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

Let me write it in Python.

Let's say that you have 50 elements to split into 7 boxes and you want at least two inside each of them.

N_init = 50
s = 2
m = 7

We put s elements by default in each box so we are left with N elements.

N = N_init - s*m

We draw m random numbers, sort them, append N on the back. This is like inserting randomly m bookmarks in a book of N pages. The number of pages between consecutive bookmarks is random. (We had s so that we are sure that each box has at least s elements)

a = sorted([random.randint(0,N+1) for i in range(m)])
a.append(N)
result = [j-i+s for(i,j) in zip(a[0:m],a[1:m+1])]

Done!