下面的递归算法从有序集中选取所有k元素组合:

选择组合中的第一个元素I 将I与从大于I的元素集中递归选择的k-1个元素的组合组合。

对集合中的每一个i进行上述迭代。

为了避免重复，您必须选择比i大的其余元素。这样[3,5]将只被选中一次，即[3]与[5]结合，而不是两次(该条件消除了[5]+[3])。没有这个条件，你得到的是变化而不是组合。

我有一个用于project euler的排列算法，用python编写:

def missing(miss,src):
    "Returns the list of items in src not present in miss"
    return [i for i in src if i not in miss]


def permutation_gen(n,l):
    "Generates all the permutations of n items of the l list"
    for i in l:
        if n<=1: yield [i]
        r = [i]
        for j in permutation_gen(n-1,missing([i],l)):  yield r+j

If

n<len(l) 

你应该有所有你需要的组合，没有重复，你需要吗?

它是一个生成器，所以你可以这样使用它:

for comb in permutation_gen(3,list("ABCDEFGH")):
    print comb 

遵循Haskell代码同时计算组合数和组合，由于Haskell的惰性，您可以得到其中的一部分而无需计算另一部分。

import Data.Semigroup
import Data.Monoid

data Comb = MkComb {count :: Int, combinations :: [[Int]]} deriving (Show, Eq, Ord)

instance Semigroup Comb where
    (MkComb c1 cs1) <> (MkComb c2 cs2) = MkComb (c1 + c2) (cs1 ++ cs2)

instance Monoid Comb where
    mempty = MkComb 0 []

addElem :: Comb -> Int -> Comb
addElem (MkComb c cs) x = MkComb c (map (x :) cs)

comb :: Int -> Int -> Comb
comb n k | n < 0 || k < 0 = error "error in `comb n k`, n and k should be natural number"
comb n k | k == 0 || k == n = MkComb 1 [(take k [k-1,k-2..0])]
comb n k | n < k = mempty
comb n k = comb (n-1) k <> (comb (n-1) (k-1) `addElem` (n-1))

它是这样工作的:

*Main> comb 0 1
MkComb {count = 0, combinations = []}

*Main> comb 0 0
MkComb {count = 1, combinations = [[]]}

*Main> comb 1 1
MkComb {count = 1, combinations = [[0]]}

*Main> comb 4 2
MkComb {count = 6, combinations = [[1,0],[2,0],[2,1],[3,0],[3,1],[3,2]]}

*Main> count (comb 10 5)
252

递归，一个很简单的答案，combo，在Free Pascal中。

    procedure combinata (n, k :integer; producer :oneintproc);

        procedure combo (ndx, nbr, len, lnd :integer);
        begin
            for nbr := nbr to len do begin
                productarray[ndx] := nbr;
                if len < lnd then
                    combo(ndx+1,nbr+1,len+1,lnd)
                else
                    producer(k);
            end;
        end;

    begin
        combo (0, 0, n-k, n-1);
    end;

“producer”处理为每个组合生成的产品数组。

一个简洁的Javascript解决方案:

Array.prototype.combine=function combine(k){    
    var toCombine=this;
    var last;
    function combi(n,comb){             
        var combs=[];
        for ( var x=0,y=comb.length;x<y;x++){
            for ( var l=0,m=toCombine.length;l<m;l++){      
                combs.push(comb[x]+toCombine[l]);           
            }
        }
        if (n<k-1){
            n++;
            combi(n,combs);
        } else{last=combs;}
    }
    combi(1,toCombine);
    return last;
}
// Example:
// var toCombine=['a','b','c'];
// var results=toCombine.combine(4);

static IEnumerable<string> Combinations(List<string> characters, int length)
{
    for (int i = 0; i < characters.Count; i++)
    {
        // only want 1 character, just return this one
        if (length == 1)
            yield return characters[i];

        // want more than one character, return this one plus all combinations one shorter
        // only use characters after the current one for the rest of the combinations
        else
            foreach (string next in Combinations(characters.GetRange(i + 1, characters.Count - (i + 1)), length - 1))
                yield return characters[i] + next;
    }
}