coins

gistfile1.txt

const S = [1, 2, 3];
const n = 4;

const f = (S, n) => {
  const stack = S.map((coin) => [coin]);
  const permuts = new Set();

  while (stack.length) {
    const current = stack.shift();
    const sum = current.reduce((s, c) => s + c);

    if (sum > n) {
      continue;
    }
    if (sum === n) {
      console.log(current);
      permuts.add(current.sort((a, b) => a - b).join(";"));
      continue;
    }

    for (const c of S) {
      stack.push([...current, c]);
    }
  }

  return permuts.size;
};

console.log(f(S, n));