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's an algorithm:

1. Divide N by m where N is your number and m is the number of subsections.
2. Round the result down to its nearest value and assign that value to all of the subsections.
3. Add one to each subsection until the values add up to N. At this point if N was 50 and m was 7, you'd have 8, 7, 7, 7, 7, 7, 7
4. Iterate from 0 to m-1, stepping by 2, and add a random number between -(currentValue-base) and currentValue-base. Add the inverse of that number to its neighboring bucket. If you have an odd number of buckets, then on the last bucket instead of adding the inverse of that number to its neighboring bucket, add it to all of the other buckets in a distributed manner similar to steps 2 and 3 above.

Performance: Step 1 is O(1), Steps 2, 3, and 4 are O(m), so overall it's O(m).