【初级算法】10.有效的数独
2018-05-03 09:16
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题目:
判断一个 9x9 的数独是否有效。只需要根据以下规则,验证已经填入的数字是否有效即可。 数字 1-9 在每一行只能出现一次。 数字 1-9 在每一列只能出现一次。 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。 上图是一个部分填充的有效的数独。 数独部分空格内已填入了数字,空白格用 '.' 表示。 示例 1: 输入: [ ["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"] ] 输出: true 示例 2: 输入: [ ["8","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"] ] 输出: false 解释: 除了第一行的第一个数字从 5 改为 8 以外,空格内其他数字均与 示例1 相同。 但由于位于左上角的 3x3 宫内有两个 8 存在, 因此这个数独是无效的。 说明: 一个有效的数独(部分已被填充)不一定是可解的。 只需要根据以上规则,验证已经填入的数字是否有效即可。 给定数独序列只包含数字 1-9 和字符 '.' 。 给定数独永远是 9x9 形式的。
解题思路:
本题初看起来比较怪异,实际只需要判断数据是否合规即可。数独9*9要求每一列的数据为1到9,每一行的数据为1到9.每一个3*3的block也为数字1到9.
因此只需要判断列,行,块是否合法即可。具体该数独有没有解不必关心。
代码:
class Solution { public: bool isValidBlock(vector<vector<char>>& board,int x,int y){ set<int> test; for(int i = x;i<x+3;++i){ for(int j = y;j < y+3;++j){ if(board[i][j] == '.'){ continue; } if(!(board[i][j] <= '9' && board[i][j] >= '1')){ return false; } if(board[i][j] <= '9' && board[i][j] >= '1'){ if(test.find(board[i][j]-'0')==test.end()){ test.insert(board[i][j]-'0'); }else{ return false; } } } } return true; } bool isValidRow(vector<vector<char>>& board,int row){ set<int> test; for(int i = 0;i < 9;++i){ if(board[row][i] == '.'){ continue; } if(!(board[row][i] >= '1' && board[row][i] <= '9')){ return false; } if(test.find(board[row][i]-'0')==test.end()){ test.insert(board[row][i]-'0'); }else{ return false; } } return true; } bool isValidColum(vector<vector<char>>& board,int colum){ set<char> test; for(int i = 0;i<9;++i){ if(board[i][colum] == '.'){ continue; } if(!(board[i][colum] <= '9' && board[i][colum] >= '1')){ return false; } if(test.find(board[i][colum]-'0')==test.end()){ test.insert(board[i][colum]-'0'); }else{ return false; } } return true; } bool isValidSudoku(vector<vector<char>>& board) { /*check row & colum*/ for(int i = 0; i < 9; ++i){ if(!isValidRow(board,i)||!isValidColum(board,i)){ cout<<i<<endl; return false; } } /*check block*/ for(int i = 0;i < 9; i += 3){ for(int j = 0;j < 9; j += 3){ if(!isValidBlock(board,i,j)){ cout<<i<<j<<endl; return false; } } } return true; } };
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