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| 1 | +// Wikipedia: https://en.wikipedia.org/wiki/Knight%27s_tour |
| 2 | + |
| 3 | +class OpenKnightTour { |
| 4 | + constructor (size) { |
| 5 | + this.board = new Array(size).fill(0).map(() => new Array(size).fill(0)) |
| 6 | + this.size = size |
| 7 | + } |
| 8 | + |
| 9 | + getMoves ([i, j]) { |
| 10 | + // helper function to get the valid moves of the knight from the current position |
| 11 | + const moves = [ |
| 12 | + [i + 2, j - 1], |
| 13 | + [i + 2, j + 1], |
| 14 | + [i - 2, j - 1], |
| 15 | + [i - 2, j + 1], |
| 16 | + [i + 1, j - 2], |
| 17 | + [i + 1, j + 2], |
| 18 | + [i - 1, j - 2], |
| 19 | + [i - 1, j + 2] |
| 20 | + ] |
| 21 | + |
| 22 | + return moves.filter(([y, x]) => y >= 0 && y < this.size && x >= 0 && x < this.size) |
| 23 | + } |
| 24 | + |
| 25 | + isComplete () { |
| 26 | + // helper function to check if the board is complete |
| 27 | + return !this.board.map(row => row.includes(0)).includes(true) |
| 28 | + } |
| 29 | + |
| 30 | + solve () { |
| 31 | + // function to find the solution for the given board |
| 32 | + for (let i = 0; i < this.size; i++) { |
| 33 | + for (let j = 0; j < this.size; j++) { |
| 34 | + if (this.solveHelper([i, j], 0)) return true |
| 35 | + } |
| 36 | + } |
| 37 | + return false |
| 38 | + } |
| 39 | + |
| 40 | + solveHelper ([i, j], curr) { |
| 41 | + // helper function for the main computation |
| 42 | + if (this.isComplete()) return true |
| 43 | + |
| 44 | + for (const [y, x] of this.getMoves([i, j])) { |
| 45 | + if (this.board[y][x] === 0) { |
| 46 | + this.board[y][x] = curr + 1 |
| 47 | + if (this.solveHelper([y, x], curr + 1)) return true |
| 48 | + // backtracking |
| 49 | + this.board[y][x] = 0 |
| 50 | + } |
| 51 | + } |
| 52 | + return false |
| 53 | + } |
| 54 | + |
| 55 | + printBoard () { |
| 56 | + // utility function to display the board |
| 57 | + for (const row of this.board) { |
| 58 | + let string = '' |
| 59 | + for (const elem of row) { |
| 60 | + string += elem + '\t' |
| 61 | + } |
| 62 | + console.log(string) |
| 63 | + } |
| 64 | + } |
| 65 | +} |
| 66 | + |
| 67 | +function main () { |
| 68 | + const board = new OpenKnightTour(5) |
| 69 | + |
| 70 | + board.printBoard() |
| 71 | + console.log('\n') |
| 72 | + |
| 73 | + board.solve() |
| 74 | + |
| 75 | + board.printBoard() |
| 76 | +} |
| 77 | + |
| 78 | +main() |
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