freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/rosetta-code/towers-of-hanoi.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5951ed8945deab770972ae56	Towers of Hanoi	5	302341	towers-of-hanoi

--description--

Solve the Towers of Hanoi problem.

Your solution should accept the number of discs as the first parameters, and three string used to identify each of the three stacks of discs, for example towerOfHanoi(4, 'A', 'B', 'C'). The function should return an array of arrays containing the list of moves, source -> destination.

For example, the array [['A', 'C'], ['B', 'A']] indicates that the 1st move was to move a disc from stack A to C, and the 2nd move was to move a disc from stack B to A.

--hints--

towerOfHanoi should be a function.

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

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

assert(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(towerOfHanoi(3, 'A', 'B', 'C'), res3Moves);

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

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']]

assert.deepEqual(towerOfHanoi(7, 'A', 'B', 'C').slice(0, 10), res7First10Moves);

--seed--

--after-user-code--

const res3 = towerOfHanoi(3, 'A', 'B', 'C');
const res3Moves = [['A', 'B'], ['A', 'C'], ['B', 'C'], ['A', 'B'], ['C', 'A'], ['C', 'B'], ['A', 'B']];
const res5 = towerOfHanoi(5, 'X', 'Y', 'Z');
const res7First10Moves = [['A', 'B'], ['A', 'C'], ['B', 'C'], ['A', 'B'], ['C', 'A'], ['C', 'B'], ['A', 'B'], ['A', 'C'], ['B', 'C'], ['B', 'A']];

--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);
  }
}