将数字列表四舍五入为用户定义的步骤，同时保留其总和

发布于 2024-11-26 12:05:24 字数 444 浏览 2 评论 0原文

我读了很多关于四舍五入数字的帖子，但我无法做到我想做的事：

我有一个正浮点数列表。要使用的无符号整数 roundOffStep 是用户定义的。除此之外我无法控制。

我希望能够进行最准确的舍入，同时保留这些数字的总和，或者至少同时保持新的总和低于原始总和。

我该怎么做呢？我对算法很糟糕，所以这对我来说太棘手了。

谢谢。

编辑：添加测试用例：

FLOATS
   29.20
   18.25
   14.60
   8.76
   2.19

sum = 73；

假设 roundOffStep = 5；

ROUNDED FLOATS
30
15
15
10
0

总和=70＜ 73 好的

原文

I've been reading a lot of posts about rounding off numbers, but I couldn't manage to do what I want :

I have got a list of positive floats.
The unsigned integer roundOffStep to use is user-defined. I have no control other it.

I want to be able to do the most accurate rounding while preserving the sum of those numbers, or at least while keeping the new sum inferior to the original sum.

How would I do that ? I am terrible with algorithms, so this is way too tricky for me.

Thx.

EDIT : Adding a Test case :

FLOATS
   29.20
   18.25
   14.60
   8.76
   2.19

sum = 73;

Let's say roundOffStep = 5;

ROUNDED FLOATS
30
15
15
10
0

sum = 70 < 73 OK

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清君侧 2024-12-03 12:05:24

通常将所有数字四舍五入到最接近的 roundOffStep 倍数。
如果新的总和低于原始总和，则完成。
对于每个数字，计算rounded_number - Original_number。按降序排列此差异列表，以便找到差异最大的数字。
选择提供最大差值 rounded_number - Original_number 的数字，然后从该数字中减去 roundOffStep。
重复步骤 4（每次选择下一个最大差值），直到新的总和小于原始总和。

此过程应确保四舍五入后的数字尽可能接近原始数字，而不超过原始总和。

例如，roundOffStep = 5：

    Original Numbers  |   Rounded  |  Difference
----------------------+------------+--------------
         29.20        |     30     |     0.80
         18.25        |     20     |     1.75
         14.60        |     15     |     0.40
         8.76         |     10     |     1.24
         2.19         |     0      |    -2.19
----------------------+------------+--------------
Sum:     73           |     75     |

总和太大，因此我们选择给出最大差值的数字（18.25，四舍五入为 20）并减去 5 得到 15。现在总和为 70，这样我们就完成了。

Round all numbers to the nearest multiple of roundOffStep normally.
If the new sum is lower than the original sum, you're done.
For each number, calculate rounded_number - original_number. Sort this list of differences in decreasing order so that you can find the numbers with the largest difference.
Pick the number that gives the largest difference rounded_number - original_number, and subtract roundOffStep from that number.
Repeat step 4 (picking the next largest difference each time) until the new sum is less than the original.

This process should ensure that the rounded numbers are as close as possible to the originals, without going over the original sum.

Example, with roundOffStep = 5:

    Original Numbers  |   Rounded  |  Difference
----------------------+------------+--------------
         29.20        |     30     |     0.80
         18.25        |     20     |     1.75
         14.60        |     15     |     0.40
         8.76         |     10     |     1.24
         2.19         |     0      |    -2.19
----------------------+------------+--------------
Sum:     73           |     75     |

The sum is too large, so we pick the number giving the largest difference (18.25 which was rounded to 20) and subtract 5 to give 15. Now the sum is 70, so we're done.

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