332.重新安排行程

力扣题目链接

class Solution {
public:
    // 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]]) {
            // 记录到达机场是否飞过
            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) {
        targets.clear();
        vector<string> result;
        for(const vector<string>& vec : tickets) {
            targets[vec[0]][vec[1]]++;
        }
        result.push_back("JFK");// 起始机场
        backtracking(tickets.size(), result);
        return result;
    }
};

51. N皇后

力扣题目链接

class Solution {
public:
    // 时间复杂度: O(n!)
    // 空间复杂度: O(n)
    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)) {
                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45度角
        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
        for (int i = row - 1, j = col + 1; i >= 0 && j < n; i--, j++) {
            if (chessboard[i][j] == 'Q') {
                return false;
            }
        }
        return true;

    }

    vector<vector<string>> solveNQueens(int n) {
        result.clear();
        vector<string> chessboard(n, string(n, '.'));
        backtracking(n, 0, chessboard);
        return result;
    }
};

37. 解数独

力扣题目链接

class Solution {
public:
    bool backtracking(vector<vector<char>>& board) {
        // 不需要返回条件，融入到了二维递归的循环中了
        for (int i = 0; i < board.size(); i++) {
            for (int j = 0; j < board[0].size(); j++) {
                if (board[i][j] == '.') {
                    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] = '.';
                        }
                    }
                    // 九个数字遍历完了，此处讲究
                    return false;
                }
            }
        }
        return true;
    }
    bool isValid(int row, int col, char val, vector<vector<char>>& board) {
        // 判断行是否重复
        for (int i = 0; i < board[0].size(); ++i) {
            if (board[row][i] == val) {
                return false;
            }
        }
        // 判断列是否重复
        for (int i = 0; i < board.size(); ++i) {
            if (board[i][col] == val) {
                return false;
            }
        }
        // *判断九宫格内是否重复
        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);
    }
};

int main() {
    vector<vector<char>> board 
    {{'.', '6', '.', '.', '9', '.', '.', '8', '2'},
    {'.', '9', '.', '7', '.', '.', '.', '4', '6'},
    {'.', '.', '8', '.', '.', '1', '.', '.', '5'},
    {'9', '3', '.', '.', '5', '.', '.', '.', '.'},
    {'8', '.', '5', '.', '7', '6', '4', '2', '9'},
    {'2', '.', '6', '1', '.', '.', '3', '5', '8'},
    {'1', '.', '.', '.', '.', '4', '2', '9', '.'},
    {'4', '.', '.', '.', '1', '2', '.', '.', '3'},
    {'6', '2', '.', '.', '3', '.', '.', '.', '.'}};
    Solution s1;
    s1.solveSudoku(board);
    for (const auto& row : board) {
        for (const auto& element : row) {
            std::cout << element << " ";
        }
        std::cout << std::endl;
    }
}