Interesting math problem

[BJörn Lindqvist]

Here is an interesting math problem:

You have a number X > 0 and another number Y > 0. The goal is to
divide X into a list with length Y. Each item in the list is an
integer. The sum of all integers is X. Each integer is either A or A +
1, those should be "evenly distributed."

Example:

17 // 5 = 3 gives the list [3, 3, 4, 3, 4]
16 // 4 = 4 gives the list [4, 4, 4, 4]
113 // 50 = 2 gives the list [2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 2,
3, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2,
3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3]

This algorithm is used a lot in programming. For example, for
projecting a line on a pixel display. Your mission, should you choose
to accept it, is to improve the code given below which is my best
attempt and make it more succinct and easier to read. Preferably by
using list comprehensions, map or even reduce....

def make_slope(distance, parts):
    step = distance / float(parts)
    intstep = int(step)
    floatstep = step - intstep

    steps = []
    acc = 0.0
    for i in range(parts):
        acc += floatstep
        step = intstep
        if acc > 0.999:
            step += 1
            acc -= 1.0
        steps.append(step)
    return steps

# Test code
distance = 130
parts = 50
L = make_slope(distance, parts)
assert(len(L) == parts)
assert(sum(L) == distance)
print L


-- 
mvh Björn