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/*-------------------*/
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/*实验：数独矩阵------*/
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/*4. 对一个不完整的“数独矩阵”进行判断，如果满足“数独矩阵”则补充完整，*/
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/*使之成为一个完整的“数独矩阵”：*/
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/*-------------------*/
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#include<stdio.h>
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#include<stdlib.h>
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#include<time.h>
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void randseedInit(){
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srand(time(NULL));
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}
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void printBoad(int _board[9][9]){
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for (int i = 0; i < 9;i++){
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if(!(i%3))printf("|-----------------------|\n");
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for (int j = 0; j < 9;j++){
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if(!(j%3))
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printf("| ");
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if(_board[i][j]==0)
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printf(". ");
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else
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printf("%d ", _board[i][j]);
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}
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printf("|\n");
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}
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printf("|-----------------------|\n");
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}
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void makeNSeq(int _seq[],int n){//产生1-n的不重复序列（传入一个数组名指针）
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int ct[9] = {0, 0, 0, 0, 0, 0, 0, 0, 0};
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for (int i = 0; i < n; i++) {
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int t = rand() % n;
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while(ct[t=rand() % n]);
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ct[t]++;
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_seq[i] = t+1;
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}
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}
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void initBoard(int _board[9][9]){
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for (int i = 0; i < 9;i++)
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for (int j = 0; j < 9;j++)
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_board[i][j] = 0;
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}
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void makeRandomBoard(int _board[9][9]){
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initBoard(_board);
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for (int i_1 = 0; i_1 < 3;i_1++){
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int seq[9];
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makeNSeq(seq, 9);
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for (int i = 0; i < 3;i++){
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int where[9];
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makeNSeq(where, 9);
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for (int idx = 0; idx < 3;idx++){
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_board[i_1 * 3 + i][where[idx+i*3]-1] = seq[idx+i*3];
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}
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}
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}
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}
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void printWhyInvalid(int num,int is_col,int index,int *valid,int ndpt){
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if(*valid){
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if(ndpt)printf("False:Invalid initial Sudoku matrix!\n The number %d in the %s %d has been used!\n", num, (is_col ? "col" : "block"), index);
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*valid = 0;
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};
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}
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int whoBeUsedInSeq(int seq[9]){
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int ct[10]={0,0,0,0,0,0,0,0,0,0};
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for (int i = 0; i < 9;i++){
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ct[seq[i]]++;
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}
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for (int i = 1; i < 10;i++){
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if(ct[i]>1)
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return i;
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}
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return 0;
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}
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void matrixT(int _board[9][9],int _output[9][9]){
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for (int i = 0; i < 9;i++)
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for (int j = 0; j < 9;j++)
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_output[j][i] = _board[i][j];
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}
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void resortByBlock(int _board[9][9], int _output[9][9]) {
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for (int i = 0; i < 9;i++){
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int p1x = i / 3;
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int p1y = i % 3;
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for (int j = 0; j < 9; j++){
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int p2x = j / 3;
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int p2y = j % 3;
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_output[i][j] = _board[p1x * 3 + p2x][p1y * 3 + p2y];
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}
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}
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}
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int judgeValid(int _board[9][9],int ndpt){
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int valid = 1;
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int boardT[9][9];
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int boardB[9][9];
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matrixT(_board, boardT);
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resortByBlock(_board, boardB);
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for (int i = 0; i < 9;i++){
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int who = whoBeUsedInSeq(boardT[i]);
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if(who)
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printWhyInvalid(who, 1, i+1, &valid,ndpt);
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who = whoBeUsedInSeq(boardB[i]);
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if(who)
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printWhyInvalid(who, 0, i+1, &valid,ndpt);
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who = whoBeUsedInSeq(_board[i]);
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if(who)
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valid = 0;
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}
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return valid;
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}
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int try(int _b[9][9],int where[]){
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int w = where[0];
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if(!judgeValid(_b,0))
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return 0;
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if(w==-1){
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printf("The Solution of Sudoku Matrix:\n");
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printBoad(_b);
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return 1;
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}
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for (int n = 1; n <= 9;n++){
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int _bt[9][9];
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for (int i = 0; i < 9;i++)
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for (int j = 0; j < 9;j++)
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_bt[i][j] = _b[i][j];
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_bt[w / 9][w % 9] = n;
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if(try(_bt, &where[1])){
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return 1;
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}
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}
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return 0;
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}
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int solve(int _board[9][9]){
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int idx = 0;
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int where[81];
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int _b[9][9];
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for (int i = 0; i < 9;i++)
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for (int j = 0; j < 9;j++)
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_b[i][j] = _board[i][j];
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for (int i = 0; i < 81;i++)
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where[i] = -3;
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int pos = 0;
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while (pos < 81) {
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if (!_b[pos / 9][pos % 9]){
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where[idx]=pos;
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idx++;
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}
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pos++;
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}
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where[idx] = -1;
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if(try(_b, where)){
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return 1;
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}
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else{
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printf("No Solution!\n");
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return 0;
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};
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}
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int main(){
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randseedInit();
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int board[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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printBoad(board);
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solve(board);
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}
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