确定两个日期范围是否重叠

问题描述：

给定两个日期范围，确定两个日期范围是否重叠的最简单或最有效的方法是什么?

Given two date ranges, what is the simplest or most efficient way to determine whether the two date ranges overlap?

举个例子，假设我们有由 DateTime 变量表示的范围 StartDate1 到 EndDate1 and StartDate2 到 EndDate2.

As an example, suppose we have ranges denoted by DateTime variables StartDate1 to EndDate1 and StartDate2 to EndDate2.

答

(StartA

证明:
让 ConditionA 表示 DateRange A 完全在 DateRange B 之后

Proof:
Let ConditionA Mean that DateRange A Completely After DateRange B

_                        |---- DateRange A ------|
|---Date Range B -----|                          _

(如果 StartA > EndB 为真)

令 ConditionB 表示 DateRange A 完全在 DateRange B 之前

Let ConditionB Mean that DateRange A is Completely Before DateRange B

|---- DateRange A -----|                        _ 
_                          |---Date Range B ----|

(如果 EndA 为真)

如果 A 和 B 都不为真，则存在重叠 -
(如果一个范围既不完全在另一个范围之后，
也不完全在另一个之前，那么它们必须重叠.)

Then Overlap exists if Neither A Nor B is true -
(If one range is neither completely after the other,
nor completely before the other, then they must overlap.)

现在德摩根定律之一说:

不是(A 或 B) 不是A也不是B

翻译成:(StartA <= EndB) and (EndA >= StartB)

注意:这包括边缘完全重叠的情况.如果你想排除那个，
将 >= 运算符更改为 >，并将 更改为 <

NOTE: This includes conditions where the edges overlap exactly. If you wish to exclude that,
change the >= operators to >, and <= to <

注意2.感谢@Baodad，见这篇博客，实际重叠的是最少的:
{ endA-startA, endA - startB, endB-startA, endB - startB }

NOTE2. Thanks to @Baodad, see this blog, the actual overlap is least of:
{ endA-startA, endA - startB, endB-startA, endB - startB }

(StartA = StartB)(StartA

注意3.感谢@tomosius，一个更短的版本如下:
DateRangesOverlap = max(start1, start2) 这实际上是更长实现的语法快捷方式，其中包括额外的检查以验证开始日期是否在 endDates 上或之前.从上面推导出来:

NOTE3. Thanks to @tomosius, a shorter version reads:
DateRangesOverlap = max(start1, start2) < min(end1, end2)
This is actually a syntactical shortcut for what is a longer implementation, which includes extra checks to verify that the start dates are on or before the endDates. Deriving this from above:

如果开始和结束日期可能乱序，即，如果 startA >endA 或 startB >endB，那么你还必须检查它们是否有序，这意味着你必须添加两个额外的有效性规则:
(StartA 或: (StartA 或者， (StartA 或: (Max(StartA, StartB)

If start and end dates can be out of order, i.e., if it is possible that startA > endA or startB > endB, then you also have to check that they are in order, so that means you have to add two additional validity rules:
(StartA <= EndB) and (StartB <= EndA) and (StartA <= EndA) and (StartB <= EndB) or:
(StartA <= EndB) and (StartA <= EndA) and (StartB <= EndA) and (StartB <= EndB) or,
(StartA <= Min(EndA, EndB) and (StartB <= Min(EndA, EndB)) or:
(Max(StartA, StartB) <= Min(EndA, EndB)

但是要实现Min()和Max()，你必须编码，(为了简洁，使用C三元)，:
(StartA > StartB? Start A: StartB)

But to implement Min() and Max(), you have to code, (using C ternary for terseness),:
(StartA > StartB? Start A: StartB) <= (EndA < EndB? EndA: EndB)

确定两个日期范围是否重叠

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