#include<stdio.h>
#include<time.h>
#include<stdlib.h>

int checkMatrix(int matrixArr[9][9], int isPrintInfo){
  int rowCnt[9][10]={0};
  int colCnt[9][10]={0};
  int bloCnt[9][10]={0};
  for(int i=0;i<9;i++){
    for(int j=0;j<9;j++){
      if(matrixArr[i][j]!=0){
        rowCnt[i][matrixArr[i][j]]++;
        if(rowCnt[i][matrixArr[i][j]]>1){
          if(isPrintInfo){
            printf("\nFalse:Invalid initial Sudoku matrix!");
            printf("\nThe number %d in the row %d has been used!",matrixArr[i][j],i+1);
          }
          return 0;
        }
        colCnt[j][matrixArr[i][j]]++;
        if(colCnt[j][matrixArr[i][j]]>1){
          if(isPrintInfo){
            printf("\nFalse:Invalid initial Sudoku matrix!");
            printf("\nThe number %d in the col %d has been used!",matrixArr[i][j],j+1);
          }
          return 0;
        }
        bloCnt[i/3*3+j/3][matrixArr[i][j]]++;
        if(bloCnt[i/3*3+j/3][matrixArr[i][j]]>1){
          if(isPrintInfo){
            printf("\nFalse:Invalid initial Sudoku matrix!");
            printf("\nThe number %d in the block %d has been used!",matrixArr[i][j],i/3*3+j/3+1);
          }
          return 0;
        }
      }
    }
  }
  if(isPrintInfo){
    printf("\nTrue:Valid initial Sudoku matrix!");
  }
  return 1;
}
void matrixOutput(int matrixArr[9][9])
{
  for (int i = 0; i < 9; i++)
  {
    for (int j = 0; j < 9; j++)
    {
      printf("%d", matrixArr[i][j]);
      if (j != 8)
        printf(" ");
    }
    if (i != 8)
      printf("\n");
  }
}
int fillMatrix(int matrixArr[9][9], int row, int col){
  if(row==9){
    return 1;
  }
  if(col==9){
    return fillMatrix(matrixArr,row+1,0);
  }
  if(matrixArr[row][col]!=0){
    return fillMatrix(matrixArr, row, col+1);
  }
  for(int i=1;i<=9;i++){
    matrixArr[row][col]=i;
    if(checkMatrix(matrixArr,0)){
      if(fillMatrix(matrixArr,row,col+1)){
        return 1;
      }
      matrixArr[row][col]=0;
    }else{
      matrixArr[row][col]=0;
    }
  }
  return 0;
}

int main()
{
  int board0[9][9] = {{5, 3, 0, 0, 7, 0, 0, 0, 0},
                      {6, 0, 0, 1, 9, 5, 0, 0, 0},
                      {0, 9, 8, 0, 0, 0, 0, 6, 0},
                      {8, 0, 0, 0, 6, 0, 0, 0, 3},
                      {4, 0, 0, 8, 0, 3, 0, 0, 1},
                      {7, 0, 0, 0, 2, 0, 0, 0, 6},
                      {0, 6, 0, 0, 0, 0, 2, 8, 0},
                      {0, 0, 0, 4, 1, 9, 0, 0, 5},
                      {0, 0, 0, 0, 8, 0, 0, 7, 9}};
  int board1[9][9] = {{8, 3, 0, 0, 7, 0, 0, 0, 0},
                      {6, 0, 0, 1, 9, 5, 0, 0, 0},
                      {0, 9, 8, 0, 0, 0, 0, 6, 0},
                      {8, 0, 0, 0, 6, 0, 0, 0, 3},
                      {4, 0, 0, 8, 0, 3, 0, 0, 1},
                      {7, 0, 0, 0, 2, 0, 0, 0, 6},
                      {0, 6, 0, 0, 0, 0, 2, 8, 0},
                      {0, 0, 0, 4, 1, 9, 0, 0, 5},
                      {0, 0, 0, 0, 8, 0, 0, 7, 9}};
  int board2[9][9] = {{5, 2, 0, 0, 7, 0, 0, 0, 0},
                      {6, 0, 0, 1, 9, 5, 0, 0, 0},
                      {0, 9, 8, 0, 0, 0, 0, 6, 0},
                      {8, 0, 0, 0, 6, 0, 0, 0, 3},
                      {4, 0, 0, 8, 0, 3, 0, 0, 1},
                      {7, 0, 0, 0, 2, 0, 0, 0, 6},
                      {0, 6, 0, 0, 0, 0, 2, 8, 0},
                      {0, 0, 0, 4, 1, 9, 0, 0, 5},
                      {0, 0, 0, 0, 8, 0, 0, 7, 9}};
  printf("The original Sudoku matrix: \n");
  matrixOutput(board0);
  if (checkMatrix(board0, 1))
  {
    if (fillMatrix(board0, 0, 0))
    {
      printf("\nThe solution of Sudoku matrix:\n");
      matrixOutput(board0);
    }
    else
    {
      printf("\nNo solution!");
    }
  }
  else
  {
    printf("\nNo solution!");
  }
  return 0;
}