Added Open Knight Tour Algorithm (#214)

* Added Open Knight Tour by @ruppysuppy

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()