Logic: short way to number (greedy).js

const ways = {
  // number: 10 => steps: [A, B, C, A, B, C]
};

const START = 3;
const FINISH = 22;

let minWayToFinish = undefined;

function check(number, steps = []) {
  if (number > FINISH) {
    return;
  }

  if (number === FINISH) {
    if (!minWayToFinish || steps.length < minWayToFinish.length) {
      minWayToFinish = steps;
      console.log(steps.length + ": " + steps.join(', '));
      return;
    }
  }

  if (ways.hasOwnProperty(number)) {
    if (steps.length <= ways[number].length) {
      ways[number] = steps;
    }
  } else {
    check(number+3, steps.concat(['A']));
    check(number*2, steps.concat(['B']));
    check(number+1, steps.concat(['C']));
  }
}

check(START);