LeetCode No36. 有效的數獨
題目
請你判斷一個 9 x 9 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。（請參考示例圖）
注意：
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。
空白格用 '.' 表示。
示例 1：
輸入：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"]]
輸出：true
示例 2：
輸入：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"]]
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。
提示：
board.length == 9
board[i].length == 9
board[i][j] 是一位數字（1-9）或者 '.'
思路
暴力模擬
數獨的定義是行和列都是沒有重複的數，那麼可以在初始的時候就直接檢查行和列是否滿足條件，然後再每個小矩陣的起點(小矩陣左上角)，檢視是否有重複的數即可。
雜湊
暴力之後看了題解才想到的原來可以用雜湊的思想，將每行，每列，每個小矩陣都雜湊到一個數組中，如果出現有重複的數，則是不合格的。
AC程式碼
暴力模擬
點選檢視程式碼
class Solution { char[][] board; private boolean initCheck() { for(int i=0; i<9; i++) { boolean[] rowOk = new boolean[10]; boolean[] colOk = new boolean[10]; for(int j=0; j<9; j++) { if(board[i][j]!='.') { int numR = (int) (board[i][j] - '0'); if( rowOk[numR] ) { return false; } rowOk[numR] = true; } if( board[j][i]!='.') { int numC = (int) (board[j][i] - '0'); if( colOk[numC] ) { return false; } colOk[numC] = true; } } } return true; } private boolean isLittleSudo(int row, int col) { // System.out.println("row = " + row + " col" + col); boolean[] arr = new boolean[10]; int endR = row + 3; int endC = col + 3; // System.out.println("endR = " + endR + " endC" + endC); for(int i=row; i<endR; i++) { for(int j=col; j<endC; j++) { // if( row==0 && col==3 ) { // System.out.print(board[i][j]); // } if(board[i][j]=='.') { continue; } int num = (int) (board[i][j] - '0'); if( arr[num] ) { return false; } arr[num] = true; } // System.out.println(); } return true; } public boolean isValidSudoku(char[][] board) { this.board = board; boolean flag = initCheck(); if( !flag ) { return false; } for(int i=0; i<9; i+=3) { for(int j=0; j<9; j+=3) { if( !isLittleSudo(i,j) ) { return false; } } } return true; } }
雜湊
點選檢視程式碼
class Solution {
public boolean isValidSudoku(char[][] board) {
boolean[][] rowOk = new boolean[10][10];
boolean[][] colOk = new boolean[10][10];
boolean[][][] littleSudo = new boolean[3][3][10];
for(int i=0; i<9; i++) {
for(int j=0; j<9; j++) {
char ch = board[i][j];
if( ch == '.' ) {
continue;
}
int num = (int)( board[i][j]-'0');
if( rowOk[i][num] || colOk[j][num] || littleSudo[i/3][j/3][num] ) {
return false;
}
rowOk[i][num] = true;
colOk[j][num] = true;
littleSudo[i/3][j/3][num] = true;
}
}
return true;
}
}