matlab 在排列组合方面的应用

关键词： matlab 排列组合 matlab 排列组合函数 matlab计算排列组合 matlab求排列组合

nchoosek

Binomial coefficient or all combinations

Syntax:
C = nchoosek(n,k)

     函数描述:      从 n 个元素中 一次选 k 个元素的所有组合数 C（注意，C是一个数值）。

                          C = n!/((n–k)! k!);

         C = nchoosek(v,k)

      函数描述: 从 向量 v 中 一次选其中 k 个元素 的所有组合 C （注意：C是一个矩阵，列数 为 k )

Description

C = nchoosek(n,k)

where n and k are nonnegative integers,

returns n!/((n–k)! k!).

This is the number of combinations of n things taken k at a time.

C = nchoosek(v,k),

where v is a row vector of length n,

creates a matrix whose rows consist of all possible combinations of the n elements of v taken k at
a time.

Matrix C contains n!/((n–k)! k!) rows and k columns.

Inputs n, k, and v support classes of float double and float single.

Examples:

The command nchoosek(2:2:10,4)

returns the even numbers from two to ten, taken four at a time:     

          2          4          6          8
2          4          6         10
2          4          8         10
2          6          8         10
4          6          8         10

combntns

All possible combinations of set of values 从给定集合set中列出所有可能的subset个元素的组合

Syntax
combos = combntns(set,subset)

combos = combntns(set,subset)       returns a matrix whose rows are the various combinations that can be taken of the elements of the vector set of length subset.

Many combinatorial applications can make use of a vector 1:n for the input set to return generalized, indexed combination subsets.

Description

The combntns function provides the combinatorial subsets of a set of numbers.

It is similar to the mathematical expression a choose b, except that instead of the number of such combinations,the actual combinations are returned.

In combinatorial counting, the ordering of the values is not significant.The numerical value of the mathematical statement a choose b is size(combos,1).

Examples

How can the numbers 1 to 5 be taken in sets of three (that is, whatis 5 choose 3)?

combos = combntns(1:5,3)

combos =
1        2        3
1        2        4
1        2        5
1        3        4
1        3        5
1        4        5
2        3        4
2        3        5
2        4        5
3        4        5
size(combos,1)     % “5 choose 3”

ans =
10

(注意事项)：Note that if a value is repeated in the input vector, each occurrence is treated as independent:

combos = combntns([2 2 5],2)

combos =
2        2
2        5
2        5

RemarksThis is a recursive function.

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