36. 有效的数独(Swift版)

一、题目

判断一个 9x9 的数独是否有效。只需要根据以下规则，验证已经填入的数字是否有效即可。

1. 数字 1-9 在每一行只能出现一次。
2. 数字 1-9 在每一列只能出现一次。
3. 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。

image

<small style="box-sizing: border-box; font-size: 10.399999618530273px;">上图是一个部分填充的有效的数独。</small>

数独部分空格内已填入了数字，空白格用 '.' 表示。

示例 1:

输入:
[
  ["5","3",".",".","7",".",".",".","."],
  ["6",".",".","1","9","5",".",".","."],
  [".","9","8",".",".",".",".","6","."],
  ["8",".",".",".","6",".",".",".","3"],
  ["4",".",".","8",".","3",".",".","1"],
  ["7",".",".",".","2",".",".",".","6"],
  [".","6",".",".",".",".","2","8","."],
  [".",".",".","4","1","9",".",".","5"],
  [".",".",".",".","8",".",".","7","9"]
]
输出: true

示例 2:

输入:
[
  ["8","3",".",".","7",".",".",".","."],
  ["6",".",".","1","9","5",".",".","."],
  [".","9","8",".",".",".",".","6","."],
  ["8",".",".",".","6",".",".",".","3"],
  ["4",".",".","8",".","3",".",".","1"],
  ["7",".",".",".","2",".",".",".","6"],
  [".","6",".",".",".",".","2","8","."],
  [".",".",".","4","1","9",".",".","5"],
  [".",".",".",".","8",".",".","7","9"]
]
输出: false
解释: 除了第一行的第一个数字从 5 改为 8 以外，空格内其他数字均与 示例1 相同。
     但由于位于左上角的 3x3 宫内有两个 8 存在, 因此这个数独是无效的。

说明:

• 一个有效的数独（部分已被填充）不一定是可解的。
• 只需要根据以上规则，验证已经填入的数字是否有效即可。
• 给定数独序列只包含数字 1-9 和字符 '.' 。
• 给定数独永远是 9x9 形式的。

二、解题

直接遍历二维数组，在第二个for循环里判断每个元素，在其对应的行、列已经子数独里验证是否有重复数字即可。
先创建三个字典rowDict:[Int:[Character:Int]]（存储所有行的数字），columnDict: [Int:[Character:Int]]（存储所有列的数字），boxDict: [Int:[Character:Int]]（存储所有3x3子数独中的数字）。
这里有个难点，就是子数独的位置计算let bIndex = i / 3 * 3 + j / 3。
详细请看代码：
时间复杂度：O(m*n)。(假设board[m][n])

三、代码实现

    class Solution {
        func isValidSudoku(_ board: [[Character]]) -> Bool {
            var rowDict: [Int:[Character:Int]] = [:]
            var columnDict: [Int:[Character:Int]] = [:]
            var boxDict: [Int:[Character:Int]] = [:]
            for i in (0..<9) {
                for j in (0..<9) {
                    let c = board[i][j]
                    if c == "." {
                        continue
                    }
                    if rowDict[i] == nil {
                        rowDict[i] = [:]
                    }
                    if rowDict[i]![c] != nil {
                        return false
                    }else{
                        rowDict[i]![c] = 1
                    }
                    
                    if columnDict[j] == nil {
                        columnDict[j] = [:]
                    }
                    if columnDict[j]![c] != nil {
                        return false
                    }else{
                        columnDict[j]![c] = 1
                    }

                    let bIndex = i / 3 * 3 + j / 3
                    if boxDict[bIndex] == nil {
                        boxDict[bIndex] = [:]
                    }
                    if boxDict[bIndex]![c] != nil {
                        return false
                    }else {
                        boxDict[bIndex]![c] = 1
                    }
                }
            }
            return true
        }
    }

Demo地址：github