Added backtracking (sudoku) (#205)

* Added backtracking (sudoku)

* Coverted into class based program

back-tracking/Sudoku.js

@@ -0,0 +1,97 @@
+class Sudoku {
+  // Sudoku Class to hold the board and related functions
+  constructor (board) {
+    this.board = board
+  }
+
+  findEmptyCell () {
+    // Find a empty cell in the board (returns [-1, -1] if all cells are filled)
+    for (let i = 0; i < 9; i++) {
+      for (let j = 0; j < 9; j++) {
+        if (this.board[i][j] === 0) return [i, j]
+      }
+    }
+    return [-1, -1]
+  }
+
+  check ([y, x], value) {
+    // checks if the value to be added in the board is an acceptable value for the cell
+
+    // checking through the row
+    for (let i = 0; i < 9; i++) {
+      if (this.board[i][x] === value) return false
+    }
+    // checking through the column
+    for (let i = 0; i < 9; i++) {
+      if (this.board[y][i] === value) return false
+    }
+
+    // checking through the 3x3 block of the cell
+    const secRow = Math.floor(y / 3)
+    const secCol = Math.floor(x / 3)
+    for (let i = (secRow * 3); i < ((secRow * 3) + 3); i++) {
+      for (let j = (secCol * 3); j < ((secCol * 3) + 3); j++) {
+        if (y !== i && x !== j && this.board[i][j] === value) return false
+      }
+    }
+
+    return true
+  }
+
+  solve () {
+    const [y, x] = this.findEmptyCell()
+
+    // checking if the board is complete
+    if (y === -1 && x === -1) return true
+
+    for (let val = 1; val < 10; val++) {
+      if (this.check([y, x], val)) {
+        this.board[y][x] = val
+        if (this.solve()) return true
+        // backtracking if the board cannot be solved using current configuration
+        this.board[y][x] = 0
+      }
+    }
+    // returning false the board cannot be solved using current configuration
+    return false
+  }
+
+  getSection (row, [start, end]) {
+    return this.board[row].slice(start, end)
+  }
+
+  printBoard () {
+    // helper function to display board
+    for (let i = 0; i < 9; i++) {
+      if (i % 3 === 0 && i !== 0) console.log('- - - - - - - - - - - -')
+      console.log(
+        ...this.getSection(i, [0, 3]), ' | ',
+        ...this.getSection(i, [3, 6]), ' | ',
+        ...this.getSection(i, [6, 9]))
+    }
+  }
+}
+
+function main () {
+  // main function with an example
+  const sudokuBoard = new Sudoku([
+    [3, 0, 6, 5, 0, 8, 4, 0, 0],
+    [5, 2, 0, 0, 0, 0, 0, 0, 0],
+    [0, 8, 7, 0, 0, 0, 0, 3, 1],
+    [0, 0, 3, 0, 1, 0, 0, 8, 0],
+    [9, 0, 0, 8, 6, 3, 0, 0, 5],
+    [0, 5, 0, 0, 9, 0, 6, 0, 0],
+    [1, 3, 0, 0, 0, 0, 2, 5, 0],
+    [0, 0, 0, 0, 0, 0, 0, 7, 4],
+    [0, 0, 5, 2, 0, 6, 3, 0, 0]
+  ])
+
+  sudokuBoard.printBoard()
+
+  console.log('\n')
+  sudokuBoard.solve()
+
+  sudokuBoard.printBoard()
+}
+
+main()