在一个LINQ查询中使用最近邻算法解决旅行商问题? [英] Solution to travelling salesman problem using nearest neighbour algorithm in one LINQ query?

问题描述

给予

List<Point> cities = /* ... */ ;
double distance(Point a, Point b) { /* ... */ };

是否有一个LINQ查询通过最近邻算法返回旅行推销员最短路线作为cities索引的List<int>?

is there a single LINQ query that returns the travelling salesman shortest route by nearest neighbour algorithm as a List<int> of the indices of cities?

推荐答案

我认为您无法在单个查询中完成所有操作，算法的某些部分将必须单独实现.

I don't think you can do everything in a single query, some parts of the algorithms will have to be implemented separately.

这是一个蛮力实施，它检查所有城市排列并返回访问所有城市的最短路径:

Here's a brute-force implementation that examines all city permutations and returns the shortest path that visits all the cities:

var bestPath =
   cities.Permutations()
      .MinBy(
        steps => steps.Aggregate(
                    new { Sum = 0, Previous = default(Point) },
                    (acc, c) =>
                        new
                        {
                            Sum = acc.Sum + (acc.Previous != null ? Distance(c, acc.Previous) : 0 ),
                            Previous = c
                        },
                    acc => acc.Sum));

Permutations扩展方法定义如下:

public static IEnumerable<IEnumerable<T>> Permutations<T>(this IEnumerable<T> source)
{
    var query =
        from item in source
        from others in source.SkipOnce(item).Permutations()
        select new[] { item }.Concat(others);
    return query.DefaultIfEmpty(Enumerable.Empty<T>());
}

public static IEnumerable<T> SkipOnce<T>(this IEnumerable<T> source, T itemToSkip)
{
    bool skipped = false;
    var comparer = EqualityComparer<T>.Default;
    foreach (var item in source)
    {
        if (!skipped && comparer.Equals(item, itemToSkip))
            skipped = true;
        else
            yield return item;
    }
}

当然，有更好的方法可以解决此问题，但是这种方法可以工作...大部分都在单个查询中，只有单独实现的部分并不特定于手头的问题，可以重用完成其他任务.

Of course there are much better approaches to solve this problem, but this one works... Most of it is in a single query, the only parts that are implemented separately are not specific to the problem at hand and can be reused for other tasks.

糟糕，我刚刚意识到我也使用了非标准的MinBy方法；您可以在MoreLinq项目中

oops, I just realized I also used the non-standard MinBy method; you can find it in the MoreLinq project

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