37. Sudoku Solver

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...



...and its solution numbers marked in red.

这道题就是做数独。。直接用深度搜索。用三个9*10的二维数组记录每一行，每一列和每一个九宫格已经有的数，然后就可以开始深度搜索，在‘.’处填进适合的数，最后只要得到答案就立刻停止，答案就存在board里。

我的代码（4ms）：

class Solution {
public:
bool flg=false;
bool rows[9][10],cols[9][10],squares[9][10];

void dfs(vector<vector<char> >&board,int i,int j)
{
if(flg) return;
if(i>=9)
{
flg=true;
return;
}
int i1=i+(j+1)/9,j1=(j+1)%9;
if(board[i][j]=='.')
{
for(int k=1;k<=9;k++)
{
if((!rows[i][k])&&(!cols[j][k])&&(!squares[(i/3)*3+j/3][k]))
{
board[i][j]=k+'0';
rows[i][k]=cols[j][k]=squares[(i/3)*3+j/3][k]=true;
dfs(board,i1,j1);
rows[i][k]=cols[j][k]=squares[(i/3)*3+j/3][k]=false;
if(flg) return;
}
}
board[i][j]='.';
}
else dfs(board,i1,j1);
}

void solveSudoku(vector<vector<char> >& board)
{
for(int i=0;i<9;i++)
{
for(int j=0;j<9;j++)
{
if(board[i][j]!='.')
{
int num=board[i][j]-'0';
rows[i][num]=cols[j][num]=squares[(i/3)*3+j/3][num]=true;
}
}
}
dfs(board,0,0);
}
};

讨论上有一个用位运算的做的。。0ms 

class Solution {
public:
bool solveSudoku(int *sequence, int begin, short *rows, short *cols, short *subs,
const int *row_index, const int *col_index, const int *sub_index)
{
for (int s = begin; s < 81; ++s)
{
int i = row_index[s], j = col_index[s], k = sub_index[s];
if (!sequence[s])
{
short candidates = ~rows[i] & ~cols[j] & ~subs[k];
while (candidates & 0x1ff)
{
short val = candidates & (-candidates);
sequence[s] = val;
rows[i] |= val; cols[j] |= val; subs[k] |= val;
if (solveSudoku(sequence, s + 1, rows, cols, subs, row_index, col_index, sub_index))
return true;
sequence[s] = 0;
rows[i] &= ~val; cols[j] &= ~val; subs[k] &= ~val;
candidates &= ~val;
}
return false;
}
}
return true;
}

void solveSudoku(vector<vector<char>> &board)
{
short rows[9]{ 0 }, cols[9]{ 0 }, subs[9]{ 0 };
int sequence[81]{ 0 }, row_index[81], col_index[81], sub_index[81];
for (int i = 0; i < 9; ++i)
{
for (int j = 0; j < 9; ++j)
{
int s = 9 * i + j;
row_index[s] = i; col_index[s] = j; sub_index[s] = (i / 3) * 3 + j / 3;
if (board[i][j] != '.')
{
sequence[s] = 1 << (board[i][j] - '1');
rows[i] |= sequence[s]; cols[j] |= sequence[s]; subs[sub_index[s]] |= sequence[s];
}
}
}
solveSudoku(sequence, 0, rows, cols, subs, row_index, col_index, sub_index);
for (int i = 0; i < 9; ++i)
{
for (int j = 0; j < 9; ++j)
{
if (board[i][j] == '.')
{
int s = 9 * i + j, n;
for (n = 0; sequence[s] != (1 << n); ++n)
;
board[i][j] = n + '1';
}
}
}
}
};