88 lines
2.2 KiB
Markdown
88 lines
2.2 KiB
Markdown
---
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id: 5951ed8945deab770972ae56
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title: Towers of Hanoi
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challengeType: 5
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forumTopicId: 302341
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dashedName: towers-of-hanoi
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---
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# --description--
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Solve the [Towers of Hanoi](https://en.wikipedia.org/wiki/Towers_of_Hanoi "wp: Towers_of_Hanoi") problem.
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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.
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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.
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<p></p>
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# --hints--
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`towerOfHanoi` should be a function.
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```js
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assert(typeof towerOfHanoi === 'function');
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```
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`towerOfHanoi(3, ...)` should return 7 moves.
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```js
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assert(res3.length === 7);
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```
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`towerOfHanoi(3, 'A', 'B', 'C')` should return `[['A','B'], ['A','C'], ['B','C'], ['A','B'], ['C','A'], ['C','B'], ['A','B']]`.
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```js
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assert.deepEqual(towerOfHanoi(3, 'A', 'B', 'C'), res3Moves);
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```
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`towerOfHanoi(5, "X", "Y", "Z")` 10th move should be Y -> X.
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```js
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assert.deepEqual(res5[9], ['Y', 'X']);
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```
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`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']]`
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```js
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assert.deepEqual(towerOfHanoi(7, 'A', 'B', 'C').slice(0, 10), res7First10Moves);
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```
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# --seed--
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## --after-user-code--
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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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## --seed-contents--
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```js
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function towerOfHanoi(n, a, b, c) {
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return [[]];
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}
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```
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# --solutions--
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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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