Trouble understanding recursion in this application - c++

Question

I am writing a recursive solver for a Sudoku puzzle. I store blank places with 0's so that my program can read them more easily. I have the original puzzle stored starting from subscript one in order to better visualize the grid. I am not sure I have a full grasp on the recursion and that is where the problem is. I am getting output that seems like it is on track to solve the puzzle, but it is leaving zeros there that shouldn't be there. I think it has something to do with the placement of my unsetSquare, or with the return statements.
Here is a sample of the output...
**************************************************
7 4 3 | 8 2 1 | 5 6 8
2 6 8 | 0 9 0 | 0 1 0
0 0 0 | 0 0 6 | 0 0 4
---------|---------|---------
0 0 0 | 0 0 0 | 2 3 9
0 0 0 | 0 0 0 | 0 0 0
4 1 5 | 0 0 0 | 0 0 0
---------|---------|---------
9 0 0 | 5 0 0 | 0 0 0
0 2 0 | 0 1 0 | 7 4 0
0 0 0 | 2 0 0 | 9 0 5
**************************************************
**************************************************
7 4 3 | 8 2 1 | 5 6 9
2 6 8 | 0 9 0 | 0 1 0
0 0 0 | 0 0 6 | 0 0 4
---------|---------|---------
0 0 0 | 0 0 0 | 2 3 9
0 0 0 | 0 0 0 | 0 0 0
4 1 5 | 0 0 0 | 0 0 0
---------|---------|---------
9 0 0 | 5 0 0 | 0 0 0
0 2 0 | 0 1 0 | 7 4 0
0 0 0 | 2 0 0 | 9 0 5
**************************************************
**************************************************
7 4 3 | 8 2 1 | 5 6 0
2 6 8 | 1 9 0 | 0 1 0
0 0 0 | 0 0 6 | 0 0 4
---------|---------|---------
0 0 0 | 0 0 0 | 2 3 9
0 0 0 | 0 0 0 | 0 0 0
4 1 5 | 0 0 0 | 0 0 0
---------|---------|---------
9 0 0 | 5 0 0 | 0 0 0
0 2 0 | 0 1 0 | 7 4 0
0 0 0 | 2 0 0 | 9 0 5
**************************************************
**************************************************
7 4 3 | 8 2 1 | 5 6 0
2 6 8 | 2 9 0 | 0 1 0
0 0 0 | 0 0 6 | 0 0 4
---------|---------|---------
0 0 0 | 0 0 0 | 2 3 9
0 0 0 | 0 0 0 | 0 0 0
4 1 5 | 0 0 0 | 0 0 0
---------|---------|---------
9 0 0 | 5 0 0 | 0 0 0
0 2 0 | 0 1 0 | 7 4 0
0 0 0 | 2 0 0 | 9 0 5
**************************************************
**************************************************
7 4 3 | 8 2 1 | 5 6 0
2 6 8 | 3 9 0 | 0 1 0
0 0 0 | 0 0 6 | 0 0 4
---------|---------|---------
0 0 0 | 0 0 0 | 2 3 9
0 0 0 | 0 0 0 | 0 0 0
4 1 5 | 0 0 0 | 0 0 0
---------|---------|---------
9 0 0 | 5 0 0 | 0 0 0
0 2 0 | 0 1 0 | 7 4 0
0 0 0 | 2 0 0 | 9 0 5
**************************************************
notice at the end of the first row, it goes to 8 looking for a solution, then to 9, 9 is not legal and it has reached the end of the for loop, so it replaces it with a zero and it continues. How can I make it go back to try different numbers in the first row to get a more complete solution?
Here is my recursion function...
bool DoTheWork::addSquare(int& depth, ostream& outStream){
for(int i = ONE; i <= NINE; ++i){
for(int j = ONE; j <= NINE; ++j){
if(i == NINE && j == NINE && board.getSquare(NINE, NINE) != ZERO){
cout << i << " " << j << endl;
return true;
}
//cout << "original" << board.getSquare(i, j) << "coord: " << i << ", " << j << endl;
if(board.getSquare(i, j) == ZERO){
//cout << "original: " << board.getSquare(i, j) << "coord: " << i << ", " << j << endl;
for(int k = ONE; k <= NINE; ++k){
board.setSquare(i, j, k);
board.display(outStream);
if(board.isLegal()){
return addSquare(depth, outStream);
}
else{
board.unsetSquare(i, j);
}
}
}
}
}
board.display(outStream);
return false;
}

Answer 1

I can see a problem:
It should be:
if(board.isLegal()){
if( addSquare(depth, outStream))
return true;
}
Means if the whole board is solved then roll back.
EDIT think about it:
you put 1 in the first square, it returns false. don't you want to try put 2?
EDIT2
More problem:
if(i == NINE && j == NINE && board.getSquare(NINE, NINE) != ZERO){
cout << i << " " << j << endl;
return true;
}
Is this suppose to be a completion check? you check only 1 square. and in your sample it is filled!
you need to check that there is no 0.
EDIT3:
bool DoTheWork::addSquare(int& depth, ostream& outStream){
//use flag to let you know if all completed
bool zeroFound = false;
for(int i = ONE; i <= NINE; ++i){
for(int j = ONE; j <= NINE; ++j){
//cout << "original" << board.getSquare(i, j) << "coord: " << i << ", " << j << endl;
if(board.getSquare(i, j) == ZERO){
zeroFound = true;
//cout << "original: " << board.getSquare(i, j) << "coord: " << i << ", " << j << endl;
for(int k = ONE; k <= NINE; ++k){
board.setSquare(i, j, k);
board.display(outStream);
if(board.isLegal()){
if(addSquare(depth, outStream)){
return true;
}
else{
board.unsetSquare(i, j);
}
}
}
}
}
}
board.display(outStream);
return !zeroFound; //true in case it is full!
}

Answer 2

It turns out I had somethings in the wrong order, and not in the right scope. After successfully doing it with a while loop, I found the solution with a for loop.
bool DoTheWork::addSquare(int& depth, ostream& outStream){
for(int i = 1; i < 10; ++i){
for(int j = 1; j < 10; ++j){
if(board.getSquare(i, j) == 0){
if(i == 10){
return true;
}
for(int k = 1; k <= 9; ++k){
board.setSquare(i, j, k);
if(board.isLegal() && addSquare(depth, outStream)){
return true;
}
}
board.unsetSquare(i, j);
return false;
}
}
}
}