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86 lines
2.2 KiB
Markdown
86 lines
2.2 KiB
Markdown
---
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id: 6a22d77ddf034bc4e35b1d5d
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title: "Challenge 356: Magic Square Solver"
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challengeType: 28
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dashedName: challenge-356
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---
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# --description--
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Given a 3x3 grid with one missing number (represented as `0`), return the missing number that completes the magic square, or `"impossible"` if no valid number exists.
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A magic square is a grid where every row, column, and diagonal adds up to the same number.
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# --hints--
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`solveMagicSquare([[2, 7, 6], [9, 0, 1], [4, 3, 8]])` should return `5`.
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```js
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assert.equal(solveMagicSquare([[2, 7, 6], [9, 0, 1], [4, 3, 8]]), 5);
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```
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`solveMagicSquare([[0, 14, 12], [18, 10, 2], [8, 6, 16]])` should return `4`.
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```js
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assert.equal(solveMagicSquare([[0, 14, 12], [18, 10, 2], [8, 6, 16]]), 4);
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```
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`solveMagicSquare([[12, 17, 16], [19, 0, 10], [14, 13, 18]])` should return `"impossible"`.
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```js
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assert.equal(solveMagicSquare([[12, 17, 16], [19, 0, 10], [14, 13, 18]]), "impossible");
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```
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`solveMagicSquare([[15, 35, 31], [43, 27, 11], [23, 19, 0]])` should return `39`.
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```js
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assert.equal(solveMagicSquare([[15, 35, 31], [43, 27, 11], [23, 19, 0]]), 39);
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```
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`solveMagicSquare([[26, 41, 14], [47, 35, 0], [32, 29, 44]])` should return `"impossible"`.
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```js
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assert.equal(solveMagicSquare([[26, 41, 14], [47, 35, 0], [32, 29, 44]]), "impossible");
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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 solveMagicSquare(grid) {
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return grid;
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}
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```
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# --solutions--
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```js
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function solveMagicSquare(grid) {
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const flat = grid.flat();
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const zeroIndex = flat.indexOf(0);
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const row = Math.floor(zeroIndex / 3);
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const col = zeroIndex % 3;
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const target = grid.find(r => !r.includes(0))
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.reduce((sum, n) => sum + n, 0);
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const missing = target - grid[row].reduce((sum, n) => sum + n, 0);
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const filled = grid.map((r, ri) =>
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r.map((n, ci) => (ri === row && ci === col) ? missing : n)
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);
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const check = (arr) => arr.reduce((sum, n) => sum + n, 0) === target;
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for (let i = 0; i < 3; i++) {
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if (!check(filled[i])) return "impossible";
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if (!check(filled.map(r => r[i]))) return "impossible";
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}
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if (!check([filled[0][0], filled[1][1], filled[2][2]])) return "impossible";
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if (!check([filled[0][2], filled[1][1], filled[2][0]])) return "impossible";
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return missing;
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}
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```
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