小编典典

给定一个数组,如何生成子集大小k的所有组合?

algorithm

因此,考虑input = [1, 2, 3]k=2将返回:

1 2
1 3
2 1
2 3
3 1
3 2

这是最接近我要寻找的内容,但不太准确:http//algorithms.tutorialhorizo​​n.com/print-all-combinations-of-subset-
of-size-k-from-given-array/

function subsetsOfSize(a, used, startIndex, currentSize, k) {

  if (currentSize === k) {

    for (var i = 0; i < a.length; i++) {

      if (used[i])

        console.log(a[i]);

    }

    console.log('-');

    return;

  }



  if (startIndex === a.length)

    return;



  used[startIndex] = true;

  subsetsOfSize(a, used, startIndex+1, currentSize+1, k);



  used[startIndex] = false;

  subsetsOfSize(a, used, startIndex+1, currentSize, k);

}



var input = [1,2,3];

subsetsOfSize(input, Array(input.length).fill(false), 0, 0, 2);

^缺少的结果,如2 13 13 2等。

其次,我不确定我是否正确地命名了此问题,因为“大小为k的子集的所有组合”的解决方案没有给出预期的答案。


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2020-07-28

共1个答案

小编典典

查找k个子集置换的递归解决方案(用伪代码):

kSubsetPermutations(partial, set, k) {
    for (each element in set) {
        if (k equals 1) {
            store partial + element
        }
        else {
            make copy of set
            remove element from copy of set
            recurse with (partial + element, copy of set, k - 1)
        }
    }
}

这是一个示例示例:

输入:[a,b,c,d,e]
k:3

partial = [], set = [a,b,c,d,e], k = 3
    partial = [a], set = [b,c,d,e], k = 2
        partial = [a,b], set = [c,d,e], k = 1 -> [a,b,c], [a,b,d], [a,b,e]
        partial = [a,c], set = [b,d,e], k = 1 -> [a,c,b], [a,c,d], [a,c,e]
        partial = [a,d], set = [b,c,e], k = 1 -> [a,d,b], [a,d,c], [a,d,e]
        partial = [a,e], set = [b,c,d], k = 1 -> [a,e,b], [a,e,c], [a,e,d]
    partial = [b], set = [a,c,d,e], k = 2
        partial = [b,a], set = [c,d,e], k = 1 -> [b,a,c], [b,a,d], [b,a,e]
        partial = [b,c], set = [a,d,e], k = 1 -> [b,c,a], [b,c,d], [b,c,e]
        partial = [b,d], set = [a,c,e], k = 1 -> [b,d,a], [b,d,c], [b,d,e]
        partial = [b,e], set = [a,c,d], k = 1 -> [b,e,a], [b,e,c], [b,e,d]
    partial = [c], set = [a,b,d,e], k = 2
        partial = [c,a], set = [b,d,e], k = 1 -> [c,a,b], [c,a,d], [c,a,e]
        partial = [c,b], set = [a,d,e], k = 1 -> [c,b,a], [c,b,d], [c,b,e]
        partial = [c,d], set = [a,b,e], k = 1 -> [c,d,a], [c,d,b], [c,d,e]
        partial = [c,e], set = [a,b,d], k = 1 -> [c,e,a], [c,e,b], [c,e,d]
    partial = [d], set = [a,b,c,e], k = 2
        partial = [d,a], set = [b,c,e], k = 1 -> [d,a,b], [d,a,c], [d,a,e]
        partial = [d,b], set = [a,c,e], k = 1 -> [d,b,a], [d,b,c], [d,b,e]
        partial = [d,c], set = [a,b,e], k = 1 -> [d,c,a], [d,c,b], [d,c,e]
        partial = [d,e], set = [a,b,c], k = 1 -> [d,e,a], [d,e,b], [d,e,c]
    partial = [e], set = [a,b,c,d], k = 2
        partial = [e,a], set = [b,c,d], k = 1 -> [e,a,b], [e,a,c], [e,a,d]
        partial = [e,b], set = [a,c,d], k = 1 -> [e,b,a], [e,b,c], [e,b,d]
        partial = [e,c], set = [a,b,d], k = 1 -> [e,c,a], [e,c,b], [e,c,d]
        partial = [e,d], set = [a,b,c], k = 1 -> [e,d,a], [e,d,b], [e,d,c]



function kSubsetPermutations(set, k, partial) {

    if (!partial) partial = [];                 // set default value on first call

    for (var element in set) {

        if (k > 1) {

            var set_copy = set.slice();         // slice() creates copy of array

            set_copy.splice(element, 1);        // splice() removes element from array

            kSubsetPermutations(set_copy, k - 1, partial.concat([set[element]]));

        }                                       // a.concat(b) appends b to copy of a

        else document.write("[" + partial.concat([set[element]]) + "] ");

    }

}

kSubsetPermutations([1,2,3,4,5], 3);
2020-07-28