Distribute an integer amount by a set of slots as evenly as possible

Question

I am trying to figure an elegant way of implementing the distribution of an amount into a given set of slots in python.

For example:

7 oranges distributed onto 4

Answer 1

Mad Physicist answer is perfect. But if you want to distribute the oranges uniformley on the plates (eg. 2 3 2 3 vs 2 2 3 3 in the 7 oranges and 4 plates example), here's an simple idea.

Easy case

Take an example with 31 oranges and 7 plates for example.

Step 1: You begin like Mad Physicist with an euclidian division: 31 = 4*7 + 3. Put 4 oranges in each plate and keep the remaining 3.

[4, 4, 4, 4, 4, 4, 4]

Step 2: Now, you have more plates than oranges, and that's quite different: you have to distribute plates among oranges. You have 7 plates and 3 oranges left: 7 = 2*3 + 1. You will have 2 plates per orange (you have a plate left, but it doesn't matter). Let's call this 2 the leap. Start at leap/2 will be pretty :

[4, 5, 4, 5, 4, 5, 4]

Not so easy case

That was the easy case. What happens with 34 oranges and 7 plates?

Step 1: You still begin like Mad Physicist with an euclidian division: 34 = 4*7 + 6. Put 4 oranges in each plate and keep the remaining 6.

[4, 4, 4, 4, 4, 4, 4]

Step 2: Now, you have 7 plates and 6 oranges left: 7 = 1*6 + 1. You will have one plate per orange. But wait.. I don't have 7 oranges! Don't be afraid, I lend you an apple:

[5, 5, 5, 5, 5, 5, 4+apple]

But if you want some uniformity, you have to place that apple elsewhere! Why not try distribute apples like oranges in the first case? 7 plates, 1 apple : 7 = 1*7 + 0. The leap is 7, start at leap/2, that is 3:

[5, 5, 5, 4+apple, 5, 5, 5]

Step 3. You owe me an apple. Please give me back my apple :

[5, 5, 5, 4, 5, 5, 5]

To summarize : if you have few oranges left, you distribute the peaks, else you distribute the valleys. (Disclaimer: I'm the author of this "algorithm" and I hope it is correct, but please correct me if I'm wrong !)

The code

Enough talk, the code:

def distribute(oranges, plates):
    base, extra = divmod(oranges, plates) # extra < plates
    if extra == 0:
        L = [base for _ in range(plates)]
    elif extra <= plates//2:
        leap = plates // extra
        L = [base + (i%leap == leap//2) for i in range(plates)]
    else: # plates/2 < extra < plates
        leap = plates // (plates-extra) # plates - extra is the number of apples I lent you
        L = [base + (1 - (i%leap == leap//2)) for i in range(plates)]
    return L

Some tests:

>>> distribute(oranges=28, plates=7)
[4, 4, 4, 4, 4, 4, 4]
>>> distribute(oranges=29, plates=7)
[4, 4, 4, 5, 4, 4, 4]
>>> distribute(oranges=30, plates=7)
[4, 5, 4, 4, 5, 4, 4]
>>> distribute(oranges=31, plates=7)
[4, 5, 4, 5, 4, 5, 4]
>>> distribute(oranges=32, plates=7)
[5, 4, 5, 4, 5, 4, 5]
>>> distribute(oranges=33, plates=7)
[5, 4, 5, 5, 4, 5, 5]
>>> distribute(oranges=34, plates=7)
[5, 5, 5, 4, 5, 5, 5]
>>> distribute(oranges=35, plates=7)
[5, 5, 5, 5, 5, 5, 5]