Update 37. Sudoku Solver.md

Author: TBXark

37. Sudoku Solver.md

@@ -174,8 +174,8 @@ class Solution {
 
 ```
 
-```
 对于测试数组 
+```
 [["5","3",".",".","7",".",".",".","."],
 ["6",".",".","1","9","5",".",".","."],
 [".","9","8",".",".",".",".","6","."],
@@ -185,8 +185,80 @@ class Solution {
 [".","6",".",".",".",".","2","8","."],
 [".",".",".","4","1","9",".",".","5"],
 [".",".",".",".","8",".",".","7","9"]]
+```
+顺序遍历调用`fillGrid` 4209次，按权重遍历调用`fillGrid` 103次
+
 
-顺序遍历调用fillGrid 4209次，按权重遍历调用fillGrid 103次
 
+
+对权重遍历就行优化，提前得到每个空位有可能的值进行遍历，由于对集合进行遍历所以时间不稳定。最优时间可能在排名在100%
+```
+Runtime: 36 ms, faster than 100.00% of Swift online submissions for Sudoku Solver.
+Memory Usage: 22.5 MB, less than 50.00% of Swift online submissions for Sudoku Solver.
 ```
 
+```
+class Solution {
+
+    static let num: Set<Character> = ["1", "2", "3", "4", "5", "6", "7", "8", "9"]
+
+    func solveSudoku(_ board: inout [[Character]]) {
+        var clo = [Set<Character>].init(repeating: Set<Character>(), count: 9)
+        var row = [Set<Character>].init(repeating: Set<Character>(), count: 9)
+        var block = [Set<Character>].init(repeating: Set<Character>(), count: 9)
+        var points = [(p: (x: Int, y: Int), c: Set<Character>)]()
+        for y in 0..<9 {
+            for x in 0..<9 {
+                let c = board[y][x]
+                guard c != "." else {
+                    points.append((p: (x: x, y: y), c: Set<Character>()))
+                    continue
+                }
+                clo[y].insert(c)
+                row[x].insert(c)
+                block[x/3 + (y/3) * 3].insert(c)
+            }
+        }
+        for i in 0..<points.count {
+            let (x, y) = points[i].p
+            points[i].c = Solution.num.subtracting(clo[y].union(row[x]).union(block[x/3 + (y/3) * 3]))
+        }
+        points.sort(by: {  $0.c.count < $1.c.count  })
+        _ = fillGrid(index: 0,
+                     point: points,
+                     board: &board,
+                     clo: &clo,
+                     row: &row,
+                     block: &block)
+    }
+
+
+    func fillGrid(index: Int,
+                  point: [(p: (x: Int, y: Int), c: Set<Character>)],
+                  board: inout [[Character]],
+                  clo: inout [Set<Character>],
+                  row: inout [Set<Character>],
+                  block: inout [Set<Character>]) -> Bool {
+        if index == point.count  {
+            return true
+        }
+        let (x, y) = point[index].p
+        
+        for c in point[index].c.subtracting(clo[y].union(row[x]).union(block[x/3 + (y/3) * 3])) {
+            board[y][x] = c
+            clo[y].insert(c)
+            row[x].insert(c)
+            block[x/3 + (y/3) * 3].insert(c)
+            if fillGrid(index: index + 1, point: point, board: &board, clo: &clo, row: &row, block: &block) {
+                return true
+            } else {
+                clo[y].remove(c)
+                row[x].remove(c)
+                block[x/3 + (y/3) * 3].remove(c)
+                board[y][x] = "."
+            }
+        }
+        return false
+    }
+}
+```