--description--

Solve the Towers of Hanoi problem. The number of objects will be given as the first parameter, followed by the strings used to identify each stack of objects. Create a nested array containing the list of moves, ["source", "destination"].

For example, the parameters (4, 'A', 'B', 'C'), will result in nested array of moves [['A', 'C'], ['B', 'A']], indicating that the 1st move was to move an object from stack A to C and the 2nd move was to move an object from stack B to A.

--instructions--

Write a function that returns the moves to stack the objects in a nested array.

--before-each--

const res3Moves = [['A', 'B'], ['A', 'C'], ['B', 'C'], ['A', 'B'], ['C', 'A'], ['C', 'B'], ['A', 'B']];
const res7First10Moves = [['A', 'B'], ['A', 'C'], ['B', 'C'], ['A', 'B'], ['C', 'A'], ['C', 'B'], ['A', 'B'], ['A', 'C'], ['B', 'C'], ['B', 'A']];

function getTowerResults_() {
  return {
    res3: towerOfHanoi(3, 'A', 'B', 'C'),
    res5: towerOfHanoi(5, 'X', 'Y', 'Z'),
    res7: towerOfHanoi(7, 'A', 'B', 'C')
  };
}

--hints--

towerOfHanoi should be a function.

assert(typeof towerOfHanoi === 'function');

towerOfHanoi(3, ...) should return 7 moves.

assert(getTowerResults_().res3.length === 7);

towerOfHanoi(3, 'A', 'B', 'C') should return [['A','B'], ['A','C'], ['B','C'], ['A','B'], ['C','A'], ['C','B'], ['A','B']].

assert.deepEqual(getTowerResults_().res3, res3Moves);

towerOfHanoi(5, "X", "Y", "Z") 10th move should be Y -> X.

const { res5 } = getTowerResults_();
assert.deepEqual(res5[9], ['Y', 'X']);

towerOfHanoi(7, 'A', 'B', 'C') first ten moves should be [['A','B'], ['A','C'], ['B','C'], ['A','B'], ['C','A'], ['C','B'], ['A','B'], ['A','C'], ['B','C'], ['B','A']]

const { res7 } = getTowerResults_();
assert.deepEqual(res7.slice(0, 10), res7First10Moves);

--seed--

--seed-contents--

function towerOfHanoi(n, a, b, c) {

  return [[]];
}

--solutions--

function towerOfHanoi(n, a, b, c) {
  const res = [];
  towerOfHanoiHelper(n, a, c, b, res);
  return res;
}

function towerOfHanoiHelper(n, a, b, c, res) {
  if (n > 0) {
    towerOfHanoiHelper(n - 1, a, c, b, res);
    res.push([a, c]);
    towerOfHanoiHelper(n - 1, b, a, c, res);
  }
}