Sudoku Solver

每日算法——leetcode系列

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问题 Sudoku Solver

Difficulty: Hard

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.

class Solution {public:    void solveSudoku(vector<vector<char>>& board) {    }};

翻译

数独解决器

难度系数：困难

写一个程序来实现通过填充空格求解数独。

空格用'.'表示。

你可以假定只有唯一解。

思路

题目的意思应该是给一个未完成的数独，然后通过程序可以自动填充来求解数独。

• 先查看现有的数字用Valid Sudoku检查符合数独的条件不
• 递归
  从board的第一格开遍历，
  
  1. 如果当前符号不为.，则遍历该行中下一格（先行后列），如果遍历到的格数大于了最大列数，则遍历行，终止条件行数也大于最大行数
  2. 为’.’时，从1-9,依次先一个插入，再重复整个过程

代码

class Solution {public:    void solveSudoku(vector<vector<char>>& board) {        if (isValidSudoku(board) == false){            return;        }        recursiveSudoKu(board, 0, 0);    }private:    bool isValidSudoku(vector<vector<char> > &board) {        for (int i = 0; i < 9; ++i){            for (int j = 0; j < 9; ++j){                rowMap[i][j] = {false};                colMap[i][j] = {false};                smallBoardMap[i][j] = {false};            }        }        for(int i = 0; i < board.size(); ++i){            for (int j = 0; j < board[i].size(); ++j){                if (board[i][j] == '.'){                    continue;                }                int idx =  board[i][j] - '0' - 1;                // 行                if (rowMap[i][idx] == true){                    return false;                }                rowMap[i][idx] = true;                // 列                if (colMap[j][idx] == true) {                    return false;                }                colMap[j][idx] = true;                // 小区域                int area = (i/3) * 3 + (j/3);                if (smallBoardMap[area][idx] == true) {                    return false;                }                smallBoardMap[area][idx] = true;            }        }        return true;    }    bool recursiveSudoKu(vector<vector<char>> &board, int row, int col){        if (row >= 9) {            return true;        }        if (col >= 9){            return recursiveSudoKu(board, row+1, 0);        }        if (board[row][col] != '.'){            return recursiveSudoKu(board, row, col+1);        }        int area;        for(int i=0; i < 9; ++i){            area = (row/3) * 3 + (col/3);            if (rowMap[row][i] || colMap[col][i] || smallBoardMap[area][i]){                continue;            }            board[row][col] = i + '1';            rowMap[row][i] = colMap[col][i] = smallBoardMap[area][i] = true;            if (recursiveSudoKu(board, row, col+1)){                return true;            }            board[row][col] = '.';            rowMap[row][i] = colMap[col][i] = smallBoardMap[area][i] = false;        }        return false;    }    bool rowMap[9][9];    bool colMap[9][9];    bool smallBoardMap[9][9];};