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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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