Valid Sudoku
Determine if a Sudoku is valid, according to: Sudoku Puzzles - The Rules.
The Sudoku board could be partially filled, where empty cells are filled with the character '.'
.
A partially filled sudoku which is valid.
Note:
A valid Sudoku board (partially filled) is not necessarily solvable. Only the filled cells need to be validated.
注意到題目中說的,只要當前已經填充的數字是合法的就可以,不一定要這個數獨是有解.(下面說的九宮格都是指3*3的網格)
因此只需要判斷9*9網格的每一行、每一列、9個小九宮格是否合法。即如果在每一行、每一列、每個9個小九宮格內,某個數字重複出現了,當前數獨就是不合法的。
如果把九宮格按照行從0開始標號,那麼數字board[i][j] 位於第 i/3*3+j/3 個九宮格內
- 在檢測行是否合法時,i 表示矩陣的行,j 表示矩陣的列;
- 檢測列是否合法時,i 表示矩陣的列,j 表示矩陣的行;
- 檢測九宮格是否合法時,i 表示九宮格的標號,j 表示九宮格里的每個元素(只是我們需要根據i、j定位相應的元素到原來的矩陣:第 i 個九宮格里面的第 j 個元素在原矩陣的第 3*(i/3) + j/3 行,第 3*(i%3) + j%3)列,“/” 表示整數除法)
class Solution {
public:
bool isValidSudoku(vector<vector<char> > &board) {
int rowValid[10] = {0};
int colValid[10] = {0};
int subBoardValid[10] = {0};
for(int i=0;i<9;i++) {
memset(rowValid,0,sizeof(rowValid));
memset(colValid,0,sizeof(colValid));
memset(subBoardValid,0,sizeof(subBoardValid));
for(int j=0;j<9;j++) {
if(!isValid(rowValid,board[i][j]) || !isValid(colValid,board[j][i]) || !isValid(subBoardValid,board[3*(i/3)+j/3][3*(i%3)+j%3])) {
return false;
}
}
}
return true;
}
bool isValid(int arr[],char index) {
if(index == '.')
return true;
if(arr[index-'0'] == 1)
return false;
arr[index-'0'] = 1;
return true;
}
};
Sudoku Solver
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.
這種類型的遊戲一般回溯法來解決,設置某個空格時,如果該空格無論設置什麼數字都無法達到合法狀態,那麼回溯重新設置上一個空格class Solution {
public:
void solveSudoku(vector<vector<char> > &board) {
solve(board,0);
}
bool solve(vector<vector<char> > &board,int index) {
if(index>80)
return true;
int i=index/9;
int j= index-i*9;
if(board[i][j] != '.')
return solve(board,index+1);
for(int k=1;k<=9;k++) {
board[i][j] = '0' + k;
if(isValid(board,i,j) && solve(board,index+1))
return true;
board[i][j] = '.';
}
return false;
}
bool isValid(vector<vector<char> > &board,int i, int j) {
for(int m=0;m<9;m++) {
if(m!=i && board[m][j] == board[i][j])
return false;
}
for(int n=0;n<9;n++) {
if(n!=j && board[i][n] == board[i][j])
return false;
}
for(int m=3*(i/3);m<3*(i/3+1);m++) {
for(int n=3*(j/3);n<3*(j/3+1);n++) {
if(m!=i && n!=j && board[m][n] == board[i][j])
return false;
}
}
return true;
}
};