Friday, February 13, 2015

LeetCode [37] Sudoku Solver

 37. Sudoku Solver

Hard

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

The '.' character indicates empty cells.

 

Example 1:

Input: board = [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]
Output: [["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]
Explanation: The input board is shown above and the only valid solution is shown below:

 

Constraints:

  • board.length == 9
  • board[i].length == 9
  • board[i][j] is a digit or '.'.
  • It is guaranteed that the input board has only one solution.
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class Solution {
    void update(int n, int i, int j, int k, vector<int> &mr, vector<int> &mc, vector<int> &mb){
        int mask = 1<<n;
        mr[i] ^= mask;
        mc[j] ^= mask;
        mb[k] ^= mask;
    }
    
    bool valid(int n, int i, int j, int k, vector<int> &mr, vector<int> &mc, vector<int> &mb){
       int mask = 1<<n;
       return (((mr[i]&mask)==0) && ((mc[j]&mask)==0) && ((mb[k]&mask)==0));
    }
    
public:
    bool bt(vector<vector<char> > &board, int N, vector<int> &mr, vector<int> &mc, vector<int> &mb){
        if(N==81) return true;
        for(int i=N/9; i<9; ++i){
            for(int j=N%9; j<9; ++j){
                int k = i/3*3+j/3;
                if(board[i][j]!='.'){
                  return bt(board, i*9+j+1, mr, mc, mb);
                }else{
                    for(int c=1; c<=9; ++c){
                        if(valid(c, i, j, k, mr, mc, mb)){
                            update(c, i, j, k, mr, mc, mb);
                            board[i][j]=('0'+c);
                            if(bt(board, i*9+j+1, mr, mc, mb))
                                return true;
                            update(c, i, j, k, mr, mc, mb);
                            board[i][j]='.';
                        }
                    }
                    return false;
                }
            }
        }
        return false;
    
    }

    void solveSudoku(vector<vector<char> > &board) {
        vector<int> mr(9, 0);
        vector<int> mc(9, 0);
        vector<int> mb(9, 0); 
        for(int i=0; i<9; ++i){
            for(int j=0; j<9; ++j){
                int k = i/3*3+j/3;
                if(board[i][j]!='.'){
                    int n = board[i][j]-'0';
                    update(n, i, j, k, mr, mc, mb);
                }
            }
        }

        bt(board, 0, mr, mc, mb);
    }
};

class Solution {
public:
    void solveSudoku(vector<vector<char>>& board) {
        int row[9][10] = {0};
        int col[9][10] = {0};
        int blk[9][10] = {0};
        for(int pos=0; pos<81; ++pos){
            int i = pos/9, j = pos%9, k = i/3*3+j/3;
            if(board[i][j]!='.'){
                 int v = board[i][j]-'0';
                 row[i][v]=1; col[j][v]=1; blk[k][v]=1;
            }
        }
        bt(board, 0, row, col, blk);
    }
    
    bool bt(vector<vector<char>>&board, int pos, int row[][10], int col[][10], int blk[][10]){
        if(pos==81) return true;
        else{
            int i = pos/9, j = pos%9, k = i/3*3+j/3;
            if(board[i][j]=='.'){
                for(int v = 1; v<=9; ++v){
                    if(row[i][v]==0 && col[j][v]==0 && blk[k][v]==0){
                        row[i][v]=1; col[j][v]=1; blk[k][v]=1;
                        board[i][j] = char('0'+v);
                        if(bt(board, pos+1, row, col, blk)) return true;
                        row[i][v]=0; col[j][v]=0; blk[k][v]=0;
                        board[i][j] = '.';
                    }
                }
            }else{
                return bt(board, pos+1, row, col, blk);
            }
        }
        return false;
    }
};


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class Solution {
    Set<Integer>[] setsR = new HashSet[9];
    Set<Integer>[] setsC = new HashSet[9];
    Set<Integer>[] setsB = new HashSet[9];
    public void solveSudoku(char[][] board) {
        for(int i=0; i<9; ++i){
            setsR[i] = new HashSet<>();
            setsC[i] = new HashSet<>();
            setsB[i] = new HashSet<>();
        }
        for(int i=0; i<9; ++i){
            for(int j=0; j<9; ++j){
                if(board[i][j]!='.'){
                    int k = board[i][j]-'0';
                    setsR[i].add(k);
                    setsC[j].add(k);
                    setsB[i/3*3 + j/3].add(k);
                }
            }
        }
        dfs(board, 0, 0);
    }
    
    boolean dfs(char[][] board, int i0, int j0){
        if(i0==9) return true; 
        if(j0==9) return dfs(board, i0+1, 0);
        if(board[i0][j0]!='.') return dfs(board, i0, j0+1); 
        for(int k=1; k<=9; ++k){
            if(setsR[i0].contains(k)) continue;
            if(setsC[j0].contains(k)) continue;
            if(setsB[i0/3*3 + j0/3].contains(k)) continue;
            setsR[i0].add(k);
            setsC[j0].add(k);
            setsB[i0/3*3 + j0/3].add(k);
            
            board[i0][j0] = (char)(k+'0');
            if(dfs(board, i0, j0+1)) return true;
            board[i0][j0] = '.';
            setsR[i0].remove(k);
            setsC[j0].remove(k);
            setsB[i0/3*3 + j0/3].remove(k);
        }
        return false;
    }
}
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