37. Sudoku Solver.md

37. Sudoku Solver

Problem

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.

tag:

Solution

java

    public void solveSudoku(char[][] board) {
        solve(board, 0);
    }

	//dfs
    public boolean solve(char[][] board, int k) {
        if(k>=81) {
            return true;
        } else {
            int i=k/9, j=k%9;
            if(board[i][j]!='.') {
                return solve(board, k+1);
            } else {
                for(char c='1'; c<='9'; c++) {
                    board[i][j] = c;
                    if(isValid(board, i,j) && solve(board, k+1)) {
                        return true;
                    } 
                    board[i][j] = '.';
                }
            }
        }
        return false;
    }
    
   //ref: [36. Valid Sudoku](https://leetcode.com/problems/valid-sudoku/)
    public boolean isValid(char[][] board, int x, int y) {
        for(int i=0; i<9; i++) {
            if( (i!=y && board[x][i]==board[x][y]) || (i!=x && board[i][y]==board[x][y]) || ( (x!=3*(x/3)+i/3) && (y!=3*(y/3)+i%3) && board[3*(x/3)+i/3][3*(y/3)+i%3]==board[x][y])) {
                return false;
            }
        }
        return true;
    }

go