LeetCode开心刷题二十一天——37. Sudoku Solver

37. Sudoku Solver

Hard

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Write a program to solve a Sudoku puzzle by filling the empty cells.

A sudoku solution must satisfy all of the following rules:

1. Each of the digits 1-9 must occur exactly once in each row.
2. Each of the digits 1-9 must occur exactly once in each column.
3. Each of the the digits 1-9 must occur exactly once in each of the 9 3x3 sub-boxes of the grid.

Empty cells are indicated by the character '.'.

A sudoku puzzle...

...and its solution numbers marked in red.

Note:

• The given board contain only digits 1-9 and the character '.'.
• You may assume that the given Sudoku puzzle will have a single unique solution.
• The given board size is always 9x9.

Idea Statement:like 8 queen problem,we have to use tranverse.but the way we easier this action is to add limitations to the tranverse.

 

#include<stdio.h>
#include<iostream>
#include<vector>
#include<algorithm>
#include<stack>
#include<string>
#include<memory>
#include<memory.h>
#include<hash_map>
#include<map>
#include<set>
#include<unordered_map>
using namespace std;
class Solution {
public:
    void solveSudoku(vector<vector<char>>& board) {
        rows_ = vector<vector<int>>(9, vector<int>(10));
        cols_ = vector<vector<int>>(9, vector<int>(10));
        boxes_ = vector<vector<int>>(9, vector<int>(10));
        for(int i=0;i<9;i++)
        {
            for(int j=0;j<9;j++)
            {
                const char c=board[i][j];
                if(c!='.')
                {
                    int n=c-'0';
                    int bx=j/3;
                    int by=i/3;
                    rows_[i][n] = 1;
                    cols_[j][n] = 1;
                    boxes_[by * 3 + bx][n] = 1;
                }
            }
        }
         fill(board, 0, 0);
    }
private:
    vector<vector<int>> rows_,cols_,boxes_;
    bool fill(vector<vector<char>>& board,int x,int y)
    {
        if(y==9) return true;
        int nx=(x+1)%9;
        int ny=(nx==0)?y+1:y;
        if(board[y][x]!='.') return fill(board,nx,ny);

        for(int i=1;i<=9;i++)
        {
            int bx=x/3;
            int by=y/3;
            int box_key=by*3+bx;
            if(!rows_[y][i]&&!cols_[x][i]&&!boxes_[box_key][i])
            {
                rows_[y][i]=1;
                cols_[x][i]=1;
                boxes_[box_key][i]=1;
                board[y][x]=i+'0';
                if(fill(board,nx,ny)) return true;
                board[y][x] = '.';
                boxes_[box_key][i] = 0;
                cols_[x][i] = 0;
                rows_[y][i] = 0;
            }

        }
        return false;
    }
};
int main()
{
    vector<vector<char>> board={
    {'.','.','4','.','.','.','6','3','.'},
    {'.','.','.','.','.','.','.','.','.'},
    {'5','.','.','.','.','.','.','9','.'},
    {'.','.','.','5','6','.','.','.','.'},
    {'4','.','3','.','.','.','.','.','1'},
    {'.','.','.','7','.','.','.','.','.'},
    {'.','.','.','5','.','.','.','.','.'},
    {'.','.','.','.','.','.','.','.','.'},
    {'.','.','.','.','.','.','.','.','.'}
    };
    Solution s;
    s.solveSudoku(board);
    for(vector<vector<char>>::iterator ite=board.begin();ite!=board.end();++ite)
    {
        vector<char> temp=*ite;
        for(vector<char>::iterator itee=temp.begin();itee!=temp.end();++itee)
        {
            cout<<*itee;
        }
        cout<<endl;
    }

//    for(auto t:board)
//    {
//        cout<<t;
//    }
    return 0;
}