leetcode problem 37 -- Sudoku Solver

解决数独

Write a program to solve a Sudoku puzzle by filling the empty cells.

Empty cells are indicated by the character ‘.‘.

You may assume that there will be only one unique solution.

A sudoku puzzle...

思路：

　　搜索加剪枝。

　　首先设立3个辅助二维数组：rows,  columns, grids来维护目前的数独状态，rows[i][k]（1<=i, k<=9）表示第i行是否占用了数字k，同理colums[i][k]表示第i列是否占用了数字k，grid[i][k]表示第i个格子是否占用了数字k，

　　然后第一次读入二维数组，更新rows, columns和grids.

　　第二次读二维数组，对每个为‘.‘的元素根据rows,columns和grid来枚举可能的值。如果没有可以枚举的值，直接剪枝返回。

代码如下：

　　Runtime: 5 ms

static int columns[9][10];
static int rows[9][10];
static int grids[9][10];

int search(char *board[9], int startI, int startJ) {

    for(int i = startI; i < 9; ++i) {
        for(int j = i == startI ? startJ : 0; j < 9; ++j) {
            if (board[i][j] == ‘.‘) {
                for (int k = 1; k <= 9; ++k) {
                    if (!rows[i][k] && !columns[j][k] && !grids[i/3 + j/3 *3][k]) {
                        rows[i][k] = 1;
                        columns[j][k] = 1;
                           grids[i/3 + j/3 *3][k] = 1;

                        if (search(board, i, j+1) == 1) {
                            board[i][j] = k + ‘0‘;
                            return 1;
                        }
                        rows[i][k] = 0;
                        columns[j][k] = 0;
                           grids[i/3 + j/3 *3][k] = 0;
                    }
                }
                return 0;
            }
        }
    }
    return 1;
}

void solveSudoku(char * board[9]) {
    memset(columns, 0, sizeof(columns));
    memset(rows, 0, sizeof(rows));
    memset(grids, 0, sizeof(grids));    

    for(int i = 0; i < 9; ++i) {
        for(int j = 0; j < 9; ++j) {
            if (board[i][j] != ‘.‘) {
                rows[i][board[i][j] - ‘0‘] = 1;
                columns[j][board[i][j] - ‘0‘] = 1;

                int tmp = i/3 + j/3 * 3;
                grids[tmp][board[i][j] - ‘0‘] = 1;
            }
        }
    }
    search(board, 0, 0);
}