose);
            return resultEnd;
        }

        for (int i = threshold_number; i <= number_to_decompose-threshold_number; i++) {
            int remain = number_to_decompose - i;
            List> partialRec = computeRepartitionNumber(remain, number_of_subnumbers - 1, threshold_number);
            for(List subList : partialRec){
                subList.add(i);             
            }
            resultRec.addAll(partialRec);
        }
        return resultRec;

    }

    public static void main(String[] args) {
        List> superlist = computeRepartitionNumber(5, 2, 1);
        System.out.println(superlist.size());
        System.out.println(superlist);

    }

}