diff --git a/back-tracking/KnightTour.js b/back-tracking/KnightTour.js new file mode 100644 index 000000000..5c7637a9e --- /dev/null +++ b/back-tracking/KnightTour.js @@ -0,0 +1,78 @@ +// Wikipedia: https://en.wikipedia.org/wiki/Knight%27s_tour + +class OpenKnightTour { + constructor (size) { + this.board = new Array(size).fill(0).map(() => new Array(size).fill(0)) + this.size = size + } + + getMoves ([i, j]) { + // helper function to get the valid moves of the knight from the current position + const moves = [ + [i + 2, j - 1], + [i + 2, j + 1], + [i - 2, j - 1], + [i - 2, j + 1], + [i + 1, j - 2], + [i + 1, j + 2], + [i - 1, j - 2], + [i - 1, j + 2] + ] + + return moves.filter(([y, x]) => y >= 0 && y < this.size && x >= 0 && x < this.size) + } + + isComplete () { + // helper function to check if the board is complete + return !this.board.map(row => row.includes(0)).includes(true) + } + + solve () { + // function to find the solution for the given board + for (let i = 0; i < this.size; i++) { + for (let j = 0; j < this.size; j++) { + if (this.solveHelper([i, j], 0)) return true + } + } + return false + } + + solveHelper ([i, j], curr) { + // helper function for the main computation + if (this.isComplete()) return true + + for (const [y, x] of this.getMoves([i, j])) { + if (this.board[y][x] === 0) { + this.board[y][x] = curr + 1 + if (this.solveHelper([y, x], curr + 1)) return true + // backtracking + this.board[y][x] = 0 + } + } + return false + } + + printBoard () { + // utility function to display the board + for (const row of this.board) { + let string = '' + for (const elem of row) { + string += elem + '\t' + } + console.log(string) + } + } +} + +function main () { + const board = new OpenKnightTour(5) + + board.printBoard() + console.log('\n') + + board.solve() + + board.printBoard() +} + +main()