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117 lines
3.0 KiB
117 lines
3.0 KiB
#include <stdio.h>
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int correct(int board[9][9]){//判断是否合法
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int col[9]={0},row[9]={0},block[9]={0};
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int i,j;
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for(i=0;i<9;++i){
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for(j=0;j<9;j++){//遍历
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int index=1<<(board[i][j]-1);//设置初始位掩码
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int blockindex=i/3*3+j/3;//分块
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if(board[i][j]!=0){//需要判断的位置
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if(row[i]&index){//行合法
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printf("False:Invalid initial Sudoku matrix!\n");
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printf("The number %d in the row %d has been used!",board[i][j],i+1);
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return 0;
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}
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row[i] |=index;//判断一个条件不成立即可 所以位掩码恢复
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if(col[j]&index){//列合法
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printf("False:Invalid initial Sudoku matrix!\n");
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printf("The number %d in the rol %d has been used!",board[i][j],j+1);
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return 0;
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}
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col[j] |=index;
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if(block[blockindex]&index){//块合法
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printf("False:Invalid initial Sudoku matrix!\n");
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printf("The number %d in the block %d has been used!",board[i][j],blockindex+1);
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return 0;
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}
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block[blockindex] |=index;
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}
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}
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}
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printf("True:Valid initial Sudoku matrix!\n");//以上都通过 成立
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return 1;
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}
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int isSafe(int board[9][9],int row,int col,int num){//判断是否合法的函数
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int x,i,j;
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for (x=0;x<=8;x++)//遍历行合法
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if(board[row][x]==num)
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return 0;
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for (x=0;x<= 8;x++)//遍历列合法
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if(board[x][col]==num)
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return 0;
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int sRow=row-row%3,sCol=col-col%3;//初始化块的起始行与列
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for(i=0;i<3;i++)
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for(j=0;j<3;j++)//遍历每个块
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if(board[i+sRow][j+sCol]==num)
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return 0;
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return 1;
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}
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int solve(int board[9][9]){
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int num;
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int i=0,j=0;
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for(i=0;i<9;i++){
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for(j=0;j<9;j++){
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if(board[i][j]==0){//需要填空的部分
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for(num=1;num<=9;++num){
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if(isSafe(board,i,j,num)){//填空中也要满足数独的定义
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board[i][j]=num;
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if(solve(board)){//函数嵌套
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return 1;
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}
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board[i][j]=0;
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}
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}
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return 0;//遍历后无法填出正确答案
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}
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}
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}
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//return 1;
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}
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void print(int board[9][9]){//格式化输出
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printf("|-----------------------|\n");
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int i=0,j=0,s=0,k=0;
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for(i=0;i<9;++i){
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for(j=0;j<9;j++){
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while(j%3==0){
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printf("| ");
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break;
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}
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printf("%d ",board[i][j]);
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}
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printf("|\n");
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while((i+1)%3==0){
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printf("|-----------------------|\n");
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break;
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}
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}
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}
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int main(){
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int board1[9][9]={{5, 2, 0, 0, 7, 0, 0, 0, 0},//初始化矩阵
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{6, 0, 0, 1, 9, 5, 0, 0, 0},
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{0, 9, 8, 0, 0, 0, 0, 6, 0},
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{8, 0, 0, 0, 6, 0, 0, 0, 3},
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{4, 0, 0, 8, 0, 3, 0, 0, 1},
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{7, 0, 0, 0, 2, 0, 0, 0, 6},
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{0, 6, 0, 0, 0, 0, 2, 8, 0},
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{0, 0, 0, 4, 1, 9, 0, 0, 5},
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{0, 0, 0, 0, 8, 0, 0, 7, 9}};
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printf("The original Sudoku matrix:\n");
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print(board1);//格式化输出原矩阵
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if(correct(board1)){//判断是否合法
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if(solve(board1)){//是否有解
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printf("The solution of Sudoku matrix:\n");
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print(board1);//格式化输出解
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}else{
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printf("No solutions!\n");//无解
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}
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}
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return 0;
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}
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