bestsum.js

const bestSum = (targetSum, numbers, memo = new Map()) => {
  const key = targetSum + '';
  if (memo.has(key)) return memo.get(key);
  if (targetSum === 0) return [];
  if (targetSum <= 0) return null;
  let smallestSum = null;
  for (let num of numbers) {
      const remainder = targetSum - num;
      const res = bestSum(remainder, numbers, memo);
      if (res === null) continue;
      const resAndCurrent = [...res, num];
      if (smallestSum === null) smallestSum = resAndCurrent;
      if (smallestSum.length > resAndCurrent.length) smallestSum = resAndCurrent;
  }
  memo.set(key, shortestNum);
  return shortestNum;
};
console.log(bestSum(8, [2, 5, 3])); // -> 5,3
console.log(bestSum(20, [1,2,3,4,5])) // -> 5,5,5,5
console.log(bestSum(125, [1,2,4,8,16,32])); // -> 32,32,32,16,8,4,1