Update the solution to the Sudoku Solver

Author: Yi Gu

DFS/SudokuSolver.swift

@@ -3,34 +3,34 @@
  * Primary idea: Iterate through the whole matrix, try to fill out empty space with all 
  *			     possible cases and check the vaildity
  *
- * Time Complexity: O(n^4), Space Complexity: O(1)
+ * Time Complexity: O((9!) ^ 9), Space Complexity: O(1)
  */
 
- class SudokuSolver {
+
+class SudokuSolver {
+    private let length = 9
+    
     func solveSudoku(_ board: inout [[Character]]) {
-        guard board.count != 0 || board[0].count != 0 else {
-            return
-        }
-        helper(&board)
+        dfs(&board)
     }
 
-    private func helper(_ board: inout [[Character]]) -> Bool {
-        let m = board.count, n = board[0].count
-    
-        for i in 0..<m {
-            for j in 0..<n {
+    private func dfs(_ board: inout [[Character]]) -> Bool {
+        let candidates = "123456789"
+        
+        for i in 0..<length {
+            for j in 0..<length {
                 if board[i][j] == "." {
-                    for num in 1...9 {
-                        if isValid(board, i, j, Character(String(num))) {
-                            board[i][j] = Character(String(num))
-                            
-                            if helper(&board) {
+                    // place 
+                    for candidate in candidates {
+                        if isValid(board, i, j, candidate) {
+                            board[i][j] = candidate
+                            if dfs(&board) {
                                 return true
-                            } else {
-                                board[i][j] = "."
                             }
+                            board[i][j] = "."
                         }
                     }
+                    
                     return false
                 }
             }
@@ -40,31 +40,25 @@
     }
 
     private func isValid(_ board: [[Character]], _ i: Int, _ j: Int, _ num: Character) -> Bool {
-        let m = board.count, n = board[0].count
-    
-        // check row
-        for x in 0..<n {
-            if board[i][x] == num {
+        
+        for n in 0..<length {
+            // check row
+            if board[n][j] == num {
                 return false
             }
-        }
-        
-        // check col
-        for y in 0..<m {
-            if board[y][j] == num {
+            
+            // check column
+            if board[i][n] == num {
                 return false
             }
-        }
-        
-        // check square
-        for x in i / 3 * 3..<i / 3 * 3 + 3 {
-            for y in j / 3 * 3..<j / 3 * 3 + 3 {
-                if board[x][y] == num {
-                    return false
-                }
+            
+            // check sub-box
+            if board[(i / 3) * 3 + n / 3][(j / 3) * 3 + n % 3 ] == num {
+                return false
             }
         }
 
         return true
     }
+}
 }