Creating an Array of Unique Combinations

Question

I have an array of components:

let components = ["a", "b", "c"];

It is possible to combine those components to make products; i.e., "a" + "b" = "ab".

I have a catalog of possible products:

let catalog = ["ab", "ac", "bc"];

Using something like lodash, we can create an array of possible products. Output array would look like ["ab", "ac", "bc"].

But the problem is that not all of those products could be built because once the component for one is used, it is no longer available for use in other products that require it.

I need an output that only shows possible outcomes. When there are only 3 components, and every catalog product requires 2, obviously it's not possible to create more than one product at a time. So an output that would express that each is either-or would look like [["ab"],["ac"],["bc"]]. But if you have 4 components it is possible to create more than one product at a time.

let components = ["a", "b", "c", "d"];

Possible catalog products with these components should look like [["ad", "cb"], ["ac", "bd"], ["ab", "cd"]].

I need some help with the logic for a function that outputs an array like the above.

Below is an example of a function that outputs possible catalog products with the provided components. But it doesn't achieve the requirements stated above.

let components = ["a", "b", "c", "e"];

let catalog = [["a", "b"], ["a", "c"], ["b", "c"], ["c", "d"]];

// Check if subset is included in superset (respecting duplicates).
const isSubset = (subset, superset) => {
  const subsetCount = _.countBy(subset)
  const supersetCount = _.countBy(superset)

  return _.every(subsetCount, (count, value) => supersetCount[value] >= count)
}

catalog.forEach(el => {
if (isSubset(catalog, components) ==  true) console.log(el)
});

// Filter all catalog items, that could be build by components
const matches = _.pickBy(catalog, (catalog, thing) => isSubset(catalog, components))

console.log(matches);

<script src="https://cdn.jsdelivr.net/npm/lodash@4.17.10/lodash.min.js"></script>

EDIT: The result should be an array of possible catalog products whose components do not overlap/conflict with other catalog products in their respective arrays. So for example, if we have...

let components = ["a", "b", "c", "d", "e"];

let catalog = ["ab", "ac", "ad", "ae", "bc", "bd", "be", "cd", "ce", "de"];

... the output should be something like:

// [ ["ab", "cd"], ["ab", "de"], ["ac", "bd"], ["ac", "be"], ["ad", "ce"], ["ad, "bc"], ["ae", "bc"], ["ae", "cd"] ]

It's possible I've missed some there, but the point is that the output should be an array that expresses the either-or relationship of its inner arrays. The products' combination order doesn't matter. For example, "cd" == "dc". No element in the inner arrays should share a component. For example, we should not have ["ab", "ac"].

Answer 1

Edited to accommodate the needs in your comment. This example uses a fairly straight forward recursive function to generate all unique combinations with the option to limit the maximum combination size (used to generate the catalog with only combinations of size 2).

The possibleProducts are a filtered array of all the unique combinations generated by passing the catalog array to the same function with no limits.

// generates unique combinations recursively
function combineRec(array, size, limit = false) {
  array = array.map(e => [e]);
  // max size of combinations.
  size = size || array.length;
 
  const acc =[];
  
  const spread = (s, arr) => arr.forEach((e, i, a) => {
    let 
      seed = [...s, ...e],
      segment = a.slice(i + 1);
    acc.push([...s, ...e]);
    if (s.length < size - 1 && segment.length > 0) {
      spread(seed, segment);
    }
  });

  array.forEach((e, i, a) => (
    spread(e, a.slice(i + 1))
  ))

  // if limit is true return only combinations of specified size.
  return r = limit ? acc.filter(({ length }) => length === size) : acc;
}

// filters out combinations with duplicate elements
const filterByElements = (array) => array.filter(arr =>
  !arr.some((a, i) => a.some(e => arr.slice(i + 1).flat().includes(e)))
);

const components = ['a', 'b', 'c', 'd', 'e', 'f'];

// generate catalog (return only combinations of 2)
let catalog = combineRec(components, 2, true);

// generate all possible catalog combinations (returns all)
let catalogCombinations = combineRec(catalog);

// filter to exlude duplicates and map combination arrays to strings.
let possibleProducts = filterByElements(catalogCombinations)
  .sort((a, b) => a.length - b.length)
  .map(p => p.map(c => c.join('')));

console.log('catalog: ', JSON.stringify(catalog));
console.log('possibleProducts: ', JSON.stringify(possibleProducts));

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Answer 2

Is below code satisfy you requirement?

