LeetCode - 36 有效的数独

前言

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难度水平：中等

1. 描述

请你判断一个 9 x 9 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。

数字 1-9 在每一行只能出现一次。
数字 1-9 在每一列只能出现一次。
数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图）

注意：

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。
空白格用 '.' 表示。

2. 示例

示例 1

输入：board = 
[["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：board = 
[["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。

约束条件：

board.length == 9
board[i].length == 9
board[i][j]`` 是一位数字（1-9）或者‘.’`

3. 答案

class ValidSudoku {
    func isValidSudoku(_ board: [[Character]]) -> Bool {
        return areRowsValid(board) && areColsValid(board) && areSubsquaresValid(board)
    }
    
    private func areRowsValid(_ board: [[Character]]) -> Bool {
        var existingDigits = Set<Character>()
        
        for i in 0..<board.count {
            existingDigits.removeAll()
            
            for j in 0..<board[0].count {
                if !isDigitValid(board[i][j], &existingDigits) {
                    return false
                }
            }
        }
        
        return true
    }
    
    private func areColsValid(_ board: [[Character]]) -> Bool {
        var existingDigits = Set<Character>()
        
        for i in 0..<board[0].count {
            existingDigits.removeAll()
            
            for j in 0..<board.count {
                if !isDigitValid(board[j][i], &existingDigits) {
                    return false
                }
            }
        }
        
        return true
    }
    
    private func areSubsquaresValid(_ board: [[Character]]) -> Bool {
        var existingDigits = Set<Character>()
        
        for i in stride(from: 0, to: board.count, by: 3) {
            for j in stride(from: 0, to: board[0].count, by: 3) {
                existingDigits.removeAll()
                
                for m in i..<i + 3 {
                    for n in j..<j + 3 {
                        if !isDigitValid(board[m][n], &existingDigits) {
                            return false
                        }
                    }
                }
            }
        }
        
        return true
    }
    
    private func isDigitValid(_ digit: Character, _ set: inout Set<Character>) -> Bool {
        if digit == "." {
            return true
        }
        
        if set.contains(digit) {
            return false
        } else {
            set.insert(digit)
            return true
        }
    }
}

主要思想：分别检查行、列和单个正方形。
时间复杂度： O(n^2)
空间复杂度： O(1)

该算法题解的仓库：LeetCode-Swift

点击前往 LeetCode 练习

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