请你判断一个 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。
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）
数独部分空格内已填入了数字，空白格用 '.' 表示。
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。
提示：
board.length == 9
board[i].length == 9
board[i][j] 是一位数字或者 '.'
摘一个示例做个说明.
示例 1：数独如上图
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
条件分析:
- 数字在行、列、3x3 宫内,只能出现一次 -> 指定区域内不能出现重复数字
- 根据规则判断是否有效,不考虑数学可解 -> 只考虑目前是否符合
- 一个9x9的矩阵 -> 9阶方阵
解决思路1:
- 根据分析1,定义三个存储哈希表,判断三个方面是否有重复数字
- 根据分析2,只要三个方向不存在重复数字即可
- 不考虑大量数据的情况,只有9x9 81个数据
采用双层循环,行哈希判断行,列哈希判断列,3阶方阵哈希判断三阶方阵,循环完成都不存在,则为真,一个为假则假.这里行列都好找.主要是三阶方阵存储.因为是9x9,所以可以划为9个3x3.这样对行和列求余,就能得到三阶方阵的哈希存储位置.
代码实现-Swift版本:
思路1代码:
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
}
测试用例:
// 数独
let board: [[Character]] =
[["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"]]
// 不是数独
let board: [[Character]] =
[["5","3",".",".","7",".","3",".","."]
,["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"]]
考察要点:
- 数组
- 哈希表
- 矩阵
