javascript-algorithms/src/algorithms/sets/combination-sum/combinationSum.js

/**
 * @param {number[]} candidates - candidate numbers we're picking from.
 * @param {number} remainingSum - remaining sum after adding candidates to currentCombination.
 * @param {number[][]} finalCombinations - resulting list of combinations.
 * @param {number[]} currentCombination - currently explored candidates.
 * @param {number} startFrom - index of the candidate to start further exploration from.
 * @return {number[][]}
 */
function combinationSumRecursive(
  candidates,
  remainingSum,
  finalCombinations = [],
  currentCombination = [],
  startFrom = 0,
) {
  if (remainingSum < 0) {
    // By adding another candidate we've gone below zero.
    // This would mean that the last candidate was not acceptable.
    return finalCombinations;
  }

  if (remainingSum === 0) {
    // If after adding the previous candidate our remaining sum
    // became zero - we need to save the current combination since it is one
    // of the answers we're looking for.
    finalCombinations.push(currentCombination.slice());

    return finalCombinations;
  }

  // If we haven't reached zero yet let's continue to add all
  // possible candidates that are left.
  for (let candidateIndex = startFrom; candidateIndex < candidates.length; candidateIndex += 1) {
    const currentCandidate = candidates[candidateIndex];

    // Let's try to add another candidate.
    currentCombination.push(currentCandidate);

    // Explore further option with current candidate being added.
    combinationSumRecursive(
      candidates,
      remainingSum - currentCandidate,
      finalCombinations,
      currentCombination,
      candidateIndex,
    );

    // BACKTRACKING.
    // Let's get back, exclude current candidate and try another ones later.
    currentCombination.pop();
  }

  return finalCombinations;
}

/**
 * Backtracking algorithm of finding all possible combination for specific sum.
 *
 * @param {number[]} candidates
 * @param {number} target
 * @return {number[][]}
 */
export default function combinationSum(candidates, target) {
  return combinationSumRecursive(candidates, target);
}