在Matlab中生成包含给定集合的至少一个元素的所有组合 [英] Generating all combinations containing at least one element of a given set in Matlab

问题描述

我使用combnk生成组合列表.如何生成组合的子集，该子集始终包含特定值.例如，对于combnk(1:10, 2)，我只需要包含3和/或5的组合.是否有快速的方法?

I use combnk to generate a list of combinations. How can I generate a subset of combinations, which always includes particular values. For example, for combnk(1:10, 2) I only need combinations which contain 3 and/or 5. Is there a quick way to do this?

推荐答案

好，在您的特定示例中，从集合{1，...，10}中选择两个整数，以使所选整数之一为3或5会产生9 + 9-1 = 17个已知组合，因此您可以枚举它们.

Well, in your specific example, choosing two integers from the set {1, ..., 10} such that one of the chosen integers is 3 or 5 yields 9+9-1 = 17 known combinations, so you can just enumerate them.

通常，要从包含整数m的整数{1，...，n}中查找所有n-choose-k组合，这与查找(n-1)-choose-(k -1)整数{1，...，m-1，m + 1，...，n}的组合.

In general, to find all of the n-choose-k combinations from integers {1, ..., n} that contain integer m, that is the same as finding the (n-1)-choose-(k-1) combinations from integers {1, ..., m-1, m+1, ..., n}.

在matlab中，应该是

In matlab, that would be

combnk([1:m-1 m+1:n], k-1)

(即使m为1或n，该代码仍然有效.)

(This code is still valid even if m is 1 or n.)

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