[LeetCode]Sudoku Solver

class Solution {
//brute-force
//modified from http://discuss.leetcode.com/questions/216/sudoku-solver @Lu-An Gong
public:
// 返回第一个空白的位置，如果没找到就返回 (-1, -1)
pair<int, int> findFirstEmpty(const vector< vector<char> >& board)
{
for (int i = 0; i < 9; ++i)
for (int j = 0; j < 9; ++j)
if (board[i][j] == '.') return make_pair(i, j);
return make_pair(-1, -1);
}

// 检查连续的 9 个格子是否有效
bool isValid(const vector< vector<char> >& board, int topX, int topY, int botX, int botY)
{
vector<bool> occur(9, false);
for (int row = topX; row <= botX; row++)
{
for (int col = topY; col <= botY; col++)
{
if ( isdigit(board[row][col]) )
{
if (occur[board[row][col]-'1']) return false;
else occur[board[row][col]-'1'] = true;
}
}
}
return true;
}

// 检查往某个位置填入一个数之后整个 board 是否有效（只需要考虑当前行、
// 当前列和所属的田字格）
bool isValidBoard(const vector< vector<char> >& board, pair<int, int> pos)
{
// 检查当前行是否有效
if (!isValid(board, pos.first, 0, pos.first, 8)) return false;
// 检查当前列是否有效
if (!isValid(board, 0, pos.second, 8, pos.second)) return false;
// 检查所在的田字格是否有效
int blockRow, blockCol;
for (blockRow = 0; blockRow < 3; ++blockRow)
{
bool flag = false;
for (blockCol = 0; blockCol < 3; ++blockCol)
{
if (blockRow*3 <= pos.first && pos.first <= blockRow*3+2
&& blockCol*3 <= pos.second && pos.second <= blockCol*3+2)
{
flag = true;
break;
}
}
if(flag) break;
}
if (!isValid(board, blockRow*3, blockCol*3, blockRow*3+2, blockCol*3+2)) return false;
// 如果以上都有效，则返回 true
return true;
}

// 检查从当前局面开始是否能够得到最终合法有效的解
bool solveSudoku(vector<vector<char> >& board)
{
// 如果没有找到空白的格子，说明已经填满了，成功返回
pair<int, int> pos = findFirstEmpty(board);
if (pos.first == -1 && pos.second == -1)
return true;
// 否则依次尝试往当前格子中填入数字 1-9，并判断能否得到可行的解
for (int i = 1; i <= 9; ++i)
{
board[pos.first][pos.second] = i + '0';
if (isValidBoard(board, pos) && solveSudoku(board))
return true;
// 恢复原样
board[pos.first][pos.second] = '.';
}
return false;
}
};

class Solution {
public:
bool checkRectangle(vector<vector<char> >& board, int x1, int y1, int x2, int y2)
{
vector<int> digitCnt(10, 0);
for(int i = x1; i <= x2; i++)
{
for(int j = y1; j <= y2; ++j)
{
if(board[i][j] != '.')
{
if(++digitCnt[board[i][j]-'0'] > 1) return false;
}
}
}
return true;
}
bool isValidSudoku(vector<vector<char> > &board, int curX, int curY) {
// Start typing your C/C++ solution below
// DO NOT write int main() function
//row check
if(!checkRectangle(board, curX, 0, curX, board.size()-1)) return false;
//column check
if(!checkRectangle(board, 0, curY, board.size()-1, curY)) return false;
//block check
for(int i = 0; i < board.size(); i+=3)
{
for(int j = 0; j < board.size(); j+=3)
{
if(i <= curX && curX <= i+2 && j <= curY && curY <= j+2
&& !checkRectangle(board, i, j, i+2, j+2)) return false;
}
}

return true;
}
bool solveSudokuUtil(vector<vector<char> > &board, int curIdx)
{
if(curIdx == 81) return true;
int curX = curIdx/9;
int curY = curIdx-curX*9;
if(board[curX][curY] != '.') return solveSudokuUtil(board, curIdx+1);
else
{
for(int i = 1; i <= 9; ++i)
{
board[curX][curY] = i+'0';
if(isValidSudoku(board, curX, curY) && solveSudokuUtil(board, curIdx+1)) return true;
board[curX][curY] = '.';
}
}
return false;
}
void solveSudoku(vector<vector<char> > &board) {
// Start typing your C/C++ solution below
// DO NOT write int main() function
solveSudokuUtil(board, 0);
}
};