用于折叠一组可能重叠的范围的好的通用算法是什么? [英] What's a good, generic algorithm for collapsing a set of potentially-overlapping ranges?

问题描述

我有一个方法可以获取这个类的一些对象

I have a method that gets a number of objects of this class

class Range<T>
{
    public T Start;
    public T End;
}

在我的例子中，T 是 DateTime，但为了简单起见，我们使用 int.我想要一种将这些范围折叠成覆盖相同区域"但不重叠的方法.

In my case T is DateTime, but lets use int for simplicity. I would like a method that collapses those ranges into ones that cover the same "area" but that do not overlap.

如果我有以下范围

• 1 到 5
• 3 到 9
• 11 至 15
• 12 至 14
• 13 到 20

方法应该给我

• 1 到 9
• 11 至 20

猜猜它会被称为工会?我想方法签名可能看起来像这样:

Guess it would be called a union? I imagine the method signature could look something like this:

public static IEnumerable<Range<T>> Collapse<T>(
    this IEnumerable<Range<T>>, 
    IComparable<T> comparer)
{
    ...
}

我在这里查看了其他一些类似的问题，但我还没有找到它的实现.这个答案 和同一问题的其他一些答案描述了算法，但我不太确定我是否理解这些算法.也不是特别擅长实现算法，所以我希望这里有人可以帮助我.

I have looked at some other questions here that are kind of similar, but I haven't found an implementation of this yet. This answer and some other answers to the same question describes algorithms, but I am not quite sure if I understand the algorithms. Not especially good at implementing algorithms either, so I was hoping someone here could help me out.

推荐答案

这似乎可行且易于理解.

This seems to works and is easy to understand.

    public static IEnumerable<Range<T>> Collapse<T>(this IEnumerable<Range<T>> me, IComparer<T> comparer)
    {
        List<Range<T>> orderdList = me.OrderBy(r => r.Start).ToList();
        List<Range<T>> newList = new List<Range<T>>();

        T max = orderdList[0].End;
        T min = orderdList[0].Start;

        foreach (var item in orderdList.Skip(1))
        {
            if (comparer.Compare(item.End, max) > 0 && comparer.Compare(item.Start, max) > 0)
            {
                newList.Add(new Range<T> { Start = min, End = max });
                min = item.Start;
            }
            max = comparer.Compare(max, item.End) > 0 ? max : item.End;
        }
        newList.Add(new Range<T>{Start=min,End=max});

        return newList;
    }

<小时>

这是我在评论中提到的变化.这基本上是一样的，但需要对结果进行一些检查和生成，而不是在返回之前收集到一个列表中.

---

Here is the variation which I mentioned in the comments. It's basically the same thing, but with some checking and yielding of the results instead of collecting in a list before returning.

    public static IEnumerable<Range<T>> Collapse<T>(this IEnumerable<Range<T>> ranges, IComparer<T> comparer)
    {
        if(ranges == null || !ranges.Any())
            yield break;

        if (comparer == null)
            comparer = Comparer<T>.Default;

        var orderdList = ranges.OrderBy(r => r.Start);
        var firstRange = orderdList.First();

        T min = firstRange.Start;
        T max = firstRange.End;

        foreach (var current in orderdList.Skip(1))
        {
            if (comparer.Compare(current.End, max) > 0 && comparer.Compare(current.Start, max) > 0)
            {
                yield return Create(min, max);
                min = current.Start;
            }
            max = comparer.Compare(max, current.End) > 0 ? max : current.End;
        }
        yield return Create(min, max);
    }

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