c# – 如何生成给定大小的所有子集？

2023年3月9日 212次阅读

给定一些数字n和一个子集大小,我想获得集合{1,…,n}的指定大小的所有可能子集.

对于n = 5和subsetSize = 4的预期结果：

{{1,2,3,4}, {1,2,3,5}, {1,3,4,5}, {1,2,4,5}, {2,3,4,5}}

(这将是一个List< List< int>>)

这意味着我需要得到(subsetSize选择n)子集(牛顿符号).

算法的任何想法可以找到我这样的整数列表列表？我正在用C#实现它,如果这很重要的话.

最佳答案

internal class Program
{
    private static IEnumerable<IEnumerable<int>> Subsets(int n, int subsetSize)
    {
        IEnumerable<int> sequence = Enumerable.Range(1, n);

        // generate list of sequences containing only 1 element e.g. {1}, {2}, ...
        var oneElemSequences = sequence.Select(x => new[] { x }).ToList();

        // generate List of int sequences
        var result = new List<List<int>>();
        // add initial empty set
        result.Add(new List<int>());

        // generate powerset, but skip sequences that are too long
        foreach (var oneElemSequence in oneElemSequences)
        {
            int length = result.Count;

            for (int i = 0; i < length; i++)
            {
                if (result[i].Count >= subsetSize)
                    continue;

                result.Add(result[i].Concat(oneElemSequence).ToList());
            }
        }

        return result.Where(x => x.Count == subsetSize);
    }

    private static void OutputSubset(int n, IEnumerable<IEnumerable<int>> subsets)
    {
        Console.WriteLine("n: {0}", n);
        foreach (var subset in subsets)
        {
            Console.WriteLine("\t{0}", string.Join(" ", subset.Select(x => x.ToString())));
        }
    }

    private static void Main()
    {
        for (int n = 1; n < 500; n++)
        {
            var subsets = Subsets(n, subsetSize: 4);
            OutputSubset(n, subsets);
        }
    }
}

输出：