题目描述
编写一个程序,通过填充空格来解决数独问题。
数独的解法需 遵循如下规则:
- 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。
数独部分空格内已填入了数字,空白格用 ‘.’ 表示。
输入示例
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"]]
输出示例
[["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]
解题思路
文章来源:https://www.toymoban.com/news/detail-820484.html
解题代码文章来源地址https://www.toymoban.com/news/detail-820484.html
class Solution {
public void solveSudoku(char[][] board) {
backtrack(board);
}
public boolean backtrack(char[][] board) {
for(int i = 0; i < board.length; i++) {
for(int j = 0; j < board[0].length; j++) {
// 跳过原始数字
if(board[i][j] != '.') {
continue;
}
// 只处理空白格,填写1-9
for(char k = '1'; k <= '9'; k++) {
if(isValid(i, j, k, board)) {
board[i][j] = k;
boolean result = backtrack(board);
if(result) {
return true;
}
board[i][j] = '.';
}
}
// 九个是尝试完了还是不行,就返回 false
return false;
}
}
// 遍历完没有返回 false,说明找到合适棋盘位置了
return true;
}
public boolean isValid(int row, int col, char k, char[][] board) {
// 判断行是否重复
for(int i = 0; i < 9; i++) {
if(board[row][i] == k) {
return false;
}
}
// 判断列是否重复
for(int j = 0; j < 9; j++) {
if(board[j][col] == k) {
return false;
}
}
// 判断九宫格是否重复
int startRow = (row / 3) * 3;
int startCol = (col / 3) * 3;
for (int i = startRow; i < startRow + 3; i++) { // 判断9方格里是否重复
for (int j = startCol; j < startCol + 3; j++) {
if (board[i][j] == k) {
return false;
}
}
}
return true;
}
}
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