98 lines
3.1 KiB
Markdown
98 lines
3.1 KiB
Markdown
---
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title: Towers of Hanoi
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id: 5951ed8945deab770972ae56
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challengeType: 5
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---
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## Description
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<section id='description'>
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Task:
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<p>Solve the <a href="https://en.wikipedia.org/wiki/Towers_of_Hanoi" title="wp: Towers_of_Hanoi">Towers of Hanoi</a> problem.</p>
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<p>
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Your solution should accept the number of discs as the first parameters, and
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three string used to identify each of the three stacks of discs, for example
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<code>towerOfHanoi(4, 'A', 'B', 'C')</code>. The function should return an
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array of arrays containing the list of moves, source -> destination. For
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example, the array <code>[['A', 'C'], ['B', 'A']]</code> indicates that the
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1st move was to move a disc from stack A to C, and the 2nd move was to move a
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disc from stack B to A.
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</p>
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>towerOfHanoi</code> is a function.
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testString: assert(typeof towerOfHanoi === 'function', '<code>towerOfHanoi</code> is a function.');
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- text: <code>towerOfHanoi(3, ...)</code> should return 7 moves.
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testString: assert(res3.length === 7, '<code>towerOfHanoi(3, ...)</code> should return 7 moves.');
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- text: <code>towerOfHanoi(3, 'A', 'B', 'C')</code> should return [['A','B'],['A','C'],['B','C'],['A','B'],['C','A'],['C','B'],['A','B']].")
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testString: assert.deepEqual(towerOfHanoi(3, 'A', 'B', 'C'), res3Moves, "<code>towerOfHanoi(3, 'A', 'B', 'C')</code> should return [['A','B'],['A','C'],['B','C'],['A','B'],['C','A'],['C','B'],['A','B']].");
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- text: <code>towerOfHanoi(5, "X", "Y", "Z")</code> 10th move should be Y -> X.
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testString: assert.deepEqual(res5[9], ['Y', 'X'], '<code>towerOfHanoi(5, "X", "Y", "Z")</code> 10th move should be Y -> X.');
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- text: <code>towerOfHanoi(7, 'A', 'B', 'C')</code> first ten moves are [['A','B'],['A','C'],['B','C'],['A','B'],['C','A'],['C','B'],['A','B'],['A','C'],['B','C'],['B','A']].")
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testString: assert.deepEqual(towerOfHanoi(7, 'A', 'B', 'C').slice(0, 10), res7First10Moves, "<code>towerOfHanoi(7, 'A', 'B', 'C')</code> first ten moves are [['A','B'],['A','C'],['B','C'],['A','B'],['C','A'],['C','B'],['A','B'],['A','C'],['B','C'],['B','A']].");
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function towerOfHanoi (n, a, b, c) {
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// Good luck!
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return [[]];
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}
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```
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</div>
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### After Test
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<div id='js-teardown'>
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```js
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const res3 = towerOfHanoi(3, 'A', 'B', 'C');
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const res3Moves = [['A', 'B'], ['A', 'C'], ['B', 'C'], ['A', 'B'], ['C', 'A'], ['C', 'B'], ['A', 'B']];
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const res5 = towerOfHanoi(5, 'X', 'Y', 'Z');
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const res7First10Moves = [['A', 'B'], ['A', 'C'], ['B', 'C'], ['A', 'B'], ['C', 'A'], ['C', 'B'], ['A', 'B'], ['A', 'C'], ['B', 'C'], ['B', 'A']];
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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function towerOfHanoi(n, a, b, c) {
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const res = [];
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towerOfHanoiHelper(n, a, c, b, res);
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return res;
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}
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function towerOfHanoiHelper(n, a, b, c, res) {
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if (n > 0) {
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towerOfHanoiHelper(n - 1, a, c, b, res);
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res.push([a, c]);
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towerOfHanoiHelper(n - 1, b, a, c, res);
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}
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}
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```
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</section>
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