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 pseudo random solution [note that solution might be biased, but will be relatively random].

input:
n - the number we should sum up to
k - the number of 'parts'
m - minimum

(1) split n into k numbers: x1,x2,...,xk such that x1+...+xk = n, and the numbers 
    are closest possible to each other [in other words, x1 = x2 = ... = n/k where 
    possible, the end might vary at atmost +-1.]
(2) for each number xi from i=1 to k-1:
       temp <- rand(m,xi)
       spread x - temp evenly among xi+1,...,xk
       xi <- temp
(3) shuffle the resulting list.

regarding part 1, for example: for n=50, k = 7, you will set: x1=x2=...=x6=7,x7=8, no problem to compute and populate such a list with linear time.

Performance:

As said, step1 is O(k).

Step2, with naive implementation is O(k^2), but since you distribute result of temp-xi evenly, there is O(k) implementation, with just storing and modifying delta.

Step3 is just a simple shuffle, O(k)

Overall performance: O(k) with delta implemntation of step2