判斷一個 9x9 的數獨是否有效。只需要根據以下規則，驗證已經填入的數字是否有效即可。
數字 1-9 在每一行只能出現一次。
數字 1-9 在每一列只能出現一次。
數字 1-9 在每一個以粗實線分隔的 3x3 宮內只能出現一次。
上圖是一個部分填充的有效的數獨。
數獨部分空格內已填入了數字，空白格用 '.' 表示。
示例 1:
輸入:
[
["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"]
]
輸出: true
示例 2:
輸入:
[
["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"]
]
輸出: false
解釋: 除了第一行的第一個數字從 5 改為 8 以外，空格內其他數字均與 示例1 相同。
但由於位於左上角的 3x3 宮內有兩個 8 存在, 因此這個數獨是無效的。
說明:
一個有效的數獨（部分已被填充）不一定是可解的。
只需要根據以上規則，驗證已經填入的數字是否有效即可。
給定數獨序列只包含數字 1-9 和字符 '.' 。
給定數獨永遠是 9x9 形式的。
1、驗證數字 1-9 在每一行只能出現一次。
2、驗證數字 1-9 在每一列只能出現一次。
3、驗證數字 1-9 在每一個以粗實線分隔的 3x3 宮內只能出現一次。
三、代碼package is_valid_sudoku; import java.util.HashMap;import java.util.Map;public class Solution { public boolean isValidSudoku(char[][] board) { int len=board.length; for(int i=0;i<len;i++){ if(!checkRow(board,i)){ System.out.println("第"+i+"行驗證失敗"); return false; }else{ System.out.println("第"+i+"行驗證成功"); } } for(int i=0;i<len;i++){ if(!checkColumn(board,i)){ System.out.println("第"+i+"列驗證失敗"); return false; } else{ System.out.println("第"+i+"列驗證成功"); } } for(int i=0;i<3;i++) { for(int j=0;j<3;j++){ if (!checkMatrix(board, i*3, j*3)) { return false; } else{ System.out.println("第"+i*3+","+j*3+"矩陣驗證成功"); } } } return true; } public boolean checkRow(char[][] board,int row){ int len=board.length; Map<Character, Integer> map=new HashMap<>(); for(int i=0;i<10;i++){ map.put(Character.forDigit(i,10),0); } for(int i=0;i<len;i++){ if(board[row][i]!='.'){ if(map.get(board[row][i])>=1){ return false; }else{ map.put(board[row][i],map.get(board[row][i])+1); } } } return true; } public boolean checkColumn(char[][] board,int column){ int len=board.length; Map<Character, Integer> map=new HashMap<>(); for(int i=0;i<10;i++){ map.put(Character.forDigit(i,10),0); } for(int i=0;i<len;i++){ if(board[i][column]!='.'){ if(map.get(board[i][column])>=1){ return false; }else{ map.put(board[i][column],map.get(board[i][column])+1); } } } return true; } public boolean checkMatrix(char[][] board,int rowStart,int columnStart){ int len=board.length; Map<Character, Integer> map=new HashMap<>(); for(int n=0;n<10;n++){ map.put(Character.forDigit(n,10),0); } int rowEnd=rowStart+3; int columnEnd=columnStart+3; for(int i=rowStart;i<rowEnd;i++){ for(int j=columnStart;j<columnEnd;j++) { if(board[i][j]!='.'){ if (map.get(board[i][j]) >= 1) { return false; } else { map.put(board[i][j], map.get(board[i][j]) + 1); System.out.println(map); } } } } System.out.println(map); return true; } public static void main(String[] args) { Solution solution=new Solution(); char[][] 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'} }; System.out.println(solution.isValidSudoku(board)); } }四、複雜度分析時間複雜度：O(1)，只對 81 個單元格進行了3次迭代。
空間複雜度：O(1)，只需要常數空間存放若干變量。