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#include <stdio.h>
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void print(int board[9][9]){
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printf("|-----------------------|\n");
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int i,j;
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for(i=0;i<9;i++){
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printf("| ");
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for(j=0;j<9;j++){
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if(board[i][j]==0) printf(". ");
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else printf("%d ",board[i][j]);
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if(j%3==2) printf("| ");
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}
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printf("\n");
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if(i%3==2){
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printf("|-----------------------|\n");
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}
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}
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}
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void check(int board[9][9]){
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printf("The original Sudoku matrix:\n");
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print(board);
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int i,j,k;
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//判断每一行数字是否重复
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for(i=0;i<9;i++){
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int cnt[10]={}; //统计每个数字出现次数
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for(j=0;j<9;j++){
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cnt[board[i][j]]++;
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}
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for(j=1;j<=9;j++){
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if(cnt[j]>1){
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printf("False:Invalid initial Sudoku matrix!\n");
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printf("The number %d in the col %d has been used!\n",j,i+1);
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return;
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}
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}
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}
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//判断每一列数字是否重复
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for(i=0;i<9;i++){
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int cnt[10]={}; //统计每个数字出现次数
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for(j=0;j<9;j++){
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cnt[board[j][i]]++;
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}
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for(j=1;j<=9;j++){
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if(cnt[j]>1){
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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!\n",j,i+1);
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return;
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}
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}
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}
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//判断每个九宫格数字是否重复
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for(k=0;k<9;k++){
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int cnt[10]={}; //统计每个数字出现次数
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//起始行为k/3*3
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for(i=k/3*3;i<k/3*3+3;i++){
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//起始列为k%3*3
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for(j=k%3*3;j<k%3*3+3;j++){
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cnt[board[i][j]]++;
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}
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}
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for(j=1;j<=9;j++){
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if(cnt[j]>1){
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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!\n",j,k+1);
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return;
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}
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}
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}
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printf("True:Valid initial Sudoku matrix!\n");
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return;
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}
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//定义check_plus函数，判断是否为数独矩阵
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int check_plus(int board[9][9]){
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int i,j,k;
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for(i=0;i<9;i++){
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int cnt[10]={};
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for(j=0;j<9;j++){
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cnt[board[i][j]]++;
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}
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for(j=1;j<=9;j++){
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if(cnt[j]>1){
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return 0;
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}
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}
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}
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for(i=0;i<9;i++){
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int cnt[10]={};
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for(j=0;j<9;j++){
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cnt[board[j][i]]++;
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}
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for(j=1;j<=9;j++){
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if(cnt[j]>1){
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return 0;
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}
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}
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}
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for(k=0;k<9;k++){
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int cnt[10]={};
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for(i=k/3*3;i<k/3*3+3;i++){
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for(j=k%3*3;j<k%3*3+3;j++){
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cnt[board[i][j]]++;
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}
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}
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for(j=1;j<=9;j++){
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if(cnt[j]>1){
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return 0;
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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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int solve(int board[9][9]){
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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++){
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if(board[i][j]==0){ //找到待填的位置
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int num; //遍历填写1~9
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for(num=1;num<=9;num++){
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board[i][j]=num;
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//若可以填，则继续递归求解新数独
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if(check_plus(board)){
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if(solve(board)){
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return 1; //成功填写，找到一组解
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}
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}
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board[i][j]=0; //无解，继续尝试下一个数
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}
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return 0; //若不管填几都无法满足，说明无解
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}
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}
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}
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}
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void final_step(int board[9][9]){
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check(board);
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if(solve(board)){
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printf("The solution of Sudoku matrix:\n");
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print(board);
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}
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else printf("No solution！\n");
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}
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int main(){
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int board0[9][9] = {{5, 3, 0, 0, 7, 0, 0, 0, 0},
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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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int board1[9][9] = {{8, 3, 0, 0, 7, 0, 0, 0, 0},
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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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int board2[9][9] = {{5, 2, 0, 0, 7, 0, 0, 0, 0},
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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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final_step(board0);
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final_step(board1);
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final_step(board2);
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return 0;
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}
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