322 lines
9.2 KiB
Markdown
322 lines
9.2 KiB
Markdown
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---
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id: 5a23c84252665b21eecc803c
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title: Sudoku
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challengeType: 5
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forumTopicId: 302329
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dashedName: sudoku
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---
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# --description--
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Write a function to solve a partially filled-in normal 9x9 [Sudoku](https://en.wikipedia.org/wiki/Sudoku) grid and return the result. The blank fields are represented by `-1`. [Algorithmics of Sudoku](https://en.wikipedia.org/wiki/Algorithmics_of_sudoku) may help implement this.
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# --hints--
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`solveSudoku` should be a function.
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```js
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assert(typeof solveSudoku == 'function');
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```
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`solveSudoku([[8, 1, 9, -1, -1, 5, -1, -1, -1],[-1, -1, 2, -1, -1, -1, 7, 5, -1],[-1, 3, 7, 1, -1, 4, -1, 6, -1],[4, -1, -1, 5, 9, -1, 1, -1, -1],[7, -1, -1, 3, -1, 8, -1, -1, 2],[-1, -1, 3, -1, 6, 2, -1, -1, 7],[-1, 5, -1, 7, -1, 9, 2, 1, -1],[-1, 6, 4, -1, -1, -1, 9, -1, -1],[-1, -1, -1, 2, -1, -1, 4, 3, 8]])` should return an array.
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```js
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assert(
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Array.isArray(
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solveSudoku([
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[8, 1, 9, -1, -1, 5, -1, -1, -1],
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[-1, -1, 2, -1, -1, -1, 7, 5, -1],
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[-1, 3, 7, 1, -1, 4, -1, 6, -1],
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[4, -1, -1, 5, 9, -1, 1, -1, -1],
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[7, -1, -1, 3, -1, 8, -1, -1, 2],
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[-1, -1, 3, -1, 6, 2, -1, -1, 7],
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[-1, 5, -1, 7, -1, 9, 2, 1, -1],
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[-1, 6, 4, -1, -1, -1, 9, -1, -1],
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[-1, -1, -1, 2, -1, -1, 4, 3, 8]
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])
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)
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);
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```
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`solveSudoku([[8, 1, 9, -1, -1, 5, -1, -1, -1],[-1, -1, 2, -1, -1, -1, 7, 5, -1],[-1, 3, 7, 1, -1, 4, -1, 6, -1],[4, -1, -1, 5, 9, -1, 1, -1, -1],[7, -1, -1, 3, -1, 8, -1, -1, 2],[-1, -1, 3, -1, 6, 2, -1, -1, 7],[-1, 5, -1, 7, -1, 9, 2, 1, -1],[-1, 6, 4, -1, -1, -1, 9, -1, -1],[-1, -1, -1, 2, -1, -1, 4, 3, 8]])` should return `[[8, 1, 9, 6, 7, 5, 3, 2, 4],[6, 4, 2, 9, 8, 3, 7, 5, 1],[5, 3, 7, 1, 2, 4, 8, 6, 9],[4, 2, 6, 5, 9, 7, 1, 8, 3],[7, 9, 5, 3, 1, 8, 6, 4, 2],[1, 8, 3, 4, 6, 2, 5, 9, 7],[3, 5, 8, 7, 4, 9, 2, 1, 6],[2, 6, 4, 8, 3, 1, 9, 7, 5],[9, 7, 1, 2, 5, 6, 4, 3, 8]]`.
