如何在列表中查找它们的总和小于或等于数字的项目

Question

我有一个数字列表，我想知道列表中哪个数字组合与特定数字（目标）的总和最接近。（如果有很多组合，找到一个就足够了）

我搜索了很多，知道这里有很多解决方案可以找到它们的总和等于特定数字的组合，但是没有找到与该数字接近的最大的解决方案。

我还写了一段代码，从零循环到“目标”以找到最大的和，但由于这个过程非常耗时，必须针对 100,000 个列表进行计算，我想知道是否有更有效的方法使用最好是linq。

var List1 = new int[] { 5, 10, 15, 20, 25, 30, 35, 40, 45 };
var target = 40;

int MaxViewers = Convert.ToInt32(txtNoRecordsToAdd.Text);

for (int UserNo = 1; UserNo <= MaxViewers; UserNo++)
{
    for (int No = 1; No <= target; No++)
    {
        var matches = from subset in MyExtensions.SubSetsOf(List1)
                        where subset.Sum() == target
                        select subset;
    }
}

public static class MyExtensions
{
    public static IEnumerable<IEnumerable<T>> SubSetsOf<T>(this IEnumerable<T> source)
    {
        if (!source.Any())
            return Enumerable.Repeat(Enumerable.Empty<T>(), 1);

        // Grab the first element off of the list
        var element = source.Take(1);

        // Recurse, to get all subsets of the source, ignoring the first item
        var haveNots = SubSetsOf(source.Skip(1));

        // Get all those subsets and add the element we removed to them
        var haves = haveNots.Select(set => element.Concat(set));

        // Finally combine the subsets that didn't include the first item, with those that did.
        return haves.Concat(haveNots);
    }

}

Answer 1

您好，让我们来看看实现这一点的巧妙方法，

var List1 = new int[] { 5, 10, 15, 20, 25, 30, 35, 40, 45 };
var target = 40;

int MaxViewers = Convert.ToInt32(txtNoRecordsToAdd.Text);

var closestSubSet = MyExtensions.SubSetsOf(List1)
.Select(o=> new{ SubSet = o, Sum = o.Sum(x=> x)})
.Select(o=> new{ SubSet = o.SubSet, Sum = o.Sum, FromTarget = (target - o.Sum >= 0 ? target - o.Sum : (target - o.Sum) * -1  ) })
.OrderBy(o=> o.FromTarget).FirstOrDefault();

我知道出于某些性能原因（不是多次调用 Sum，而是使用它），我选择了第二个选择很棘手。这应该找到与您指定的目标最接近的总和 ^^ 玩得开心

---

优化：

var List1 = new int[] { 5, 10, 15, 20, 25, 30, 35, 40, 45 }; 变量目标 = 40;

int MaxViewers = Convert.ToInt32(txtNoRecordsToAdd.Text);
int minClosestTargetRequired = 0;
int closestSum = int.maxValue;
int closestSetIndex = -1;
var subsets = MyExtensions.SubSetsOf(List1);
for(var c = 0 ; c < subsets.Count() ; c++)
{
  int currentSum = subsets[c].Sum(o=> o);
  if(currentSum < closestSum)
  {
    closestSum = currentSum;
    closestSetIndex = c;
  }
  if(closestSum <= minClosestTargetRequired)
    break;
}
Console.WriteLine("Closest Sum Is {0} In Set Index {1},closestSum,closestSetIndex);