[leetcode]37. Sudoku Solver 解数独
Write a program to solve a Sudoku puzzle by filling the empty cells.
A sudoku solution must satisfy all of the following rules:
- Each of the digits
1-9
must occur exactly once in each row. - Each of the digits
1-9
must occur exactly once in each column. - Each of the the digits
1-9
must occur exactly once in each of the 93x3
sub-boxes of the grid.
Empty cells are indicated by the character '.'
.
A sudoku puzzle...
...and its solution numbers marked in red.
Note:
- The given board contain only digits
1-9
and the character'.'
. - You may assume that the given Sudoku puzzle will have a single unique solution.
- The given board size is always
9x9
.
题意:
解数独
Solution1: Backtracking
code
class Solution {
public void solveSudoku(char[][] board) {
if (board == null || board.length != 9 || board[0].length != 9) return;
boolean tmp = helper(board, 0, 0);
} public boolean helper(char[][] board, int row, int col) {
if (board == null || board.length != 9 || board[0].length != 9) return false; while (row < 9 && col < 9) {
if (board[row][col] == '.') break; // find the 1st empty spot
if (col == 8) {// 说明要换行了
col = 0;
row++;
} else {
col++;
}
}
if (row >= 9) return true;
int nextRow = row + col / 8;
int nextCol = (col + 1) % 9; for (int num = 1; num <= 9; num++) {
if (isValid(board, row, col, num)) { // 该num在行,列,box都没出现过
board[row][col] = (char) (num + '0'); // 试着将num填入cur spot
boolean result = helper(board, nextRow, nextCol); // 递归调用,下一个
if (result) return true;
board[row][col] = '.'; // 如果num在cur spot不合法,回溯。 还原。
}
}
return false;
} // check num is valid at such spot
// which means in cur row, col or box, this num hasn't appeared before
public boolean isValid(char[][] board, int row, int col, int num) {
// check row
for (int i = 0; i < 9; i++) {
if (board[row][i] == num + '0')
return false;
}
//check col
for (int i = 0; i < 9; i++) {
if (board[i][col] == num + '0')
return false;
}
//check box
int rowoff = (row / 3) * 3;
int coloff = (col / 3) * 3;
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
if (board[rowoff + i][coloff + j] == num + '0') return false;
}
}
return true;
}
}
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