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JavaScript functions to calculate combinations of elements in Array.
/**
* Copyright 2012 Akseli Palén.
* Created 2012-07-15.
* Licensed under the MIT license.
*
* <license>
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files
* (the "Software"), to deal in the Software without restriction,
* including without limitation the rights to use, copy, modify, merge,
* publish, distribute, sublicense, and/or sell copies of the Software,
* and to permit persons to whom the Software is furnished to do so,
* subject to the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
* </lisence>
*
* Implements functions to calculate combinations of elements in JS Arrays.
*
* Functions:
* k_combinations(set, k) -- Return all k-sized combinations in a set
* combinations(set) -- Return all combinations of the set
*/
/**
* K-combinations
*
* Get k-sized combinations of elements in a set.
*
* Usage:
* k_combinations(set, k)
*
* Parameters:
* set: Array of objects of any type. They are treated as unique.
* k: size of combinations to search for.
*
* Return:
* Array of found combinations, size of a combination is k.
*
* Examples:
*
* k_combinations([1, 2, 3], 1)
* -> [[1], [2], [3]]
*
* k_combinations([1, 2, 3], 2)
* -> [[1,2], [1,3], [2, 3]
*
* k_combinations([1, 2, 3], 3)
* -> [[1, 2, 3]]
*
* k_combinations([1, 2, 3], 4)
* -> []
*
* k_combinations([1, 2, 3], 0)
* -> []
*
* k_combinations([1, 2, 3], -1)
* -> []
*
* k_combinations([], 0)
* -> []
*/
function k_combinations(set, k) {
var i, j, combs, head, tailcombs;
// There is no way to take e.g. sets of 5 elements from
// a set of 4.
if (k > set.length || k <= 0) {
return [];
}
// K-sized set has only one K-sized subset.
if (k == set.length) {
return [set];
}
// There is N 1-sized subsets in a N-sized set.
if (k == 1) {
combs = [];
for (i = 0; i < set.length; i++) {
combs.push([set[i]]);
}
return combs;
}
// Assert {1 < k < set.length}
// Algorithm description:
// To get k-combinations of a set, we want to join each element
// with all (k-1)-combinations of the other elements. The set of
// these k-sized sets would be the desired result. However, as we
// represent sets with lists, we need to take duplicates into
// account. To avoid producing duplicates and also unnecessary
// computing, we use the following approach: each element i
// divides the list into three: the preceding elements, the
// current element i, and the subsequent elements. For the first
// element, the list of preceding elements is empty. For element i,
// we compute the (k-1)-computations of the subsequent elements,
// join each with the element i, and store the joined to the set of
// computed k-combinations. We do not need to take the preceding
// elements into account, because they have already been the i:th
// element so they are already computed and stored. When the length
// of the subsequent list drops below (k-1), we cannot find any
// (k-1)-combs, hence the upper limit for the iteration:
combs = [];
for (i = 0; i < set.length - k + 1; i++) {
// head is a list that includes only our current element.
head = set.slice(i, i + 1);
// We take smaller combinations from the subsequent elements
tailcombs = k_combinations(set.slice(i + 1), k - 1);
// For each (k-1)-combination we join it with the current
// and store it to the set of k-combinations.
for (j = 0; j < tailcombs.length; j++) {
combs.push(head.concat(tailcombs[j]));
}
}
return combs;
}
/**
* Combinations
*
* Get all possible combinations of elements in a set.
*
* Usage:
* combinations(set)
*
* Examples:
*
* combinations([1, 2, 3])
* -> [[1],[2],[3],[1,2],[1,3],[2,3],[1,2,3]]
*
* combinations([1])
* -> [[1]]
*/
function combinations(set) {
var k, i, combs, k_combs;
combs = [];
// Calculate all non-empty k-combinations
for (k = 1; k <= set.length; k++) {
k_combs = k_combinations(set, k);
for (i = 0; i < k_combs.length; i++) {
combs.push(k_combs[i]);
}
}
return combs;
}

I think it doesnt work for 4 elements

It works great. Thanks. I tested it for 4 elements as well and it works great. Thanks.

So it works but only generates combinations in the same original order - how could you get all combinations in any order?

thanks a lot

skibulk commented Sep 10, 2015

@chrisgoddard you're looking for a permutations function, not a combinations function.

danbars commented Sep 28, 2015

@chrisgoddard you can run each combination through a permutation algorithm with something like this: https://github.com/eriksank/permutation-engine
Or, use permutation/combination engine, like this one:
https://github.com/dankogai/js-combinatorics

rhalff commented Feb 23, 2016

Is the above gist available on npm somewhere? I want to use it in my library, right now I've just copy & pasted it.

sallar commented Feb 24, 2016

@danbars Thanks for the links. +1

foluis commented Aug 5, 2016

Does Not work for this set "ababb" it repeats elements and also "abbba", "babab" are missing

@foluis all member elements must be considered unique in order to form a set mathematically

possible combination of 1, 2, 3 are following,may be i am wrong

[1], [2], [3], [1, 2], [1, 3], [2, 3], [2, 1], [3, 1], [3, 2], [1, 2, 3], [3, 2, 1]

Thanks a lot!

Thanks!

@imVinayPandya Looks like he is using N choose K which should only return unique combinations. Such as 1,2 and 2,1 are the same. Also, you are setting the number of members for the k combination. Thus this will only return single member combinations, or double member combinations or triple member combinations etc etc etc.

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