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title	id	challengeType	isHidden	forumTopicId
Towers of Hanoi	5951ed8945deab770972ae56	5	false	302341

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.

Instructions

Tests

tests:
  - text: <code>towerOfHanoi</code> should be a function.
    testString: assert(typeof towerOfHanoi === 'function');
  - text: <code>towerOfHanoi(3, ...)</code> should return 7 moves.
    testString: assert(res3.length === 7);
  - text: <code>towerOfHanoi(3, 'A', 'B', 'C')</code> should return <code>[['A','B'], ['A','C'], ['B','C'], ['A','B'], ['C','A'], ['C','B'], ['A','B']]</code>.
    testString: assert.deepEqual(towerOfHanoi(3, 'A', 'B', 'C'), res3Moves);
  - text: <code>towerOfHanoi(5, "X", "Y", "Z")</code> 10th move should be Y -> X.
    testString: assert.deepEqual(res5[9], ['Y', 'X']);
  - text: <code>towerOfHanoi(7, 'A', 'B', 'C')</code> first ten moves should be <code>[['A','B'], ['A','C'], ['B','C'], ['A','B'], ['C','A'], ['C','B'], ['A','B'], ['A','C'], ['B','C'], ['B','A']]</code>
    testString: assert.deepEqual(towerOfHanoi(7, 'A', 'B', 'C').slice(0, 10), res7First10Moves);

Challenge Seed

function towerOfHanoi(n, a, b, c) {
  // Good luck!
  return [[]];
}

After Test

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']];

Solution

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);
  }
}

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