Given an array, how to generate all combinations of subset size k?

问题

So given input = [1, 2, 3] and k=2 this would return:

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

This is the closest to what I am looking for, but not quite: http://algorithms.tutorialhorizon.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);

^ Missing results such as 2 1, 3 1, 3 2, etc.

Secondly, I am not sure if I am naming this problem correctly because solutions to "all combinations of subset of size k" do not give the expected answer.

回答1:

A recursive solution to find k-subset permutations (in pseudo-code):

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)
        }
    }
}

Here's a run-through for an example:

input: [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);

回答2:

Instead of combinations, try permutations.

Try generating permutations, then resizing the array.

Here's it implemented, modified from here

var permArr = [],
  usedChars = [];

function permute(input, k) {
  var i, ch;
  for (i = 0; i < input.length; i++) {
    ch = input.splice(i, 1)[0];
    usedChars.push(ch);
    if (input.length == 0) {
      var toadd = usedChars.slice(0,k);
      if(!permArr.includes(toadd)) permArr.push(toadd); // resizing the returned array to size k
    }
    permute(input, k);
    input.splice(i, 0, ch);
    usedChars.pop();
  }
  return permArr
};
console.log(JSON.stringify(permute([1, 2, 3], 2)));

回答3:

I'm a simple person:

make an array M with size k

fill M with zeroes

loop this:

M[0] += 1

loop through M: *if (M[i] >= size of N) then set M[i]=0 and increase M[i+1] += 1

if M has only different numbers then you've find yourself the indices of a subset of n

loop ends when the last element of M reaches size of n - minus one a.k.a. when the * condition would cause an error

来源：https://stackoverflow.com/questions/46880094/given-an-array-how-to-generate-all-combinations-of-subset-size-k