class Solution {
public:
    vector<vector<int>> result;
    vector<int> path;
    void backtracking(vector<int>& nums, int startIndex){
        if(path.size() > 1){
            result.push_back(path);
        }
        unordered_set<int> uset;
        for(int i = startIndex; i < nums.size(); i ++){
            if ((!path.empty() && nums[i] < path.back())
                    || uset.find(nums[i]) != uset.end()) {
                    continue;
            }
            uset.insert(nums[i]);
            path.push_back(nums[i]);
            backtracking(nums, i + 1);
            path.pop_back();
        }
    }
    vector<vector<int>> findSubsequences(vector<int>& nums) {
        backtracking(nums, 0);
        return result;
    }
};

class Solution {
public:
    vector<vector<int>> result;
    vector<int> path;
    void backtracking(vector<int>& nums, vector<bool> used){
        if(path.size() == nums.size()){
            result.push_back(path);
            return;
        }
        for(int i = 0; i < nums.size(); i ++){
            if(used[i] == true) continue;
            used[i] = true;
            path.push_back(nums[i]);
            backtracking(nums, used);
            path.pop_back();
            used[i] = false;
        }

    }
    vector<vector<int>> permute(vector<int>& nums) {
        vector<bool> used(nums.size(), false);
        backtracking(nums, used);
        return result;
    }
};

class Solution {
public:
    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){
                result.push_back(target.first);
                target.second --;
                if(backtracking(ticketNum, result)) return true;
                result.pop_back();
                target.second++;
            }
        }
        return false;
    }
    vector<string> findItinerary(vector<vector<string>>& tickets) {
        vector<string> result;
        for(const vector<string>& vec:tickets){
            targets[vec[0]][vec[1]] ++;
        }
        result.push_back("JFK");
        backtracking(tickets.size(), result);
        return result;
    }
};

class Solution {
public:
  vector<vector<string>> result;
  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)) {
        chessboard[row][col] = 'Q';
        backtracking(n, row + 1, chessboard);
        chessboard[row][col] = '.';
      }
    }
  }
  bool isvalid(int row, int col, vector<string> &chessboard, int n) {
    // 检查列
    for (int i = 0; i < row; i++) {
      if (chessboard[i][col] == 'Q') {
        return false;
      }
    }
    // 检查左上到右下的对角线
    for (int i = row - 1, j = col - 1; i >= 0 && j >= 0; i--, j--) {
      if (chessboard[i][j] == 'Q') {
        return false;
      }
    }
    // 检查右上到左下的对角线
    for (int i = row - 1, j = col + 1; i >= 0 && j < n; i--, j++) {
      if (chessboard[i][j] == 'Q') {
        return false;
      }
    }
    // 检查水平方向的对角线
    for (int i = row - 1, k = 1; i >= 0 && col + k < n; i--, k++) {
      if (chessboard[i][col + k] == 'Q') {
        return false;
      }
    }
    for (int i = row - 1, k = 1; i >= 0 && col - k >= 0; i--, k++) {
      if (chessboard[i][col - k] == 'Q') {
        return false;
      }
    }
    return true;
  }
  vector<vector<string>> solveNQueens(int n) {
    vector<string> chessboard(n, string(n, '.'));
    backtracking(n, 0, chessboard);
    return result;
  }
};

class Solution {
public:
    bool backtracking(vector<vector<char>>& board){
        for(int i = 0; i < board.size(); i ++){
            for(int j = 0; j < board[0].size(); j ++){
                if(board[i][j] != '.') continue ;
                for(char k = '1'; k <= '9'; k ++){
                    if(isvalid(i, j, k, board)){
                        board[i][j] = k;
                        if(backtracking(board)) return true;
                        board[i][j] = '.';
                    }
                }
                return false;
            }
        }
        return true;
    }
    bool isvalid(int row, int col, char val, vector<vector<char>>& board){
        for(int i = 0; i< 9; i ++){
            if(board[row][i] == val){
                return false;
            }
        }
        for(int j = 0; j < 9; j ++){
            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 ++){
            for(int j = startCol; j < startCol+3; j ++){
                if(board[i][j] == val){
                    return false;
                }
            }
        }
        return true;
    }
    void solveSudoku(vector<vector<char>>& board) {
        backtracking(board);
    }
};