1. Shuffle the components array as many as posible;
2. Use array's splice function to splice with length of requires;

let components = ["a", "b", "c", "d", "e", "f"];

function getCatalogProducts(components: string[], requires: number) {
  if (components.length < requires) return [];

  if (components.length === requires) return [components];

  let results: string[] = [];
  let cloneComponents = [...components];
  while (cloneComponents.length) {
    let cur = cloneComponents.splice(0, requires);
    let curStr = cur.sort().join('');
    results.push(curStr);
  }

  return results;
}

let shuffleComponentsArray = permute(components);

console.clear();
let results: any = [];
for (let i = 0; i < shuffleComponentsArray.length; i++) {
  let posibleCatalogProducts = getCatalogProducts(shuffleComponentsArray[i], 2);
  if (!results.some((item: any) => posibleCatalogProducts.sort().join('') === item.sort().join(''))) {
    results.push(posibleCatalogProducts);
  }
}

console.log(results);


// Below 3 functions are shuffle array related

function swap(arr: any, a: number, b: number) {
  var temp = arr[a];
  arr[a] = arr[b];
  arr[b] = temp;
}

function factorial(n: number) {
  var val = 1;
  for (var i = 1; i < n; i++) {
    val *= i;
  }
  return val;
}

function permute(perm: any) {
  let results = [];
  var total = factorial(perm.length);

  for (var j = 0, i = 0, inc = 1; j < total; j++, inc *= -1, i += inc) {

    for (; i < perm.length - 1 && i >= 0; i += inc) {
      results.push([...perm]);
      swap(perm, i, i + 1);
    }

    results.push([...perm]);

    if (inc === 1) {
      swap(perm, 0, 1);
    } else {
      swap(perm, perm.length - 1, perm.length - 2);
    }
  }

  return results;
}

Answer 3

In addition to the other solution, with this one, you can adjust the size of the products. (Assuming that COMPONENTS % SIZE_OF_EACH_PRODUCT === 0, in this case).

const COMPONENTS = ["a", "b", "c", "d", "e", "f", "g", "h", "i"];
const SIZE_OF_EACH_PRODUCT = 3;

const getCombinations = (inputArr, r) => {
  const res = [];
  const f = (inputArr, tmpArr, r, inputIndex, tmpIndex) => {
    if (tmpIndex == r) {
      let s = [];
      for (let x = 0; x < r; x++) s.push(tmpArr[x]);
      res.push(s);
      return;
    }
    if (inputIndex >= inputArr.length) return;
    tmpArr[tmpIndex] = inputArr[inputIndex];

    f(inputArr, tmpArr, r, inputIndex + 1, tmpIndex + 1);
    f(inputArr, tmpArr, r, inputIndex + 1, tmpIndex);
  };
  f(inputArr, [], r, 0, 0);
  return res;
};

const catalog = getCombinations(COMPONENTS, SIZE_OF_EACH_PRODUCT);

const uniqueCombinations = getCombinations(catalog, COMPONENTS.length / SIZE_OF_EACH_PRODUCT).filter((arrays) => {
  for (let i = 0; i < arrays.length; i++)
    for (let u = 0; u < arrays.length; u++) 
      if (!(i === u))
        if (arrays[i].some((char) => arrays[u].includes(char))) return false;
  return true;
});

console.log(uniqueCombinations);

Answer 4

Based on your other recent related question, I think I understand that what you want would be for something like this:

const catalog= ["ad", "aab", "ace", "cd", "ba", "bd", "adf", "def"]
const components = ["a", "b", "a", "c", "d", "e"]

simultaneousItems (catalog, components) 

to yield

[["ad", "ace"], ["ad", "ba"], ["aab", "cd"], ["ace", "ba"], ["ace", "bd"], ["cd", "ba"]]

where every array in the result is a maximal subset of catalog items that can be made together out of the components supplied. So, for instance, none of the output arrays contains "adf" or "def", since we have no "f" in the components, and none of them contain both "ad" and "aab" since we only have two "a"s in the component list.

If this is correct, then the following snippet would seem to do. The code explanation in that answer serves for this, with two modifications:

• The collect function is simplified here to a more logical core

• The wrapper simultaneousItems is altered to split the input strings into arrays and joint back the output ones. And it no longer has to handle extracting the values from your itemCatalog format.

const dropFirst = (x, xs, i = xs .indexOf (x)) =>
  i < 0 ? [... xs] : [... xs .slice (0, i), ... xs .slice (i + 1)]

const dropEach = ([x, ...xs], ys) => 
  x == undefined ? ys : dropEach (xs, dropFirst (x, ys))

const canMake = ([c, ...cs], comps) => 
  c == undefined ? true : comps .includes (c) ? canMake (cs, dropFirst (c, comps)) : false

const isSubset = (xs, ys) =>
  xs .every (x => ys .includes (x))

const maximize = (xs) => 
  xs .filter (x => ! (xs .some (y => x !== y && isSubset (x, y))))

const collect = ([x, ...xs], ys) => 
  x == undefined
    ? [[]]
  : canMake (x, ys)
    ? [
        ... collect (xs, dropEach (x, ys)) .map (coll => [x, ... coll]), 
        ... collect (xs, ys)
      ]
    : collect (xs, ys)

const simultaneousItems = (catalog, components) => 
  maximize (collect (catalog .map (s => s .split ('')), components)) 
    .map (g => g .map (ss => ss .join ('')))


const catalog = ["ad", "aab", "ace", "cd", "ba", "bd", "adf", "def"]

const components = ["a", "b", "a", "c", "d", "e"]

console .log (
  simultaneousItems (catalog, components)
)

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