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```js
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assert.deepEqual(
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solveSudoku([
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[8, 1, 9, -1, -1, 5, -1, -1, -1],
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[-1, -1, 2, -1, -1, -1, 7, 5, -1],
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[-1, 3, 7, 1, -1, 4, -1, 6, -1],
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[4, -1, -1, 5, 9, -1, 1, -1, -1],
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[7, -1, -1, 3, -1, 8, -1, -1, 2],
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[-1, -1, 3, -1, 6, 2, -1, -1, 7],
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[-1, 5, -1, 7, -1, 9, 2, 1, -1],
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[-1, 6, 4, -1, -1, -1, 9, -1, -1],
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[-1, -1, -1, 2, -1, -1, 4, 3, 8]
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]),
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[
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[8, 1, 9, 6, 7, 5, 3, 2, 4],
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[6, 4, 2, 9, 8, 3, 7, 5, 1],
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[5, 3, 7, 1, 2, 4, 8, 6, 9],
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[4, 2, 6, 5, 9, 7, 1, 8, 3],
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[7, 9, 5, 3, 1, 8, 6, 4, 2],
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[1, 8, 3, 4, 6, 2, 5, 9, 7],
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[3, 5, 8, 7, 4, 9, 2, 1, 6],
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[2, 6, 4, 8, 3, 1, 9, 7, 5],
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[9, 7, 1, 2, 5, 6, 4, 3, 8]
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]
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);
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```
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`solveSudoku([[5, 3, -1, -1, 2, 4, 7, -1, -1],[-1, -1, 2, -1, -1, -1, 8, -1, -1],[1, -1, -1, 7, -1, 3, 9, -1, 2],[-1, -1, 8, -1, 7, 2, -1, 4, 9],[-1, 2, -1, 9, 8, -1, -1, 7, -1],[7, 9, -1, -1, -1, -1, -1, 8, -1],[-1, -1, -1, -1, 3, -1, 5, -1, 6],[9, 6, -1, -1, 1, -1, 3, -1, -1],[-1, 5, -1, 6, 9, -1, -1, 1, -1]])` should return `[[5, 3, 9, 8, 2, 4, 7, 6, 1],[6, 7, 2, 1, 5, 9, 8, 3, 4],[1, 8, 4, 7, 6, 3, 9, 5, 2],[3, 1, 8, 5, 7, 2, 6, 4, 9],[4, 2, 5, 9, 8, 6, 1, 7, 3],[7, 9, 6, 3, 4, 1, 2, 8, 5],[8, 4, 1, 2, 3, 7, 5, 9, 6],[9, 6, 7, 4, 1, 5, 3, 2, 8],[2, 5, 3, 6, 9, 8, 4, 1, 7]]`.
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```js
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assert.deepEqual(
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solveSudoku([
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[5, 3, -1, -1, 2, 4, 7, -1, -1],
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[-1, -1, 2, -1, -1, -1, 8, -1, -1],
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[1, -1, -1, 7, -1, 3, 9, -1, 2],
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[-1, -1, 8, -1, 7, 2, -1, 4, 9],
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[-1, 2, -1, 9, 8, -1, -1, 7, -1],
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[7, 9, -1, -1, -1, -1, -1, 8, -1],
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[-1, -1, -1, -1, 3, -1, 5, -1, 6],
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[9, 6, -1, -1, 1, -1, 3, -1, -1],
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[-1, 5, -1, 6, 9, -1, -1, 1, -1]
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]),
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[
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[5, 3, 9, 8, 2, 4, 7, 6, 1],
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[6, 7, 2, 1, 5, 9, 8, 3, 4],
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[1, 8, 4, 7, 6, 3, 9, 5, 2],
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[3, 1, 8, 5, 7, 2, 6, 4, 9],
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[4, 2, 5, 9, 8, 6, 1, 7, 3],
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[7, 9, 6, 3, 4, 1, 2, 8, 5],
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[8, 4, 1, 2, 3, 7, 5, 9, 6],
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[9, 6, 7, 4, 1, 5, 3, 2, 8],
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[2, 5, 3, 6, 9, 8, 4, 1, 7]
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]
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);
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```
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`solveSudoku([[-1, -1, 3, -1, 2, -1, 6, -1, -1],[9, -1, -1, 3, -1, 5, -1, -1, 1],[-1, -1, 1, 8, -1, 6, 4, -1, -1],[-1, -1, 8, 1, -1, 2, 9, -1, -1],[7, -1, -1, -1, -1, -1, -1, -1, 8],[-1, -1, 6, 7, -1, 8, 2, -1, -1],[-1, -1, 2, 6, -1, 9, 5, -1, -1],[8, -1, -1, 2, -1, 3, -1, -1, 9],[-1, -1, 5, -1, 1, -1, 3, -1, -1]])` should return `[[4, 8, 3, 9, 2, 1, 6, 5, 7],[9, 6, 7, 3, 4, 5, 8, 2, 1],[2, 5, 1, 8, 7, 6, 4, 9, 3],[5, 4, 8, 1, 3, 2, 9, 7, 6],[7, 2, 9, 5, 6, 4, 1, 3, 8],[1, 3, 6, 7, 9, 8, 2, 4, 5],[3, 7, 2, 6, 8, 9, 5, 1, 4],[8, 1, 4, 2, 5, 3, 7, 6, 9],[6, 9, 5, 4, 1, 7, 3, 8, 2]]`.
