代表间隔或范围？ [英] Representing intervals or ranges?

问题描述

通常，无论何时表示任何类型的范围，都可以选择几种类型的值作为范围的开始和结束。例如，如果要包含整数1、2、3、4、5的范围，则可以选择以下可能的值：

In general, whenever you're representing a range of any kind, you have several choices for what kinds of values to choose for the beginning and ending of your range. For example, if you want to have a range containing the integers 1, 2, 3, 4, 5 you could choose these possible values:

• 开始= 0，结束= 5（又名开始< x< =结束）


• 开始= 1，结束= 5（又名开始< = x< =结束）


• 开始= 0，结束= 6（又名开始< x< end）


• 开始= 1，结束= 6（又名开始< = x< end（C ++ STL和许多其他库似乎选择了此）。

• begin = 0, end = 5 (aka begin < x <= end)
• begin = 1, end = 5 (aka begin <= x <= end)
• begin = 0, end = 6 (aka begin < x < end)
• begin = 1, end = 6 (aka begin <= x < end (the C++ STL and many other libraries seem to choose this)).

我不确定采取什么措施我应该使用这些选项之一。

I'm not sure what measures I should use to choose one of these options.

推荐答案

我希望有人能给我一个指向电子战Dijkstra 写了关于这个话题的文章。我设法将正确的搜索字词插入Google，并找到了我要找的链接。该文件为为什么编号应从0开始，还介绍了为什么范围应以半开间隔[begin，end）表示。

I was hoping someone would give me a link to a nice paper that E.W. Dijkstra wrote on the topic. I managed to plug just the right search terms into Google, and found the link I was looking for. The paper is "Why numbering should start at 0" and also covers why ranges should be represented with a half open interval [begin, end).

基本参数有几段：

1. 对编程环境（Xerox PARC的Mesa编程语言）有直接的经验，该环境支持所有4种不同的选择，导致人们经常在[开始，结束]上进行标准化操作，


2. 如果您的间隔从0开始，则开始为-1或类似的东西就很尴尬和残缺。这充分说明了从开始开始的间隔（即所有开始< = x选择）。


3. 用于确定间隔大小，用于计算下一个相邻间隔的开始，并且如果end是一个过去的开始，那么一大堆其他类似的东西也可以很好地解决。例如，大小为结束-开始。 end 是下一个相邻间隔的开始。在您的计算中出现一次错误的机会就更少了。
   
   
   
   • 在相关说明中，空白范围是 [开始，开始），非常明显。如果两端都关闭，它必须是相当笨拙的 [开始，开始-1] 。这个范围从0开始特别尴尬。
   
   

1. Direct experience with a programming environment (the programming language Mesa at Xerox PARC) that had support for all 4 different choices resulted in people standardizing on [start, end) because of frequent errors made with all the other choices.
2. If you have an interval that starts at 0, having the start be -1 or something similar is just awkward and broken. This argues strongly for the interval starting at begin (i.e. all the begin <= x choices).
3. The math for determining the interval size, for computing the start of the next adjacent interval, and a whole bunch of other similar things just works out nicely if end is one past start. For example, the size is end - begin. And end is the begin of the next adjacent interval. There are fewer chances for off-by-one errors in your calculations.
   • On a related note, the empty range is [begin, begin), and very obvious. It would have to be the rather awkward [begin, begin - 1] if it were closed on both sides. This is especially awkward of your range begins at 0.

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