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JavaScript functions to calculate combinations of elements in Array.
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| /** | |
| * 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} | |
| combs = []; | |
| // 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: | |
| 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; | |
| } |
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