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```js
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assert.deepEqual(
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solveSudoku([
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[-1, -1, 3, -1, 2, -1, 6, -1, -1],
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[9, -1, -1, 3, -1, 5, -1, -1, 1],
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[-1, -1, 1, 8, -1, 6, 4, -1, -1],
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[-1, -1, 8, 1, -1, 2, 9, -1, -1],
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[7, -1, -1, -1, -1, -1, -1, -1, 8],
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[-1, -1, 6, 7, -1, 8, 2, -1, -1],
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[-1, -1, 2, 6, -1, 9, 5, -1, -1],
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[8, -1, -1, 2, -1, 3, -1, -1, 9],
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[-1, -1, 5, -1, 1, -1, 3, -1, -1]
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]),
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[
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[4, 8, 3, 9, 2, 1, 6, 5, 7],
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[9, 6, 7, 3, 4, 5, 8, 2, 1],
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[2, 5, 1, 8, 7, 6, 4, 9, 3],
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[5, 4, 8, 1, 3, 2, 9, 7, 6],
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[7, 2, 9, 5, 6, 4, 1, 3, 8],
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[1, 3, 6, 7, 9, 8, 2, 4, 5],
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[3, 7, 2, 6, 8, 9, 5, 1, 4],
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[8, 1, 4, 2, 5, 3, 7, 6, 9],
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[6, 9, 5, 4, 1, 7, 3, 8, 2]
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]
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);
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```
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# --seed--
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## --seed-contents--
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```js
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function solveSudoku(puzzle) {
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}
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```
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# --solutions--
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```js
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function solveSudoku(puzzle) {
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var solution;
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class DoX {
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constructor(V, H) {
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this.V = V;
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this.L = this;
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this.R = this;
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this.U = this;
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this.D = this;
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this.S = 1;
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this.H = H || this;
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H && (H.S += 1);
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}
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}
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const addRight = (e, n) => {
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n.R = e.R;
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n.L = e;
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e.R.L = n;
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return (e.R = n);
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};
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const addBelow = (e, n) => {
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n.D = e.D;
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n.U = e;
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e.D.U = n;
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return (e.D = n);
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};
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const search = function(h, s) {
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if (h.R == h) {
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printSol(s);
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} else {
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let c = chooseColumn(h);
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cover(c);
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for (let r = c.D; r != c; r = r.D) {
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s.push(r);
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for (let j = r.R; r != j; j = j.R) {
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cover(j.H);
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}
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search(h, s);
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r = s.pop();
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for (let j = r.R; j != r; j = j.R) {
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uncover(j.H);
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}
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}
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uncover(c);
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}
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};
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const chooseColumn = h => {
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let s = Number.POSITIVE_INFINITY;
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let c = h;
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for (let j = h.R; j != h; j = j.R) {
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if (j.S < s) {
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c = j;
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s = j.S;
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}
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}
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return c;
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};
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const cover = c => {
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c.L.R = c.R;
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c.R.L = c.L;
