class Solution {
private:
// unordered_map<出发机场, map<到达机场, 航班次数>> targets
unordered_map<string, map<string, int>> targets;
bool backtracking(int ticketNum, vector<string>& result) {
    if (result.size() == ticketNum + 1) {
        return true;
    }
    for (pair<const string, int>& target : targets[result[result.size() - 1]]) {
        if (target.second > 0 ) { // 记录到达机场是否飞过了
            result.push_back(target.first);
            target.second--;
            if (backtracking(ticketNum, result)) return true;
            result.pop_back();
            target.second++;
        }
    }
    return false;
}
public:
    vector<string> findItinerary(vector<vector<string>>& tickets) {
        targets.clear();
        vector<string> result;
        for (const vector<string>& vec : tickets) {
            targets[vec[0]][vec[1]]++; // 记录映射关系
        }
        result.push_back("JFK"); // 起始机场
        backtracking(tickets.size(), result);
        return result;
    }
};

class Solution {
private:
vector<vector<string>> result;
// n 为输入的棋盘大小
// row 是当前递归到棋盘的第几行了
void backtracking(int n, int row, vector<string>& chessboard) {
    if (row == n) {
        result.push_back(chessboard);
        return;
    }
    for (int col = 0; col < n; col++) {
        if (isValid(row, col, chessboard, n)) { // 验证合法就可以放
            chessboard[row][col] = 'Q'; // 放置皇后
            backtracking(n, row + 1, chessboard);
            chessboard[row][col] = '.'; // 回溯，撤销皇后
        }
    }
}
bool isValid(int row, int col, vector<string>& chessboard, int n) {
    // 检查列
    for (int i = 0; i < row; i++) { // 这是一个剪枝
        if (chessboard[i][col] == 'Q') {
            return false;
        }
    }
    // 检查 45度角是否有皇后
    for (int i = row - 1, j = col - 1; i >=0 && j >= 0; i--, j--) {
        if (chessboard[i][j] == 'Q') {
            return false;
        }
    }
    // 检查 135度角是否有皇后
    for(int i = row - 1, j = col + 1; i >= 0 && j < n; i--, j++) {
        if (chessboard[i][j] == 'Q') {
            return false;
        }
    }
    return true;
}
public:
    vector<vector<string>> solveNQueens(int n) {
        result.clear();
        std::vector<std::string> chessboard(n, std::string(n, '.'));
        backtracking(n, 0, chessboard);
        return result;
    }
};

class Solution {
private:
bool backtracking(vector<vector<char>>& board) {
    for (int i = 0; i < board.size(); i++) {        // 遍历行
        for (int j = 0; j < board[0].size(); j++) { // 遍历列
            if (board[i][j] == '.') {
                for (char k = '1'; k <= '9'; k++) {     // (i, j) 这个位置放k是否合适
                    if (isValid(i, j, k, board)) {
                        board[i][j] = k;                // 放置k
                        if (backtracking(board)) return true; // 如果找到合适一组立刻返回
                        board[i][j] = '.';              // 回溯，撤销k
                    }
                }
                return false;  // 9个数都试完了，都不行，那么就返回false
            }
        }
    }
    return true; // 遍历完没有返回false，说明找到了合适棋盘位置了
}
bool isValid(int row, int col, char val, vector<vector<char>>& board) {
    for (int i = 0; i < 9; i++) { // 判断行里是否重复
        if (board[row][i] == val) {
            return false;
        }
    }
    for (int j = 0; j < 9; j++) { // 判断列里是否重复
        if (board[j][col] == val) {
            return false;
        }
    }
    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] == val ) {
                return false;
            }
        }
    }
    return true;
}
public:
    void solveSudoku(vector<vector<char>>& board) {
        backtracking(board);
    }
};