# Minimum Total Loss Rounding in Python

Minimum Total Loss Rounding algorithms are quite useful for distribution problems if you need whole numbers after the distribution, as the final result of distribution.

For example, you want to distribute a certain number of students to a number of available classrooms, approximately in proportion to the ground area (measured in square meter) of each classroom:
```Distribute 180 students to 5 classrooms with given ground areas [25, 30, 20, 15, 35] Sum of all given areas = 25 + 30 + 20 + 15 + 35 = 125 = sum([25, 30, 20, 15, 35]) ```
If you distribute students to classrooms you will obtain following fractional numbers:
```areas = [25, 30, 20, 15, 35] d1 = [x*180.0/125.0 for x in areas] ([36.0, 43.2, 28.8, 21.6, 50.4]) ```
Because there can’t be 43.2 or 28.8 students in a class, we need to round all these fractional numbers with minimum total loss, that is, with minimum total deviation from the original fractional number.

In my case, I defined rounding losses in proportionate terms. For example, proportionate round-down loss (deviation) for 43.2 is calculated by the function RoundDownLoss() as follows:``` (43.2 - 43.0) / 43.2 = 0.2 / 43.2 = 0.004629629629629695 ```
And round-up loss (deviation) by the function RoundUpLoss() as follows:``` (44.0 - 43.2) / 43.2 = 0.8 / 43.2 = 0.01851851851851845 ```
You can adjust the functions RoundDownLoss() and RoundUpLoss() if you have another concept of loss (deviation) in mind.

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