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for (let i = c.D; i != c; i = i.D) {
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for (let j = i.R; j != i; j = j.R) {
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j.U.D = j.D;
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j.D.U = j.U;
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j.H.S = j.H.S - 1;
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}
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}
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};
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const uncover = c => {
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for (let i = c.U; i != c; i = i.U) {
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for (let j = i.L; i != j; j = j.L) {
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j.H.S = j.H.S + 1;
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j.U.D = j;
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j.D.U = j;
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}
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}
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c.L.R = c;
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c.R.L = c;
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};
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const printSol = a => {
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solution = a.reduce((p, c) => {
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let [i, v] = c.V.split(':');
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p[i * 1] = v;
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return p;
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}, new Array(a.length).fill('.'));
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};
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const gridMeta = s => {
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const g = s.split('');
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const cellCount = g.length;
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const tokenCount = Math.sqrt(cellCount);
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const N = Math.sqrt(tokenCount);
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const g2D = g.map(e =>
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isNaN(e * 1)
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? new Array(tokenCount).fill(1).map((_, i) => i + 1)
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: [e * 1]
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);
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return [cellCount, N, tokenCount, g2D];
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};
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const indexesN = n => i => {
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let c = Math.floor(i / (n * n));
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i %= n * n;
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return [c, i, Math.floor(c / n) * n + Math.floor(i / n)];
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};
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const reduceGrid = puzString => {
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const [
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numCells, // The total number of cells in a grid (81 for a 9x9 grid)
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N, // the 'n' value of the grid. (3 for a 9x9 grid)
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U, // The total number of unique tokens to be placed.
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g2D // A 2D array representation of the grid, with each element
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// being an array of candidates for a cell. Known cells are
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// single element arrays.
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] = gridMeta(puzString);
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const getIndex = indexesN(N);
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const headRow = new Array(4 * numCells)
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.fill('')
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.map((_, i) => new DoX(`H${i}`));
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let H = new DoX('ROOT');
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headRow.reduce((p, c) => addRight(p, c), H);
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for (let i = 0; i < numCells; i++) {
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const [ri, ci, bi] = getIndex(i);
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g2D[i].forEach(num => {
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let id = `${i}:${num}`;
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let candIdx = num - 1;
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// The 4 columns that we will populate.
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const A = headRow[i];
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const B = headRow[numCells + candIdx + ri * U];
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const C = headRow[numCells * 2 + candIdx + ci * U];
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const D = headRow[numCells * 3 + candIdx + bi * U];
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// The Row-Column Constraint
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let rcc = addBelow(A.U, new DoX(id, A));
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// The Row-Number Constraint
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let rnc = addBelow(B.U, addRight(rcc, new DoX(id, B)));
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// The Column-Number Constraint
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let cnc = addBelow(C.U, addRight(rnc, new DoX(id, C)));
|
||
|
|
|
||
|
|
// The Block-Number Constraint
|
||
|
|
addBelow(D.U, addRight(cnc, new DoX(id, D)));
|
||
|
|
});
|
||
|
|
}
|
||
|
|
search(H, []);
|
||
|
|
};
|
||
|
|
|
||
|
|
var stringPuzzle = '';
|
||
|
|
|
||
|
|
for (var i = 0; i < puzzle.length; i++) {
|
||
|
|
puzzle[i].forEach(function(e) {
|
||
|
|
if (e == -1) stringPuzzle += '.';
|
||
|
|
else stringPuzzle += e;
|
||
|
|
});
|
||
|
|
}
|
||
|
|
|
||
|
|
reduceGrid(stringPuzzle);
|
||
|
|
|
||
|
|
var result = [];
|
||
|
|
|
||
|
|
for (var i = 0; i < 9; i++) {
|
||
|
|
result.push(solution.slice(i * 9, (i + 1) * 9).map(e => parseInt(e)));
|
||
|
|
}
|
||
|
|
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
```
|