如何使四舍五入的百分比加起来为 100% [英] How to make rounded percentages add up to 100%

问题描述

考虑以下四个百分比，用float数字表示:

Consider the four percentages below, represented as float numbers:

    13.626332%
    47.989636%
     9.596008%
    28.788024%
   -----------
   100.000000%

我需要将这些百分比表示为整数.如果我简单地使用 Math.round()，我最终会得到 101%.

I need to represent these percentages as whole numbers. If I simply use Math.round(), I end up with a total of 101%.

14 + 48 + 10 + 29 = 101

如果我使用 parseInt()，我最终得到了 97%.

If I use parseInt(), I end up with a total of 97%.

13 + 47 + 9 + 28 = 97

将任意数量的百分比表示为整数同时仍保持总数为 100% 的好算法是什么?

What's a good algorithm to represent any number of percentages as whole numbers while still maintaining a total of 100%?

编辑:在阅读了一些评论和答案后，显然有很多方法可以解决这个问题.

Edit: After reading some of the comments and answers, there are clearly many ways to go about solving this.

在我看来，为了保持真实的数字，正确"的结果是最小化整体误差的结果，定义为相对于实际值会引入多少误差:

In my mind, to remain true to the numbers, the "right" result is the one that minimizes the overall error, defined by how much error rounding would introduce relative to the actual value:

        value  rounded     error               decision
   ----------------------------------------------------
    13.626332       14      2.7%          round up (14)
    47.989636       48      0.0%          round up (48)
     9.596008       10      4.0%    don't round up  (9)
    28.788024       29      2.7%          round up (29)

在平局 (3.33, 3.33, 3.33) 的情况下，可以做出任意决定(例如 3, 4, 3).

In case of a tie (3.33, 3.33, 3.33) an arbitrary decision can be made (e.g. 3, 4, 3).

推荐答案

由于这里的答案似乎都无法正确解决，这里是我使用 underscorejs:

Since none of the answers here seem to solve it properly, here's my semi-obfuscated version using underscorejs:

function foo(l, target) {
    var off = target - _.reduce(l, function(acc, x) { return acc + Math.round(x) }, 0);
    return _.chain(l).
            sortBy(function(x) { return Math.round(x) - x }).
            map(function(x, i) { return Math.round(x) + (off > i) - (i >= (l.length + off)) }).
            value();
}

foo([13.626332, 47.989636, 9.596008, 28.788024], 100) // => [48, 29, 14, 9]
foo([16.666, 16.666, 16.666, 16.666, 16.666, 16.666], 100) // => [17, 17, 17, 17, 16, 16]
foo([33.333, 33.333, 33.333], 100) // => [34, 33, 33]
foo([33.3, 33.3, 33.3, 0.1], 100) // => [34, 33, 33, 0]

这篇关于如何使四舍五入的百分比加起来为 100%的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！