src/helpers/base-combinations.js

/**
 * 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.
 */

/**
 * Get k-sized combinations of elements in a set.
 *
 * Usage: `combinations(set, k)`
 *
 * Examples:
 *
 *   combinations([1, 2, 3], 1)
 *   -> [[1], [2], [3]]
 *
 *   combinations([1, 2, 3], 2)
 *   -> [[1,2], [1,3], [2, 3]]
 *
 *   combinations([1, 2, 3], 3)
 *   -> [[1, 2, 3]]
 *
 *   combinations([1, 2, 3], 4)
 *   -> []
 *
 *   combinations([1, 2, 3], 0)
 *   -> []
 *
 *   combinations([1, 2, 3], -1)
 *   -> []
 *
 *   combinations([], 0)
 *   -> []
 *
 *
 * @param {Array} set - Array of objects of any type. They are treated as unique.
 * @param {Number} k - size of combinations to search for.
 * @returns {Array} - Array of found combinations; the size of a combination is k.
 */
function combinations(set, k) {
	if (k > set.length || k <= 0) {
		return []
	}

	else if (k === set.length) {
		return [set]
	}

	else if (k === 1) {
		let combs = []
		for (let i = 0; i < set.length; i++) {
			combs.push([set[i]])
		}
		return combs
	}

	else {
		// Assert {1 < k < set.length}
		let combs = []
		for (let i = 0; i < set.length - k + 1; i++) {
			let head = set.slice(i, i + 1)
			let tailcombs = combinations(set.slice(i + 1), k - 1)
			for (let j = 0; j < tailcombs.length; j++) {
				combs.push(head.concat(tailcombs[j]))
			}
		}
		return combs
	}
}

export default combinations