这是一个银行家四舍五入的例子，又名“四舍五入半偶数”。BigDecimal支持。它的目的是确保四舍五入平衡，即不偏袒银行或客户。

我写了一个c#版本的舍入帮助器，算法和Varun Vohra的答案一样，希望对你有帮助。

public static List<decimal> GetPerfectRounding(List<decimal> original,
    decimal forceSum, int decimals)
{
    var rounded = original.Select(x => Math.Round(x, decimals)).ToList();
    Debug.Assert(Math.Round(forceSum, decimals) == forceSum);
    var delta = forceSum - rounded.Sum();
    if (delta == 0) return rounded;
    var deltaUnit = Convert.ToDecimal(Math.Pow(0.1, decimals)) * Math.Sign(delta);

    List<int> applyDeltaSequence; 
    if (delta < 0)
    {
        applyDeltaSequence = original
            .Zip(Enumerable.Range(0, int.MaxValue), (x, index) => new { x, index })
            .OrderBy(a => original[a.index] - rounded[a.index])
            .ThenByDescending(a => a.index)
            .Select(a => a.index).ToList();
    }
    else
    {
        applyDeltaSequence = original
            .Zip(Enumerable.Range(0, int.MaxValue), (x, index) => new { x, index })
            .OrderByDescending(a => original[a.index] - rounded[a.index])
            .Select(a => a.index).ToList();
    }

    Enumerable.Repeat(applyDeltaSequence, int.MaxValue)
        .SelectMany(x => x)
        .Take(Convert.ToInt32(delta/deltaUnit))
        .ForEach(index => rounded[index] += deltaUnit);

    return rounded;
}

通过以下单元测试:

[TestMethod]
public void TestPerfectRounding()
{
    CollectionAssert.AreEqual(Utils.GetPerfectRounding(
        new List<decimal> {3.333m, 3.334m, 3.333m}, 10, 2),
        new List<decimal> {3.33m, 3.34m, 3.33m});

    CollectionAssert.AreEqual(Utils.GetPerfectRounding(
        new List<decimal> {3.33m, 3.34m, 3.33m}, 10, 1),
        new List<decimal> {3.3m, 3.4m, 3.3m});

    CollectionAssert.AreEqual(Utils.GetPerfectRounding(
        new List<decimal> {3.333m, 3.334m, 3.333m}, 10, 1),
        new List<decimal> {3.3m, 3.4m, 3.3m});


    CollectionAssert.AreEqual(Utils.GetPerfectRounding(
        new List<decimal> { 13.626332m, 47.989636m, 9.596008m, 28.788024m }, 100, 0),
        new List<decimal> {14, 48, 9, 29});
    CollectionAssert.AreEqual(Utils.GetPerfectRounding(
        new List<decimal> { 16.666m, 16.666m, 16.666m, 16.666m, 16.666m, 16.666m }, 100, 0),
        new List<decimal> { 17, 17, 17, 17, 16, 16 });
    CollectionAssert.AreEqual(Utils.GetPerfectRounding(
        new List<decimal> { 33.333m, 33.333m, 33.333m }, 100, 0),
        new List<decimal> { 34, 33, 33 });
    CollectionAssert.AreEqual(Utils.GetPerfectRounding(
        new List<decimal> { 33.3m, 33.3m, 33.3m, 0.1m }, 100, 0),
        new List<decimal> { 34, 33, 33, 0 });
}

对于那些在熊猫系列中有百分比的人，这里是我的最大余数方法的实现(就像Varun Vohra的答案一样)，在那里你甚至可以选择你想要四舍五入的小数。

import numpy as np

def largestRemainderMethod(pd_series, decimals=1):

    floor_series = ((10**decimals * pd_series).astype(np.int)).apply(np.floor)
    diff = 100 * (10**decimals) - floor_series.sum().astype(np.int)
    series_decimals = pd_series - floor_series / (10**decimals)
    series_sorted_by_decimals = series_decimals.sort_values(ascending=False)

    for i in range(0, len(series_sorted_by_decimals)):
        if i < diff:
            series_sorted_by_decimals.iloc[[i]] = 1
        else:
            series_sorted_by_decimals.iloc[[i]] = 0

    out_series = ((floor_series + series_sorted_by_decimals) / (10**decimals)).sort_values(ascending=False)

    return out_series

下面是一个实现了最大余数方法的Ruby宝石: https://github.com/jethroo/lare_round

使用方法:

a =  Array.new(3){ BigDecimal('0.3334') }
# => [#<BigDecimal:887b6c8,'0.3334E0',9(18)>, #<BigDecimal:887b600,'0.3334E0',9(18)>, #<BigDecimal:887b4c0,'0.3334E0',9(18)>]
a = LareRound.round(a,2)
# => [#<BigDecimal:8867330,'0.34E0',9(36)>, #<BigDecimal:8867290,'0.33E0',9(36)>, #<BigDecimal:88671f0,'0.33E0',9(36)>]
a.reduce(:+).to_f
# => 1.0

我的JS实现由Varun Vohra投票的答案

const set1 = [13.626332, 47.989636, 9.596008, 28.788024];
// const set2 = [24.25, 23.25, 27.25, 25.25];

const values = set1;

console.log('Total: ', values.reduce((accum, each) => accum + each));
console.log('Incorrectly Rounded: ', 
  values.reduce((accum, each) => accum + Math.round(each), 0));

const adjustValues = (values) => {
  // 1. Separate integer and decimal part
  // 2. Store both in a new array of objects sorted by decimal part descending
  // 3. Add in original position to "put back" at the end
  const flooredAndSortedByDecimal = values.map((value, position) => (
    {
        floored: Math.floor(value),
        decimal: value - Number.parseInt(value),
        position
    }
  )).sort(({decimal}, {decimal: otherDecimal}) => otherDecimal - decimal);

  const roundedTotal = values.reduce((total, value) => total + Math.floor(value), 0);
  let availableForDistribution = 100 - roundedTotal;

  // Add 1 to each value from what's available
  const adjustedValues = flooredAndSortedByDecimal.map(value => {
    const { floored, ...rest } = value;
    let finalPercentage = floored;
    if(availableForDistribution > 0){
        finalPercentage = floored + 1;
        availableForDistribution--;
    }

    return {
        finalPercentage,
        ...rest
    }
  });

  // Put back and return the new values
  return adjustedValues
    .sort(({position}, {position: otherPosition}) => position - otherPosition)
    .map(({finalPercentage}) => finalPercentage);
}

const finalPercentages = adjustValues(values);
console.log({finalPercentages})

// { finalPercentage: [14, 48, 9, 29]}

下面是@varun-vohra答案的一个简单的Python实现:

def apportion_pcts(pcts, total):
    proportions = [total * (pct / 100) for pct in pcts]
    apportions = [math.floor(p) for p in proportions]
    remainder = total - sum(apportions)
    remainders = [(i, p - math.floor(p)) for (i, p) in enumerate(proportions)]
    remainders.sort(key=operator.itemgetter(1), reverse=True)
    for (i, _) in itertools.cycle(remainders):
        if remainder == 0:
            break
        else:
            apportions[i] += 1
            remainder -= 1
    return apportions

你需要math, itertools, operator。